Who in your opinion is the greatest mathematician ever? Some canidates:

Who in your opinion is the greatest mathematician ever? Some canidates:
Dunno but number 4 has the best hair
That is Sofia Kovalevskayaa brilliant female mathematician that made enormous contributions to real and complex analysis.
#4 looks a lot more like Leibniz.Originally Posted by Ellatha
In orderOriginally Posted by Ellatha
Rene Descartes
Blaise Pascal
Srivinasa Ramanujan
Gottfried Liebniz
Sofia Kovalevskaya
If you wanted to include a more important and influential female mathematician I would have suggested Emmy Noether.
My vote is on Fermat, who's tricky conjecture inspired 350+ years of mathematical research, and I'd closely follow him with Leibniz and Newton.
My personal favorite mathematician is Gauss, though.
I suppose it is considered to 'bad form' to vote for yourself on this one
I certainly think no. 4 would have if he were alive today!!
You are correct; that's odd, I thought he said "the last one" has the best hair? Thank you for correcting me, though.Originally Posted by DrRocket
Obviously.
Fermat does not hold a candle to Newton. Not even close.Originally Posted by Arcane_Mathematician
The usual oversimplified list of the top 3 mathematicians of all time is
Archimedes
Newton
Gauss
It is not a bad list, but as with all such lists, it is a bit arbitrary.
If I had to add a fourth I would pick Gauss's student, Riemann. Other honorable mentions would include Euler and Cauchy.
When you get to more modern mathematicians the list becomes extremely long. All, or at least almost all, of the names in posts earlier in the thread made big contributions, but it takes quite a bit of background to appreciate a lot of it.
While Fermat himself wasn't a truly "great" mathematician, he had conjectures galore that just ticked off some more current mathematicians to the point that they created new ways of dealing with the topics JUST to prove him right or wrong. While FTL wasn't exactly a great bit of math on Fermat's part, it was a small idea he had that caused MASSIVE advancements for hundreds of years, some of which going on the simple basis that it is true. Now, I see the inspiration he gave as a one of the greatest things to ever happen to both math AND science, which is why I'd give him the title.
I must confess, I'm not incredibly familiar with Archimedes contributions to Mathematics, though I know he was one HECK of an engineer, for sure.
Fermat's last theorem was not as influential as you might think. The proof finally came from a very difficult theorem in algebraic geometry. Wiles had noted that a proof of the TaniyamaShimura conjecture would result in a proof of FTL, and that was a motivating factor, but algebraic geometry was cooking along just fine and would have continued to do so with or without FTL.Originally Posted by Arcane_Mathematician
FTL was not on the list of Hilbert problems and those problems were instrumental in shaping 20th Century mathematical research. http://en.wikipedia.org/wiki/Hilbert's_problems
The reason that you hear as much as you do about FTL is that it is easily stated and defied solution for so long. You can explain the conjecture to any high school junior. But the proof is extremely difficult.
There is another set of problems currently outstanding, the Milenium Problems that have been identified by the Clay Institute. They will be influential in shaping research for the near future. http://www.claymath.org/millennium/
One of the Milennium Problems, the Poincare conjecture has been solved. The rest remain open. Of the list, only the Riemann Hypothesis was also a Hilbert Problem. It is generally regarded as the most difficult open problem in mathematics.
There was a lot more in the solving of that theorem than just the ShimuraTaniyama conjecture, and as I've read it had a lot more to do with than JUST algebraic geometry. And accounting just what was accomplished in the immediate solving of the conjecture seems a little undercutting to me, not giving any credit to all the other branches of mathematics that made advances though mathematicians that were motivated by solving the theorem.
I have a book that outlines the general history of the theorem and the math involved (quite brief and abridged) by Amir D. Aczel. Fermat's Last Theorem: Unlocking the Secret of an Ancient Problem The actual math inside isn't THAT complicated (I understand a decent amount of it), nor is it representative, mostly, of the theorem itself, but gives a good background I would hope of what it took before Wiles actually had all of the necessary developments to form his proof.
Have to side with DrRocket on this one. Except for one minor detail: I think Ken Ribet is usually given credit for proving that TaniyamaShimura implies FLT.
Incidentally, TaniyamaShimura was considered to be of great importance before anyone realized it could be used to prove FLT. So, in my (nonexpert) opinion on this issue, I think that the mathematical advances that preceded TaniyamaShimura would have occurred with or without FLT.
Gauss for me.
Newton was a giant, no doubt, but Leibniz was paralleling his work so we may have had the calculus in any case. And Archimedes was too far away in time for me to have any scale for comparison.
