your fav scientist

[raul]

not counting bruce lee
1. david hilbert-this is perfectly ridiculuos
2-paul adrian maurice dirac-in physics just as ridiculous(almost)
3-augustin louis cauchy
4-pierre de fermat
5-leonhard euler
6-carl friedrich gauss
7-paul erdos
8-bernhard riemann
9-karl weierstrass
10-john vo neumann
11-pierre simon de laplace
12.jean baptiste fourier
13-joseph louis lagrange
14-jules henri poincare
15-evariste galois
16-niels henrik abel
17-shrinivasa ramanujan
18-ludwig gentzen
19-peter gustav lejeune dirichlet
20-leopold kronecker
20-carl gustav jacob jacobi
21-jacques salamon Hadamard
22-valery de le valee poussin
23-georg cantor
24-luitizius brouwer
25-emile artin
26-ernst eduard Kummer
27-hermann amadeus schwartz
28-ernst zermelo
29-richard wilhelm julius von dedekind
30-polya
31-camille jordan
32-emile borel
33-stokes
34-legendre
35-pierre deligne
36-andre weil
37-andrew wiles
38-euclide
39-archimedes
40-pythagoras
41-arthur cayley
42-rowan hamilton
43-brooke taylor
44-leibniz
45-newton
46-henri leon lebesgue
47-hermann minkowski
48-coulomb
49-andre marie ampere
50-emmy noether
51-sophie germain
52-maria agnesi
53-paul cohen
54-kurt godel
55-charles hermite
56-joseph lieuville
57-stefan banach
58-felix hausdorff
59-jean d'alambert
60-čebišev
61-volterra
62-felix klein
63-giuseppe peano
64-gottfrey harald hardy
65-charles darwin
66-alexander flemming
67-carl gustav jung
68-erwin schrodinger
69-niels bohr
70-werner heisenberg
71-enrico fermi
72-roger penrose
73-stephen nhawking
74-maxwell
75-christian huygens
76-antoine lavoisier
77-lomonosov
78-mendeljejev
79-christian bernhard
80-norbert wiener
81-sidis
82-gelfond
83-fromm
84-everest

[jesgear]

I don't see Professor Frink.

[raul]

whos that?

[joenamherst]

Tho not a scientist in the strict sense, my choice is Steven Hawking. If you don't know who he is google him.

[BadLittleKid]

whos that?

It's Eddie Murphy. Sorry... :blush4:

[jesgear]

Professor Frink:

http://z.about.com/d/animatedtv/1/0/t/9/frink_small.jpg

[BadLittleKid]

Professor Frink:

http://z.about.com/d/animatedtv/1/0/t/9/frink_small.jpg

Oh, sorry again. :blush1:

Murphy was Klumpit or something similar.

[raul]

Tho not a scientist in the strict sense, my choice is Steven Hawking. If you don't know who he is google him.

hes a cosmologist. cosmologys a science. conclusion hes a scientist. its a science about universe. But, so is physics. The difference is cosmology is a science about history of universe, big bang, being the most known theory. hes considered as maybe greatest living mind, although i completely disagree. it was him who gave honor speech to dirac at funeral.

but, why not give pics of greatest mathematicians ever, i hope at leats rob is interested.

http://upload.wikimedia.org/wikipedia/commons/7/79/Hilbert.jpg

david hilbert

http://www.softpanorama.org/Algorithms/Images/euler.jpg

leonhard euler

http://www.math.uni-hamburg.de/spag/ign/bild/gauss-kl.jpg

carl friedrich gauss

http://www.bibmath.net/bios/images/cauchy.jpg

augustin louis cauchy

[FPSHOT]

i hope at leats rob is interested.

I am interested in many many research type of things including various sciences.. however not this type. From the 84 names on your list + the poll I recognise maybe 4 to be honest...and 'recognise' is the word... and if you would ask me to then add the ones I know... it would stay blank... so I will skip this one...but will challange you to another one soon.

[raul]

Dirac is best known for laying the mathematical foundation for quantuum mechanics. He is generaly considered as one of the greatest physicists ever, many physicists consider him the greatest physicist of 20th century.

born on aug 8 1902, he was a British theoretical physicist and a founder of the field of quantum mechanics. He held the Lucasian chair of mathematics at the university of Cambridge, which was held by Isaac Newton, and is now held by Stephen Hawking. among other discoveries, he formulated the so-called Dirac equation, which describes the behavior of fermions and which led to the prediction of the existence of antimatter. He shared the Nobel prize in physics for 1933 with Erwin Schrodinger "for the discovery of the new productive forms of atomic theory".

His father, Charles Dirac, was an immigrant from Saint-Maurice in the canton of Valais, Swutzerland and thought French for a living. He had a brother who commited suicide in 1925. His early life seems to appear unhappy because of his father's unusually strict and authoritan nature. Around 1921 he decided that his true calling layed in mathematical sciences.

Dirac noticed an analogy between the old Poisson brackets of classical mechanics and the recently-proposed quantization rules in Werner Heisenberg's matrix formulation of quantum mechanics. This observation allowed Dirac to obtain the quantization rules in a novel and more illuminating manner. For this work, published in 1926, he received a Ph.D. from Cambridge.

In 1928, building on Wolfgang Pauli's work on non-relativistic spin systems, he proposed the Dirac equation as a relativistic equation of motion for the wavefunction of the electron. This work led Dirac to predict the existence of the positron, the electron's antiparticle, which he interpreted in terms of what came to be called the Dirac sea. The positron was subsequently observed by Carl Anderson in 1932. Dirac's equation also contributed to explaining the origin of quantum spin as a relativistic phenomenon.

The necessity of electron matter being created and destroyed in Enrico Fermi's 1934 theory of beta decay, however, led to a reinterpretation of Dirac's equation as a "classical" field equation for any point matter of spin ħ/2, itself subject to quantization conditions involving anti-commutators. Thus reinterpreted, the Dirac equation is as central to theoretical physics as the Maxwell, Yang-Mills and Einstein field equations. Dirac is regarded as the founder of quantum electrodynamics, being the first to use that term. He also introduced the idea of vacuum polarization in the early 1930s.

Dirac's Principles of Quantum Mechanics, published in 1930, is a landmark in the history of science. It quickly became one of the standard textbooks on the subject and is still used today. In that book, Dirac incorporated the previous work of Werner Heisenberg on matrix mechanics and of Erwin Schrödinger on wave mechanics into a single mathematical formalism that associates measurable quantities to operators acting on the Hilbert space of vectors that describe the state of a physical system. The book also introduced the delta function. Following his 1939 article, he also included the bra-ket notation in the third edition of his book, thereby contributing to their universal use nowadays.

Guided by a comment in Dirac's textbook and by Dirac's 1933 article "The Lagrangian in quantum mechanics" (published in the Soviet journal Physikalische Zeitschrift der Sowjet Union), Richard Feynman developed the path integral formulation of quantum mechanics in 1948. This work would prove exceedingly useful in relativistic quantum field theory, in part because it is based on the Lagrangian, whose relativistic invariance is explicit, while the invariance is only implicit in the Hamiltonian formulation.

In 1933 Dirac showed that the existence of a single magnetic monopole in the universe would suffice to explain the observed quantization of electrical charge. This proposal received much attention, but there is to date no convincing evidence for the existence of magnetic monopoles. However, in 1975, intriguing evidence of a moving magnetic monopole was announced by P. Buford Price based on the discovery by the lead researcher W.L. Wagner of ionization tracks in over 30 sheets of a particle detector that were equivalent to an electric charge of 137, the same as predicted by Dirac. No known particle plausibly explains those tracks.

He married Eugene Wigner's sister, Margit, in 1937. He adopted Margit's two children, Judith and Gabriel. Paul and Margit Dirac had two children together, daughters Mary Elizabeth and Florence Monica.

[raul]

Later years
Dirac was the Lucasian Professor of Mathematics at Cambridge from 1932 to 1969. During World War II, he conducted important theoretical and experimental research on uranium enrichment by gas centrifuge. In 1937, he proposed a speculative cosmological model based on the so called large numbers hypothesis. Dirac would write, "I am very disturbed by the situation because the so-called good theory quantum theory does involve neglecting infinities in an arbitrary way. This is not sensible. Sensible Mathematics involves neglecting a quantity when it's small; not because it's infinitely great and we do not want it." Dirac became unsatisfied with the renormalization approach to dealing with these infinities in quantum field theory and his work on the subject moved increasingly out of the mainstream.

Death and afterwards
In 1984 Dirac died in Tallahassee, Florida where he is buried. The Dirac-Hellmann Award at FSU was endowed by Dr Bruce P. Hellmann (Dirac's last doctoral student) in 1997 to reward outstanding work in theoretical physics by FSU researchers. The Dirac Prize is also awarded by the International Centre for Theoretical Physics in his memory. The Paul A.M. Dirac Science Library at FSU is named in his honor. In 1995, a plaque in his honour bearing his equation was unveiled at Westminster Abbey in London with a speech from Stephen Hawking. A commemorative garden has been established opposite the railway station in Saint-Maurice, Switzerland, the town of origin of his father's family.

Honours and tributes

Dirac shared the 1933 Nobel Prize for physics with Erwin Schrödinger "for the discovery of new productive forms of atomic theory." Dirac was also awarded the Royal Medal in 1939 and both the Copley Medal and the Max Planck medal in 1952. He was elected a Fellow of the Royal Society in 1930, and of the American Physical Society in 1948.

Immediately after his death, two organizations of professional physicists established annual awards in Dirac's memory. The Institute of Physics, the United Kingdom's professional body for physicists, awards the Paul Dirac Medal and Prize for "outstanding contributions to theoretical (including mathematical and computational) physics". The first three recipients were Stephen Hawking (1987), John Bell (1988), and Roger Penrose (1989). The Abdus Salam International Centre for Theoretical Physics (ICTP) awards the Dirac Medal of the ICTP each year on Dirac's birthday (August 8).

The street on which the National High Magnetic Field Laboratory in Tallahassee, Florida, is located was named Paul Dirac Drive. There is also a road named after him in his home town of Bristol, UK. The BBC named its video codec Dirac in his honour. And in the popular British television show Doctor Who, the character Adric was named after him (Adric is an anagram of Dirac).


Personality

Dirac was known among his colleagues for his precise and taciturn nature. When Niels Bohr complained that he did not know how to finish a sentence in a scientific article he was writing, Dirac replied, "I was taught at school never to start a sentence without knowing the end of it." When asked about his views on poetry, he responded, "In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in poetry, it's the exact opposite".

Some psychologists, including Simon Baron-Cohen have speculated that Dirac may have suffered from Asperger syndrome, an autistic spectrum disorder, due to his taciturn nature, and logical rather than emotional mindset. Dirac himself wrote in his diary during his postgraduate years that he concentrated solely on his research, and only stopped on Sunday, when he took long strolls alone.

Dirac was also noted for his personal modesty. He called the equation for the time-evolution of a quantum-mechanical operator, which Dirac was in fact the first to write down, the "Heisenberg equation of motion". Most physicists speak of Fermi-Dirac statistics for half-integer spin particles and Bose-Einstein statistics for integer spin particles. While lecturing later in life, Dirac always insisted on calling the former "Fermi statistics". He referred to the latter as "Einstein statistics" for reasons, he explained, of "symmetry".

[raul]

Religious Views
Dirac did not believe in God. He once said "God used beautiful mathematics in creating the world," but here he used 'God' as a metaphor for nature.

Werner Heisenberg recollects a friendly conversation among young participants at the 1927 Solvay Conference about Einstein and Planck's views on religion. Wolfgang Pauli, Heisenberg and Dirac took part in it. Dirac's contribution was a poignant and clear criticism of the political manipulation of religion, that was much appreciated for its lucidity by Bohr, when Heisenberg reported it to him later. Among other things, Dirac said: "I cannot understand why we idle discussing religion. If we are honest - and as scientists honesty is our precise duty - we cannot help but admit that any religion is a pack of false statements, deprived of any real foundation. The very idea of God is a product of human imagination. ... I do not recognize any religious myth, at least because they contradict one another. ..." Heisenberg's view was tolerant. Pauli had kept silent, after some initial remarks, but when finally he was asked for his opinion, jokingly he said: "Well, I'd say that also our friend Dirac has got a religion and the first commandment of this religion is 'God does not exist and Paul Dirac is his prophet.'" Everybody burst into laughter, including Dirac.

Legacy
Dirac is widely regarded as one of the greatest physicists of all time. He was one of the founders of quantum mechanics and quantum electrodynamics. Many physicists consider Dirac the greatest physicist of the 20th century. Physicist Antonino Zichichi, a professor of advanced physics at the University of Bologna, believes that Dirac had a much bigger impact on modern science in the 20th century than Albert Einstein.

The work of Dirac in the early Sixties proved extremely useful to modern practitioners of Superstring theory and its closely related successor, M-Theory.

Dirac is famous as the creator of the complete theoretical formulation of quantum mechanics.

Paul was one of three children, his older brother being Reginald Charles Felix Dirac and his younger sister being Beatrice Isabelle Marguerite Walla Dirac. Paul had a very strict family upbringing. His father insisted that only French be spoken at the dinner table and, as a result, Paul was the only one to eat with his father in the dining room. Paul's father was so strict with his sons that both were alienated and Paul was brought up in a somewhat unhappy home.

The first school which Paul attended was Bishop Primary school and already in this school his exceptional ability in mathematics became clear to his teachers. When he was twelve years old he entered secondary school, attending the secondary school where his father taught which was part of the Merchant Venturers Technical College. At about the time Paul entered this school, World War I began and this had a beneficial effect for Paul since the older boys in the school left for military service and the younger boys had more access to the science laboratories and other facilities. Paul himself wrote about his school years in

The Merchant Venturers was an excellent school for science and modern languages. There was no Latin or Greek, something of which I was rather glad, because I did not appreciate the value of old cultures. I consider myself very lucky in having been able to attend the school. ... I was rushed through the lower forms, and was introduced at an especially early age to the basis of mathematics, physics and chemistry in the higher forms. In mathematics I was studying from books which mostly were ahead of the rest of the class. This rapid advancement was a great help to me in my latter career.

[raul]

He completed his school education in 1918 and then studied electrical engineering at the University of Bristol. By this time the University had combined with the Merchant Venturers Technical College so Dirac remained in the same building as he had studied during his four years at secondary school. Although mathematics was his favourite subject he chose to study an engineering course at university since he thought that the only possible career for a mathematician was school teaching and he certainly wanted to avoid that profession. He obtained his degree in engineering in 1921 but following this, after an undistinguished summer job in an engineering works, he did not find a permanent position. By this time he was developing a real passion for mathematics but his attempts to study at Cambridge failed for rather strange reasons.

Taking the Cambridge scholarship examinations in June 1921 he was awarded a scholarship to study mathematics at St John's College, Cambridge, but it did not provide enough to support him. Additional support would have been expected from his local education authority, but he was refused support on the grounds that his father had not been a British citizen for long enough. Dirac was offered the chance to study mathematics at Bristol without paying fees and he did so being awarded first class honours in 1923. Following this he was awarded a grant to undertake research at Cambridge and he began his studies there in 1923.

Fowler was then the leading theoretician in Cambridge, well versed in the quantum theory of atoms; his own research was mostly on statistical mechanics. He recognised in Dirac a student of unusual ability. Under his influence Dirac worked on some problems in statistical mechanics. Within six months of arriving in Cambridge he wrote two papers on these problems. No doubt Fowler aroused his interest in the quantum theory, and in May 1924 Dirac completed his first paper dealing with quantum problems. Four more papers were completed by November 1925.

Despite the obvious academic success Dirac enjoyed as a research student this was no easy time for him. His brother Reginald Dirac committed suicide during this period. No reason for the suicide seems to be known but Dirac's relations with his father, already strained, seemed almost to end completely after this which does suggest that Dirac felt that his father carried at least some responsibility. Already a person who had few friends, this personal tragedy had the effect of making him even more withdrawn.

Although he had already made an excellent start to his research career, even more impressive work was to follow. This was as a result of Dirac being given proofs of a paper by Heisenberg to read in the summer of 1925. The significance of the algebraic properties of Heisenberg's commutators struck Dirac when he was out for a walk in the country. He realised that Heisenberg's uncertainty principle was a statement of the noncommutativity of the quantum mechanical observables. He realised the analogy with Poisson brackets in Hamiltonian mechanics. Higgs wrote

This similarity provided the clue which led him to formulate for the first time a mathematically consistent general theory of quantum mechanics in correspondence with Hamiltonian mechanics.

The ideas were laid out in Dirac's doctoral thesis Quantum mechanics for which he was awarded a Ph.D. in 1926. It is remarkable that Dirac had eleven papers in print before submitting his doctoral dissertation. Following the award of the degree he went to Copenhagen to work with Niels Bohr, moving on to Göttingen in February 1927 where he interacted with Robert Oppenheimer, Max Born, James Franck and the Russian Igor Tamm. Accepting an invitation from Ehrenfest, he spent a few weeks in Leiden on his way back to Cambridge. He was elected a Fellow of St John's College, Cambridge in 1927.

Dirac visited the Soviet Union in 1928. It was the first of many visits for he went again in 1929, 1930, 1932, 1933, 1935, 1936, 1937, 1957, 1965, and 1973. Also in 1928 he found a connection between relativity and quantum mechanics, his famous spin-1/2 Dirac equation. In 1929 he made his first visit to the United States, lecturing at the Universities of Wisconsin and Michigan. After the visit, along with Heisenberg, he crossed the Pacific and lectured in Japan. He returned via the trans-Siberian railway.

De Facio wrote about Dirac's famous book

Dirac was not influenced by the feeding frenzy in experimental phenomenology of the time. This has given Dirac's book ... a lasting quality that few works can match.

other comments:

... reflects Dirac's very characteristic approach: abstract but simple, always selecting the important points and arguing with unbeatable logic.

The obituary notes:-

His lectures at Cambridge were closely modelled on [The principles of Quantum Mechanics], and they conveyed to generations of students a powerful impression of the coherence and elegance of quantum theory. They constituted his principal contribution to education, for he took very few research students.

Also in 1930 Dirac was elected a Fellow of the Royal Society. This honour came on the first occasion that his name was put forward, in itself quite an unusual event which says much about the extremely high opinion that Dirac's fellow scientists had of him.

It is an interesting comment on Dirac's nature that his first thought was to turn down the Nobel prize on the grounds that he hated publicity. However when it was pointed out to him that he would receive far more publicity if he turned down the prize, he accepted it. Another comment about this event is that Dirac was told that he could invite his parents to the award ceremony in Stockholm, but he chose to invite only his mother and not his father.

[raul]

In 1937, the same year that he married, Dirac published his first paper on large numbers and cosmological matters. We comment further on his ideas on cosmology below. He published his famous paper on classical electron theory, which included mass renormalisation and radiative reaction in 1938. Dirac worked during World War II on uranium separation and nuclear weapons. In particular he acted as a consultant to a group in Birmingham working on atomic energy. This association led to Dirac being prevented by the British government from visiting the Soviet Union after the end of the war; he was not able to visit again until 1957.

We noted above that Dirac was elected a fellow of the Royal Society in 1930. He was awarded the Royal Society's Royal Medal in 1939 and the Society awarded him their Copley Medal in 1952:-

... in recognition of his remarkable contributions to relativistic dynamics of a particle in quantum mechanics.

In 1973 and 1975 Dirac lectured in the Physical Engineering Institute in Leningrad. In these lectures he spoke about the problems of cosmology or, to be more precise, to the problems of non-dimensional combinations of world constants.

Although Dirac made vastly important contributions to physics, it is important to realise that he was always motivated by principles of mathematical beauty. Dirac unified the theories of quantum mechanics and relativity theory, but he also is remembered for his outstanding work on the magnetic monopole, fundamental length, antimatter, the d-function, bra-kets, etc.

There is a standard folklore of Dirac stories, mostly revolving around Dirac saying exactly what he meant and no more. Once when someone, making polite conversation at dinner, commented that it was windy, Dirac left the table and went to the door, looked out, returned to the table and replied that indeed it was windy. It has been said in jest that his spoken vocabulary consisted of "Yes", "No", and "I don't know". Certainly when Chandrasekhar was explaining his ideas to Dirac he continually interjected "yes" then explained to Chandrasekhar that "yes" did not mean that he agreed with what he was saying, only that he wished him to continue. He once said:-

I was taught at school never to start a sentence without knowing the end of it.

This may explain much about his conversation, and also about his beautifully written sentences in his books and papers.

Dirac received many honours for his work, some of which we have mentioned above. He refused to accept honorary degrees but he did accept honorary membership of academies and learned societies. The list of these is long but among them are USSR Academy of Sciences (1931), Indian Academy of Sciences (1939), Chinese Physical Society (1943), Royal Irish Academy (1944), Royal Society of Edinburgh (1946), Institut de France (1946), National Institute of Sciences of India (1947), American Physical Society (1948), National Academy of Sciences (1949), National Academy of Arts and Sciences (1950), Accademia delle Scienze di Torino (1951), Academia das Ciencias de Lisboa (1953), Pontifical Academy of Sciences, Vatican City (1958), Accademia Nazionale dei Lincei, Rome (1960), Royal Danish Academy of Sciences (1962), and Académie des Sciences Paris (1963). He was appointed to the Order of Merit in 1973.

A memorial meeting was held at the University of Cambridge on 19 April 1985 and the papers presented at this meeting were published in Tributes to Paul Dirac, Cambridge, 1985 (Bristol, 1987).

Achutan writes:

... we vividly see everywhere the brilliant imprints of Dirac, unifier of quantum mechanics and relativity theory. Each of the pieces not only is in praise of an exceptionally gifted intellect but also places on record how deeply and abidingly the human mind can delve into the realms of mathematical insight and modelling, keeping intact the spirit of beauty and clarity of a creative genius. Only a few Nobel laureates ever can compare as well with this giant of mathematical sciences in whose demise the world of original thinking certainly has lost one of the most precious souls retaining fortunately still the glory for others to sing and emulate for a long time to come.

The importance of Dirac's work lies essentially in his famous wave equation, which introduced special relativity into Schrödinger's equation. Taking into account the fact that, mathematically speaking, relativity theory and quantum theory are not only distinct from each other, but also oppose each other, Dirac's work could be considered a fruitful reconciliation between the two theories.

http://upload.wikimedia.org/wikipedia/commons/7/74/Dirac.gif

almost all info from wiki, snt andrews math groups and Nobelprize.org

[Sarandipity]

I'm a sucker for Darwin.

I'm also a big fan of Gregor Mendel, aka the "Father of Modern Genetics." (You may have heard of so-called Mendelian or one-gene traits such as attached/detached earlobes, having a widow's peak, rolling your tongue, etc.).

Also James Watson and Francis Crick, co-discoverers of the DNA double-helix and basically modern molecular biology... Even though they stole some research from another scientist (Rosalind Franklin) in doing so.

Okay, so I'm a sucker for a lot of scientists. :smile1:

[raul]

I'm a sucker for Darwin.

I'm also a big fan of Gregor Mendel, aka the "Father of Modern Genetics." (You may have heard of so-called Mendelian or one-gene traits such as attached/detached earlobes, having a widow's peak, rolling your tongue, etc.).

Also James Watson and Francis Crick, co-discoverers of the DNA double-helix and basically modern molecular biology... Even though they stole some research from another scientist (Rosalind Franklin) in doing so.

Okay, so I'm a sucker for a lot of scientists. :smile1:

Me too, a sucker for Darwin, that is, although i wouldn't call my self, or anyone "sucker". The theory of evolution is fascinating, as is his work "on the origin of species", i think that's it.

Yeah, ive heard of them traits. But that's it.

Watson-Crick, of course, one of the most important discoveries in the history of science. But I'd say the most important, in the practical sense, is Flemming's discovery of peniciline. It's estimated it saved 200 million lives since then. (For a reference, estimation on ww2 deaths is 70 million). I like what he said when someone told him he invented peniciline. he said "i've been told that i've invented it, but no one could of done it. The nature has been creating it for millions of years. I only discovered it."

But what about the scientists from my list? Especially Hilbert, Euler, Gauss, Cauchy, Fermat, Dirac. You're not into any of them? Are you into math or physics?

and yeah, there have been many steals in the history of science. For example, it's almost unknown that general relativity wasn't Einstein's idea, it was Riemann's, a mathematician. It concearns non-euclidean geometry. Einstein only applied it to the real world. Maybe that's not a steal, though. Plus, special relativity is also not his idea, it's Poincare's, also a mathematician. Have you read what I posted on Dirac? If you did, you'll see why i consider him the greatest physicist ever. Also, if you google Hilbert, Gauss, Euler, Cauchy, Fermat, Galois, Ramanujan, Godel, Von Neumann (who was a bastard, though), you might find it interesting. Are you familiar with some of them?

[Asha]

Mine would be Foot

[digdad]

I'm also a big fan of Gregor Mendel, aka the "Father of Modern Genetics." (You may have heard of so-called Mendelian or one-gene traits such as attached/detached earlobes, having a widow's peak, rolling your tongue, etc.).
Mendel was right on, but he probably faked (that is, overinflated or embellished) his results. For one of my statistics classes, we analyzed his results. If you do a statistical study of his results from multiple experiments, the probability that he could have come up with such perfect outcomes becomes nearly infinitesimally small. He was one sneaky monk.

[raul]

Mine would be Foot

who is that? is this another joke? seriously.

[raul]

Pierre De Fermat, 17 aug 1601-1665, was a French lawyer and an informal mathematician, a mathematical genius. Essentially, between ancient greeks and him there's no great mathematician, Rene Descartes and Blaise Pascal were his contemporaries, but nowhere near mathematically gifted. Considered one of the all time greats, he essentially begun modern mathematics. He was a meathematical explosion. In a sense, creator of number theory, he produced more math, and more importantly more seminal math than the rest of the world in around the preceeding 2 milenia. Thats so insane, it sounds like a joke. he also did, seminal, CRUCIAL work in analysis. He claimed he had a proof of his last theorem, but there's no evidence. The thing is, the whole world, within reason was solving it, up until 1994, when Wiles finally proved it. The techniques and math aparatus that Wiles used in his proof (over 200 pages long) is so advanced, only 50 people in the world understand it. And, yet, look at the actual problem:

theorem

x^n + y^n = z^n has no integer solutions in x, y, z, for natural n > 2.

this, not surprisingly, was being "solved" not only by all mathematicians who mean something in the world since Fermat,except Hilbert, who was the only one wise enough not to even make an ATTEMPT at it, when asked why, he said "why should i work on something for years, and in the end probably fail?" but also by laymen, cause anyone can understand it. There have been like 100 more false proofs of this than any other problem in history-god knows how many milions. The thing is, he, in fact, really could have of had an ELEMENTARY proof, lets say quarter page long, but didnt let anyone know of it on purpose.

this is actually not from wiki, cause i know it by heart

Fermat's pioneering work in analytic geometry, Ad Locos Planos et Solidos Isagoge, was circulated in manuscript form in 1636, predating the publication of Descartes' famous La géométrie. This manuscript was published posthumously in 1679.

In Methodus ad disquirendam maximam et minima and in De tangentibus linearum curvarum, Fermat developed a method for determining maxima, minima, and tangents to various curves that was equivalent to differentiation. In these works, Fermat also obtained a technique for finding the centers of gravity of various plane and solid figures, which led to his further work in quadrature.

Fermat was the first person known to have evaluated the integral of general power functions. Using an ingenious trick, he was able to reduce this evaluation to the sum of geometric series. The resulting formula was helpful to Newton, and then Leibniz, when they independently developed the fundamental theorem of calculus.

In number theory, Fermat studied Pell's equation, Fermat numbers, perfect, and amicable numbers. It was while researching perfect numbers that he discovered the little theorem. He also invented a factorization method which has been named for him as well as the proof technique of infinite descent, which he used to prove Fermat's Last Theorem for the case n = 4. Fermat also developed the two-square theorem, and the polygonal number theorem, which states that each number is a sum of three triangular numbers, four square numbers, five pentagonal numbers, and so on.

Although Fermat claimed to have proved all his arithmetic theorems, few records of his proofs have survived. Many mathematicians, including Gauss, doubted several of his claims, especially given the difficulty of some of the problems and the limited mathematical tools available to Fermat. His famous Last Theorem was first discovered by his son in the margin on his father's copy of an edition of Diophantus, and included the statement that the margin was too small to include the proof. He had not bothered to inform even Mersenne of it. It was not proved until 1994, using techniques unavailable to Fermat.


Buste in the Salle des Illustres in Capitole de ToulouseAlthough he carefully studied, and drew inspiration from Diophantus, Fermat began a different tradition. Diophantus was content to find a single solution to his equations, even if it were an undesired fractional one. Fermat was interested only in integer solutions to his Diophantine equations, and he looked for all possible general solutions. He also often proved that certain equations had no solution, which usually baffled his contemporaries.

Through his correspondence with Blaise Pascal in 1654, Fermat and Pascal helped lay the fundamental groundwork for the theory of probability. From this brief but productive collaboration on the problem of points, they are now regarded as joint founders of probability theory.

Fermat's principle of least time (which he used to derive Snell's law in 1657) was the first variational principle enunciated in physics since Hero of Alexandria described a principle of least distance in the first century CE. In this way, Fermat is recognized as a key figure in the historical development of the fundamental principle of least action in physics. The term Fermat functional was named in recognition of this role.

Together with René Descartes, Fermat was one of the two leading mathematicians of the first half of the 17th century. Independently of Descartes, he discovered the fundamental principles of analytic geometry. With Blaise Pascal, he was a founder of the theory of probability.

Regarding Fermat's work in analysis, Isaac Newton wrote that his own early ideas about calculus came directly from "Fermat's way of drawing tangents."

Of Fermat's number theoretic work, the great 20th century mathematician André Weil wrote that "... what we possess of his methods for dealing with curves of genus 1 is remarkably coherent; it is still the foundation for the modern theory of such curves. It naturally falls into two parts; the first one ... may conveniently be termed a method of ascent, in contrast with the descent which is rightly regarded as Fermat's own." Regarding Fermat's use of ascent, Weil continued "The novelty consisted in the vastly extended use which Fermat made of it, giving him at least a partial equivalent of what we would obtain by the systematic use of the group theoretical properties of the rational points on a standard cubic." With his gift for number relations and his ability to find proofs for many of his theorems, Fermat essentially created the modern theory of numbers.

http://www.mathematik.de/mde/information/landkarte/gebiete/wahrscheinlichkeitstheorie/bilder/fermat.jpeg

jeeeez...looks like something out of monty python in here

[Magill]

Dr. Frankenfurter is my favorite scientist.

[raul]

Pierre De Fermat, 17 aug 1601-1665, was a French lawyer and an informal mathematician, a mathematical genius. Essentially, between ancient greeks and him there's no great mathematician, Rene Descartes and Blaise Pascal were his contemporaries, but nowhere near mathematically gifted. Considered one of the all time greats, he essentially begun modern mathematics. He was a meathematical explosion. In a sense, creator of number theory, he produced more math, and more importantly more seminal math than the rest of the world in around the preceeding 2 milenia. Thats so insane, it sounds like a joke. he also did, seminal, CRUCIAL work in analysis. He claimed he had a proof of his last theorem, but there's no evidence. The thing is, the whole world, within reason was solving it, up until 1994, when Wiles finally proved it. The techniques and math aparatus that Wiles used in his proof (over 200 pages long) is so advanced, only 50 people in the world understand it. And, yet, look at the actual problem:

theorem

x^n + y^n = z^n has no integer solutions in x, y, z, for natural n > 2.

this, not surprisingly, was being "solved" not only by all mathematicians who mean something in the world since Fermat,except Hilbert, who was the only one wise enough not to even make an ATTEMPT at it, when asked why, he said "why should i work on something for years, and in the end probably fail?" but also by laymen, cause anyone can understand it. There have been like 100 more false proofs of this than any other problem in history-god knows how many milions. The thing is, he, in fact, really could have of had an ELEMENTARY proof, lets say quarter page long, but didnt let anyone know of it on purpose.

this is actually not from wiki, cause i know it by heart

Fermat's pioneering work in analytic geometry, Ad Locos Planos et Solidos Isagoge, was circulated in manuscript form in 1636, predating the publication of Descartes' famous La géométrie. This manuscript was published posthumously in 1679.

In Methodus ad disquirendam maximam et minima and in De tangentibus linearum curvarum, Fermat developed a method for determining maxima, minima, and tangents to various curves that was equivalent to differentiation. In these works, Fermat also obtained a technique for finding the centers of gravity of various plane and solid figures, which led to his further work in quadrature.

Fermat was the first person known to have evaluated the integral of general power functions. Using an ingenious trick, he was able to reduce this evaluation to the sum of geometric series. The resulting formula was helpful to Newton, and then Leibniz, when they independently developed the fundamental theorem of calculus.

In number theory, Fermat studied Pell's equation, Fermat numbers, perfect, and amicable numbers. It was while researching perfect numbers that he discovered the little theorem. He also invented a factorization method which has been named for him as well as the proof technique of infinite descent, which he used to prove Fermat's Last Theorem for the case n = 4. Fermat also developed the two-square theorem, and the polygonal number theorem, which states that each number is a sum of three triangular numbers, four square numbers, five pentagonal numbers, and so on.

Although Fermat claimed to have proved all his arithmetic theorems, few records of his proofs have survived. Many mathematicians, including Gauss, doubted several of his claims, especially given the difficulty of some of the problems and the limited mathematical tools available to Fermat. His famous Last Theorem was first discovered by his son in the margin on his father's copy of an edition of Diophantus, and included the statement that the margin was too small to include the proof. He had not bothered to inform even Mersenne of it. It was not proved until 1994, using techniques unavailable to Fermat.


Buste in the Salle des Illustres in Capitole de ToulouseAlthough he carefully studied, and drew inspiration from Diophantus, Fermat began a different tradition. Diophantus was content to find a single solution to his equations, even if it were an undesired fractional one. Fermat was interested only in integer solutions to his Diophantine equations, and he looked for all possible general solutions. He also often proved that certain equations had no solution, which usually baffled his contemporaries.

Through his correspondence with Blaise Pascal in 1654, Fermat and Pascal helped lay the fundamental groundwork for the theory of probability. From this brief but productive collaboration on the problem of points, they are now regarded as joint founders of probability theory.

Fermat's principle of least time (which he used to derive Snell's law in 1657) was the first variational principle enunciated in physics since Hero of Alexandria described a principle of least distance in the first century CE. In this way, Fermat is recognized as a key figure in the historical development of the fundamental principle of least action in physics. The term Fermat functional was named in recognition of this role.

Together with René Descartes, Fermat was one of the two leading mathematicians of the first half of the 17th century. Independently of Descartes, he discovered the fundamental principles of analytic geometry. With Blaise Pascal, he was a founder of the theory of probability.

Regarding Fermat's work in analysis, Isaac Newton wrote that his own early ideas about calculus came directly from "Fermat's way of drawing tangents."

Of Fermat's number theoretic work, the great 20th century mathematician André Weil wrote that "... what we possess of his methods for dealing with curves of genus 1 is remarkably coherent; it is still the foundation for the modern theory of such curves. It naturally falls into two parts; the first one ... may conveniently be termed a method of ascent, in contrast with the descent which is rightly regarded as Fermat's own." Regarding Fermat's use of ascent, Weil continued "The novelty consisted in the vastly extended use which Fermat made of it, giving him at least a partial equivalent of what we would obtain by the systematic use of the group theoretical properties of the rational points on a standard cubic." With his gift for number relations and his ability to find proofs for many of his theorems, Fermat essentially created the modern theory of numbers.

http://www.mathematik.de/mde/information/landkarte/gebiete/wahrscheinlichkeitstheorie/bilder/fermat.jpeg
jeeeez...looks like something out of monty python in here

[raul]

Srinivasa Ramanujan

http://en.wikipedia.org/wiki/Ramanujan

isnt 22 dec close to your birthday, Rob?

http://www-groups.dcs.st-and.ac.ok/~history/Biographies/Ramanujan.html (http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Ramanujan.html)

http://www.usna.edu/Users/math/meh/ramanujan.html

[IWantToTellYou]

I don't see Professor Frink.

:laugh5: Glayyy-viiiin!!!!

Marie Curie would have to be my favourite.

I spent a long night one night back in high school trying to write a paper for physics class. Of course I cursed her, and physics back then, but I learned a lot about her in the process. She lead a very interesting life, and made quite interesting dicoveries about radium. She won two Nobel prizes, one for Physics and the other for Chemistry. Unfortunately, learning about radioactivity probably lead to her early death. No one really knew just how dangerous radium and radioactive materials were back then...

(Of course, there was also Pierre Curie, but behind every smart man is an even smarter woman). :teeth1:

[raul]

:laugh5: Glayyy-viiiin!!!!

Marie Curie would have to be my favourite.

I spent a long night one night back in high school trying to write a paper for physics class. Of course I cursed her, and physics back then, but I learned a lot about her in the process. She lead a very interesting life, and made quite interesting dicoveries about radium. She won two Nobel prizes, one for Physics and the other for Chemistry. Unfortunately, learning about radioactivity probably lead to her early death. No one really knew just how dangerous radium and radioactive materials were back then...

(Of course, there was also Pierre Curie, but behind every smart man is an even smarter woman). :teeth1:

im not imposing anything here, and she's definatelly one of the best choices, but Dirac is certainly a better. He's the greatest physicist of all tima, thats what i, and almost all the great physicists of 20th century, when he lived, believe. This includes Niels Bohr, Werner Heisenberg, to cut it short almost all the greats of 20 th century. It excludes Einstein, maybe cause he was too vain, and he definatelly was EXTREMELLY vain and a VERY conflicted person, he was mad, plus stole "his" magma opus relativity. Special from Poincare and Lorenz, general from Gauss, Lobačevski and Boylay, founders of non-euclidean geometry, but there0s controversy even there, Riemman, Minkowski, and Hilbert. And maybe it excludes him cause his status of a star had to be maintained, if he said Dirac was greater, it would diminuish him, as it should 10000000000 times, and 1000000000 times less posters, t-shirts etc of him would be sold. When someone's blown to that proportion of fame, I argue that in the usa more people have heard of him than anyone else, just cause he was made as a synonime for "genius". I gave loads of facts on Dirac in this thread, and you can feel free to read it all. Yeah, sure everyone's heard of albert, and noone of Dirac. Who's to say who's the greatest, laymen, or physicists them selves? Albert was an idiot, a complete mathematical anti-talent, and how can you be a physicist that way, may i ask? Plus experimental physics is also idiotic. For example, Couloumb determined his electric law, by repeating experiment 4 times! And who's to say that the 6th time of doing it won't disprove the law. No metter how many times an experiment has been done, there's no way of saying it won't disprove a law the very next time.

[IWantToTellYou]

That is all well and good, raul, but Marie Curie is still my favourite.

Besides, you asked people to post their favourites, not who they think is the best and greatest scientist of all time.

[raul]

its ok, i got a little carried away, sorry. When there's so much lie in the world, SOMEONE has to tell the TRUTH!

[raul]

Pierre-Simon Laplace

http://en.wikipedia.org/wiki/Pierre-Simon_Laplace

http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Laplace.html

http://upload.wikimedia.org/wikipedia/commons/e/e3/Pierre-Simon_Laplace.jpg

[Fran]

being the maths geek that I am I recognise every name on that list.
but I voted for Euler. He's my favourite :teeth1:

[raul]

being the maths geek that I am I recognise every name on that list.
but I voted for Euler. He's my favourite :teeth1:

hey! finally someone! whats your area of expertise? mine are transcedental number theory, game theory, and analysis, including topology and functional analysis, especially complex analysis, special functions, integral transformations...

there's a topic of mine on math, you can look it up

anyway i agree on euler, not as in my fav, he's my no 4, but, its a simple fact that he's the greatest, in terms of total output. what he wrote fits in 1500 books of "normal" size! and what other criteria is there but output?

my fav is hilbert

fav mathematicians

1 hilbert
2 cauchy
3 fermat
4 euler
5 von neumann
6 ramanujan
7 gauss

[Fran]

hey! finally someone! whats your area of expertise? mine are transcedental number theory, game theory, and analysis, including topology and functional analysis, especially complex analysis, special functions, integral transformations...

there's a topic of mine on math, you can look it up

anyway i agree on euler, not as in my fav, he's my no 4, but, its a simple fact that he's the greatest, in terms of total output. what he wrote fits in 1500 books of "normal" size! and what other criteria is there but output?

my fav is hilbert

fav mathematicians

1 hilbert
2 cauchy
3 fermat
4 euler
5 von neumann
6 ramanujan
7 gauss


Well I'm still only a student at the moment so haven't really got an area of expertise as such. However my favourite areas are number theory, graph theory (hence why i voted for Euler), and some areas of group theory and analyisis (I agree on complex analysis).

I haven't come across much of Hilbert's work yet

[raul]

Well I'm still only a student at the moment so haven't really got an area of expertise as such. However my favourite areas are number theory, graph theory (hence why i voted for Euler), and some areas of group theory and analyisis (I agree on complex analysis).

I haven't come across much of Hilbert's work yet

yeah, i saw in your profile youre a student in the meantime. college student? studying math? at cambridge? has alan baker been your prof? well, i guess his too old. he wrote the classic book Transcendental number theory, i have it, get it, its fantastic. I forgot to add algebraic geometry to my favs. what year of college are you?

yeah Euler basically founded number theory with Konongsberg walk, plus he did other stuff in it.

well i guess youre not in the final year of college, otherwise you would come across of A LOT of hilbert. that's it-the math he did is so advanced, you only come across him at the final year, at the earliest. thats also why many havent heard of him, which makes me mad, im quite sure he's the smartest person ever, always bordering between math and philosophy. i estimate his iq (although iq is relative) 500. this may be hard to grasp, but so is his work in math and philosophy.

[HoneyPie]

I don't see Professor Frink.

& I don't see Dr. Frankenstein, either. :nono3:

[scouseofdistinction]

Tho not a scientist in the strict sense, my choice is Steven Hawking. If you don't know who he is google him.

I'm with you. Steven Hawking would get my vote if he was a choice on there. He is considered as the Albert Einstein of our day.

[Fran]

yeah, i saw in your profile youre a student in the meantime. college student? studying math? at cambridge? has alan baker been your prof? well, i guess his too old. he wrote the classic book Transcendental number theory, i have it, get it, its fantastic. I forgot to add algebraic geometry to my favs. what year of college are you?

yeah Euler basically founded number theory with Konongsberg walk, plus he did other stuff in it.

well i guess youre not in the final year of college, otherwise you would come across of A LOT of hilbert. that's it-the math he did is so advanced, you only come across him at the final year, at the earliest. thats also why many havent heard of him, which makes me mad, im quite sure he's the smartest person ever, always bordering between math and philosophy. i estimate his iq (although iq is relative) 500. this may be hard to grasp, but so is his work in math and philosophy.

Yeah I'm at University studying math though not at Cambridge (or Oxford).

I'm in my third year of a four year course so going into my final year in the autumn. I looked up hilbert on the internet and the maths is advanced! although looking at the courses i'm taking next year it appears that we do look at his work. we look at the Basis Theorem and algebraic sets and hibert's Nullstellensatz?

[raul]

Yeah I'm at University studying math though not at Cambridge (or Oxford).

I'm in my third year of a four year course so going into my final year in the autumn. I looked up hilbert on the internet and the maths is advanced! although looking at the courses i'm taking next year it appears that we do look at his work. we look at the Basis Theorem and algebraic sets and hibert's Nullstellensatz?

greaT! may hilbert be with you! well im gonna do info on him here, but im saving the best for last!-il meastro him self, or THE grand master, as i call him. Surely youve heard of his 23 problems. The 2nd one is particulery interesting, cause it's about math it self. is math true, or false? Well, according to the 2 godel's incompletennes theorems, math cannot be substained, and is therefore a lie! But that's if you're a platonist among the philosophies of math, which almost every great mathematician of today is. But i cant stand platonisme. Im a formalist. That means i think mathematical truths are about nothing at all! So, it's still an open problem for me, in fact it is an open problem. (since godel's theorems dont count, if you're a formalist). That is the case with many of the 23-not that some are still open (posed in 1900), for some, it is not KNOWN if theyre solved!

basis theorem was first proven by hilbert in 1892. When paul Gordan, world's leading authority on algebraic invariants at the time first saw it he famously commented: "this is not mathematics. this is theology!" To this very day, even the greatest mathematicians cant grasp hold of it, and it was his first major (groundbreaking) work! He went on to write Grundlagen der Geometrie-Foundations of Geometry, along with Gauss' Disquisitiones arithmeticae and Euclide's Elements, most famous work in math history. In it, he established a complete, systematic and rigorous treatise of geometry, first time for anyone to do so, through a consistent and complete formalistic system of axioms (consistent means that from any subsystem of the system, one cant, through a finite number of logical steps, come to a negation of an axiom (that is, come to the conclusion that the axiom is a lie) from the system. complete means that from those axioms (around 20 of them), one can , for any statement in geometry, establish if it's true or false, again through a finite number of logical steps. The key to the whole thing is, that it's not important what a point, line, plane, or space is, rather, the RELATION between them. theyre not even defined, it could be the relation between beer bottles and tables, as hilbert said.

yes, thats it you're finally reach him next academic year! Besides, I forgot, you can ask me anything, if you don't get a step in the proof of a theorem, for example, I'll answer if I can! My math knowledge is greater than that of an average ordinary professor at a math dept. of a university, seriously. What are you studying this year? topology, algebraic topology, geometric topology, functional analysis, partial differential equations, algebraic number theory, analytic number theory, transcedental number theory, operator theory, automorhphic forms, what?

Next I'll give info on Godel, from my books (i have hundreds of math books), cause giving it from the internet makes little sense, one can simply look him up.

[Fran]

greaT! may hilbert be with you! well im gonna do info on him here, but im saving the best for last!-il meastro him self, or THE grand master, as i call him. Surely youve heard of his 23 problems. The 2nd one is particulery interesting, cause it's about math it self. is math true, or false? Well, according to the 2 godel's incompletennes theorems, math cannot be substained, and is therefore a lie! But that's if you're a platonist among the philosophies of math, which almost every great mathematician of today is. But i cant stand platonisme. Im a formalist. That means i think mathematical truths are about nothing at all! So, it's still an open problem for me, in fact it is an open problem. (since godel's theorems dont count, if you're a formalist). That is the case with many of the 23-not that some are still open (posed in 1900), for some, it is not KNOWN if theyre solved!

basis theorem was first proven by hilbert in 1892. When paul Gordan, world's leading authority on algebraic invariants at the time first saw it he famously commented: "this is not mathematics. this is theology!" To this very day, even the greatest mathematicians cant grasp hold of it, and it was his first major (groundbreaking) work! He went on to write Grundlagen der Geometrie-Foundations of Geometry, along with Gauss' Disquisitiones arithmeticae and Euclide's Elements, most famous work in math history. In it, he established a complete, systematic and rigorous treatise of geometry, first time for anyone to do so, through a consistent and complete formalistic system of axioms (consistent means that from any subsystem of the system, one cant, through a finite number of logical steps, come to a negation of an axiom (that is, come to the conclusion that the axiom is a lie) from the system. complete means that from those axioms (around 20 of them), one can , for any statement in geometry, establish if it's true or false, again through a finite number of logical steps. The key to the whole thing is, that it's not important what a point, line, plane, or space is, rather, the RELATION between them. theyre not even defined, it could be the relation between beer bottles and tables, as hilbert said.

yes, thats it you're finally reach him next academic year! Besides, I forgot, you can ask me anything, if you don't get a step in the proof of a theorem, for example, I'll answer if I can! My math knowledge is greater than that of an average ordinary professor at a math dept. of a university, seriously. What are you studying this year? topology, algebraic topology, geometric topology, functional analysis, partial differential equations, algebraic number theory, analytic number theory, transcedental number theory, operator theory, automorhphic forms, what?

Next I'll give info on Godel, from my books (i have hundreds of math books), cause giving it from the internet makes little sense, one can simply look him up.

Yeah I've heard of the 23 problems although I don't know the details.

Thanks for the offer of help! At the moment I'm studying graph theory, a course about knot theory, complex analysis, metric spaces and a course on the history of mathematics (although its very select parts - we've studied Euclid, Fermat and Gauss). some of those you've mentioned I study next year (algebraic topology, analytic number theory).

I saw a documentary on the tv about Godel about a year ago. Well it was about Godel, Cantor, Boltzmann and Alan Turing but it was more about their lives and didn't go into much detail of their work. Was still really interesting though!

[raul]

Yeah I've heard of the 23 problems although I don't know the details.

Thanks for the offer of help! At the moment I'm studying graph theory, a course about knot theory, complex analysis, metric spaces and a course on the history of mathematics (although its very select parts - we've studied Euclid, Fermat and Gauss). some of those you've mentioned I study next year (algebraic topology, analytic number theory).

I saw a documentary on the tv about Godel about a year ago. Well it was about Godel, Cantor, Boltzmann and Alan Turing but it was more about their lives and didn't go into much detail of their work. Was still really interesting though!

Welcome! graph theory-have you studied Cayley's formula for the number of trees that form a basis? Matrix theorem on trees? Euler tours and Hamilton's cycluses? planar graphs? Ramsey's graph theory?

that info on Godel is comming up, it's from the book The Honors class-Hilbert problems and their solvers by Benjamin Yandell

almost forgot-here's a nice proof of nullstelensatz from planet math:

statement

http://planetmath.org/encyclopedia/HilbertsNullstellensatz.html

proof

http://planetmath.org/?op=getobj&from=objects&id=7314

if you dont understand something, just ask!

[raul]

Kurt Godel was born on April 28, 1906, into a prosperous German-speaking family in the textile manufacturing town of Brunn, Moravia (now Brno in the Czech Republic). Godel's father has not completed his academic schooling, but studied weaving instead and went to work for the Friedrich Redlich factory, where he rose to become managing director and part-owner. Godel's grandfather on his mother's side had also risen from a poor background to a high position in a textile firm, after his own father, who had come from the Rhineland to work in Brunn as a hand-loom weaver, lost his livelihood with the advent of machine looms. Godel's grandfather educated himself, hand-copying books when he couldn't afford to buy them, and provided a good education to his children. He sent Godel's mother to a French school, which was not common among families of their social position. A good gymnast and ice skater, she had a happy childhood, with many friends, and loved the romantic German and French literature she was schooled on. Rudolf Godel, Kurt's brother, wrote that their father and mother's marriage was not a "love match" but described it as "built on affection and sympathy." Their mother was the dominant figure for the boys.

In 1913, when Kurt was seven, the family built a well-situated villa with a beautiful garden. Rudolf fondly remembered the two dogs they had. At Christmas there was a round of parties, one stop memorable for the decorated three that was hung from the ceiling so it could spin around. Presents were purchased by catalog from a Vienna toy shop, though Godel's mother found this "unpoetic." The family read political and historical novels, and Godel's mother had great sympathy after the First World War for the deposed Hapsburgs. She was fond of fairy tales. According to Rudolf, "Even in old age she could recite poems by Goethe, Heine, Lenau and others by heart. As a young woman she composed poems herself." She loved the garden and is reported to have said, "It would not be so terrible having to die, but not being able to experienceSpring any more...." Kurt spoke German at home and at gymnasium and did not study Czech. His mother had childhood memories of tension in Brunn between the German community and the "Czech element." The "clatter of horse's hooves" could often be heard as dragoons broke up clashes in the cobblestone streets.

Godel was unusually attached to his mother as a child and was in a state of anxiety when she left the house, according to Rudolf. Kurt got along well with Rudolf, playing "quiet games: bricks, model trains, also board games and chess." Kurt was not a good loser. His intelligence and persistance were recognized early, and he acquired the nickname "Mr. Why." At about age eight he fell seriously ill with rheumatic fever and after he recovered, upon reading a medical book, become convinced beyond any reasoning that he had a bad heart. No doctor ever won a logical argument with Kurt Godel. Sureness of opinion was a lifelong trait. In Rudolf's words, "My brother had a very individual and fixed opinion about everything and could hardly be convinced otherwise."

I'll continue later.

[Lucy]

I said Newton. My husband likes him.

[Fran]

Welcome! graph theory-have you studied Cayley's formula for the number of trees that form a basis? Matrix theorem on trees? Euler tours and Hamilton's cycluses? planar graphs? Ramsey's graph theory?

that info on Godel is comming up, it's from the book The Honors class-Hilbert problems and their solvers by Benjamin Yandell

almost forgot-here's a nice proof of nullstelensatz from planet math:

statement

http://planetmath.org/encyclopedia/HilbertsNullstellensatz.html

proof

http://planetmath.org/?op=getobj&from=objects&id=7314

if you dont understand something, just ask!

Yeah we've done Cayley's formula and Hamilton's cycluses. and planar graphs.

ah think i'm going to have to sit down and look at that proof to understand it properly!

[raul]

Kurt Godel was born on April 28, 1906, into a prosperous German-speaking family in the textile manufacturing town of Brunn, Moravia (now Brno in the Czech Republic). Godel's father has not completed his academic schooling, but studied weaving instead and went to work for the Friedrich Redlich factory, where he rose to become managing director and part-owner. Godel's grandfather on his mother's side had also risen from a poor background to a high position in a textile firm, after his own father, who had come from the Rhineland to work in Brunn as a hand-loom weaver, lost his livelihood with the advent of machine looms. Godel's grandfather educated himself, hand-copying books when he couldn't afford to buy them, and provided a good education to his children. He sent Godel's mother to a French school, which was not common among families of their social position. A good gymnast and ice skater, she had a happy childhood, with many friends, and loved the romantic German and French literature she was schooled on. Rudolf Godel, Kurt's brother, wrote that their father and mother's marriage was not a "love match" but described it as "built on affection and sympathy." Their mother was the dominant figure for the boys.

In 1913, when Kurt was seven, the family built a well-situated villa with a beautiful garden. Rudolf fondly remembered the two dogs they had. At Christmas there was a round of parties, one stop memorable for the decorated three that was hung from the ceiling so it could spin around. Presents were purchased by catalog from a Vienna toy shop, though Godel's mother found this "unpoetic." The family read political and historical novels, and Godel's mother had great sympathy after the First World War for the deposed Hapsburgs. She was fond of fairy tales. According to Rudolf, "Even in old age she could recite poems by Goethe, Heine, Lenau and others by heart. As a young woman she composed poems herself." She loved the garden and is reported to have said, "It would not be so terrible having to die, but not being able to experienceSpring any more...." Kurt spoke German at home and at gymnasium and did not study Czech. His mother had childhood memories of tension in Brunn between the German community and the "Czech element." The "clatter of horse's hooves" could often be heard as dragoons broke up clashes in the cobblestone streets.

Godel was unusually attached to his mother as a child and was in a state of anxiety when she left the house, according to Rudolf. Kurt got along well with Rudolf, playing "quiet games: bricks, model trains, also board games and chess." Kurt was not a good loser. His intelligence and persistance were recognized early, and he acquired the nickname "Mr. Why." At about age eight he fell seriously ill with rheumatic fever and after he recovered, upon reading a medical book, become convinced beyond any reasoning that he had a bad heart. No doctor ever won a logical argument with Kurt Godel. Sureness of opinion was a lifelong trait. In Rudolf's words, "My brother had a very individual and fixed opinion about everything and could hardly be convinced otherwise."

I'll continue later.

In school Kurt was precise, thorough, and excellent. His favorite subjects were mathematics and languages, including Latin, French, and English. At his death he owned dictionaries in many languages. He also excelled in theology and showed some interest in history, but this faded. Godel enjoyed "light" music-operetta and, later in life, American show tunes. He studied a now-obscure type of German shorthand, the Gabelsberger script, in order to write more efficiently (and possibly more privately). Godel's collected personal papers and his many notebooks are page after page in this shorthand. John W. Dawson Jr., who catalogued Godel's Nachlass, or literary estate, was assisted by his wife, who learned the shorthand, and by an aging German emigrant who knew it. In 1997 Dawson published Logical dilemmas: the life and work of Kurt Godel. In any conflict of biographical detail I have followed Dawson.
It was rumored that Godel managad to make it through gymnasium without making a single mistake in Latin grammar. He always recieved the highest possible marks except once, in mathematics. Surviving examples of his homework show his meticulousness. According to Rudolf, he surprised everyone by learning most university mathematics on his own in gymnasium. Godel himself dated his interest in mathematics from age fourteen and certainly studied calculus before university. He had an unusual number of excused absences

[raul]

paul erdos-26 march 1913-20 september 1996

number theorist. Though a remarkably productive mathematician (Janos Pach in Mathematical intelligencer counts more than 1500 papers), Erdos never held, in the words of Mark Kac, writing in 1985, 'anything resembling a regular job'. Erdos published his first papers at eighteen. He left his native Hungary in the 1930s and remained an expatriate, wandering from colloquium to temporary appointment all his life and sleeping on the living room couches of friends. He died while attending a conference in Warshaw in 1996. Stanislav Ulam met him when Erdos was invited to give a colloquium at the University of Wisconsin at Madison and writes, "His visit to Madison became the beginning of our long, intense-albeit intermittent- friendship. Being hard-up financially- 'poor', as he used to say -he tended to extend his visits to the limits of welcome"
Later in their friendship, Ulam was leaving the hospital in Los Angeles after an acute inflammation of the brain, never clearly diagnosed, then left him temporarily aphasic and partially paralyzed. Erdos appeared, suitcase in hand, and said, "Stan, I am so glad to see you are alive. I thought you were going to die and that I would have to write your obituary and our joint papers." And then, "You are going home? Good, I can go with you."
Ulam welcomed this, though he says his wife was "somewhat more dubious". In the car on the way down to the house on Balboa Island where the Ulams were staying, Erdos started talking mathematics to the trepanned and bandaged Ulam, who was able to respond to his satisfaction. Erdos pronounced : "Stan, you are just like before", which greatly cheered Ulam, who had been entertaining dire thoughts about impairment. When Ulam won two games of chess later, to Erdos' visible disappointment, he was further convinced of the possibility of recovery. Erdos was not one to throw a game.
Erdos stayed through the recuperation and the two took increasingly long walks on the beach. On one of those walks Erdos noticed a particulary sweet little child

[raul]

In school Kurt was precise, thorough, and excellent. His favorite subjects were mathematics and languages, including Latin, French, and English. At his death he owned dictionaries in many languages. He also excelled in theology and showed some interest in history, but this faded. Godel enjoyed "light" music-operetta and, later in life, American show tunes. He studied a now-obscure type of German shorthand, the Gabelsberger script, in order to write more efficiently (and possibly more privately). Godel's collected personal papers and his many notebooks are page after page in this shorthand. John W. Dawson Jr., who catalogued Godel's Nachlass, or literary estate, was assisted by his wife, who learned the shorthand, and by an aging German emigrant who knew it. In 1997 Dawson published Logical dilemmas: the life and work of Kurt Godel. In any conflict of biographical detail I have followed Dawson.
It was rumored that Godel managad to make it through gymnasium without making a single mistake in Latin grammar. He always recieved the highest possible marks except once, in mathematics. Surviving examples of his homework show his meticulousness. According to Rudolf, he surprised everyone by learning most university mathematics on his own in gymnasium. Godel himself dated his interest in mathematics from age fourteen and certainly studied calculus before university. He had an unusual number of excused absences,

both for the full day and from exercise. At home he did not share his mother's and brother's love of nature and the garden, and when the family took Sunday walks he tended to stay behind, cooped up with a book. While still in school he formed a relationship with the daughter of family friends, described as an 'eccentric beauty' ten years his senior. It was stopped by opposition from his family.
Godel went to the University of Vienna in 1924 intending to study physics but was wooed to mathematics by the three-year lecture cycle given by Philipp Furtwangler. The lectures were undoubtely excellent. But logician Georg Kreisel, who had a lifelong relationship with Godel, writes: "Another singular aspect of those lectures (which Godel did not mention, possibly because of the medical history involved) may have had equal weight.

[the ninth walrus]

i voted

http://t1.gstatic.com/images?q=tbn:ANd9GcSquc7dPBGysAyxnwsBidWJT5dEPHwjQ 8k-FLU2MC-uGtRKqzq5CQ