I believe Evariste Galois would have been among the greatest mathematicians (comparable to Gauss or Cauchy) had he not been so quick to anger and foolish enough to accept a duel he knew he would lose. By the age of 20 he had laid the foundation for Galois theory which has a massive scope of applications within abstract algebra and discovered the conditions of a polynomial that must be met in order for a solution to be derived through use of radicals. Blaise Pascal is another honorable mentionhe had such a precocious mentality that Rene Descartes refused to believe that the work Pascal wrote as a teenager could have come from one his age.
Galois was an excellent mathematician. But a lousy shot. Perhaps because he was al angebraist but not an algebraic geometer. Angles are important when shooting. 8)Originally Posted by Ellatha
Not nearly as influential as Gauss or Newton overall. Gauss and Newton are giants among giants.
Galois didn't live to 83 or 77 years old as Newton or Gauss did respectively, though :wink:. I still don't see how Newton was so great a mathematicianI consider Gauss, Riemann, Leibniz, and Bernoulli as more developed mathematicians. I believe Newton is the greatest scientiest (and physicist) in history, but his contribution to pure mathematics seems to only hold true for inventing calculus (obviously an extremely great contribution, but I don't think it's enough to make him the greatest, especially considering Leibniz was credited for inventing calculus for over a decade before Newton came forward and claimed rights to it) and applying polar coordinates. Maybe we'll never agree here, however.
Pascal was an outstanding genius who studied geometry as a child. At the age of sixteen he stated and proved Pascal's Theorem, a fact relating any six points on any conic section. The Theorem is sometimes called the ``Cat's Cradle'' or the ``Mystic Hexagram.'' Returning to geometry late in life, he advanced the theory of the cycloid. In addition to classic and projective geometry, Pascal founded probability theory, made contributions to axiomatic theory, and the invention of calculus.
Inappropriate signature link removed. IS
Pascal was indeed an extraordinary mathematician and an extremely gifted child. I believe that Leibniz was the most intelligent mathematician overall, howeverwhen he left for Paris for reasons related to law in order of the Duke, knowing little about mathematics he came back about four years later as one of the top two or three mathematicians in Europe. Leibniz showed remarkable depth of thought as a child, and at the age of five his father believed he would grow to be an eminent figure in whatever course of study he took, and he taught himself Latin as a child as well. At fourteen Leibniz enrolled in the University of Leipzig, and recieved his bachelor's degree within two years, and his master's within four years. At Leipzig there was some issue with the other students not allowing him to recieve his Doctorates, so he left Leipzig University to attend the University of Altdorf, recieving his Doctorate of Law within an extremely small interval of time. Leibniz's genius spans over an extremely large amount of subjects, and he is sometimes regarded as the last true Universal Genius. Leibniz also anticapted Gauss in his technique of Gaussian Elimination, knowing that he could arrange a matrix in a certain fashion to solve systems of equations, and his work on topology is probably his second most eminment after calculus. Leibniz's genius was analyzed along with 300 others in the 1920s tp 1960s, where he recieved an estimated IQ of 205the second highest in the study, Pascal was estimated at 195.Originally Posted by nasir
Leibniz also invented his notion of "monads" (not be confused with same word as used in category theory)  deduct 100 points.Originally Posted by Ellatha
Remember that Newton not only invented ordinary calculus, he also started the calculus of variations. And was Chancellor of the Exchequeer. And developed a system of mechanics that dominates may applications today. And developed the theory of universal gravitation that is important even in formulation of general relativity. And developed a theory of optics. And .....
Estimated IQ is an even worse measure than measured IQ. Feynman declined membership in Mensa, saying that he was delighted that he dis not qualify. I don't know what IQ really measures but if Feynman's score was insufficient for anything then I have no confidence in the measure. One of the more intelligent mathematicians of my acquaintence told me that he had a measured IQ of 105, not particularly distinguishing. I am quite sure that he was smarter than whoever made up the test.
Frankly the game of trying to decide "who was smartest" is a fool's errand. It doesn't mean anything. If you are sufficiently knowledgeable you can make a reasonable assessment of the impact of someone's work on the subsequent development of a field. Even that is very subjective. But on that basis neither Leibniz nor Pascal hold a candle to Newton or Gauss.
Dr. Rocket,
Those who generally question the utility of IQ tests as a means of psychometrical analysis are also those generally know very little about it; it wouldn't be too different than arguing whether or not an algebraic expression can be made that fully defines pi considering the evidence there is to support it. I'm sure you're simply overexaggerating about condensing Leibniz's IQ to 105, however. Genius and IQ are not compatible first of all, IQ measures the level of g, which is a term psychologists use for a factor that is common within all factors of intelligence, in particular those tested by the StanfordBinet 5 IQ test (fluid reasoning, quantitive reasoning, knowledge, visualspacial processing, and working memory). It would be unbeneficial for IQ tests to measure genius and intelligence, as a weight factor of each could easily skew the results and reveal nothing one's aptitude. Simply because Leibniz made a theory that you disagree with (actually the theory of monads shares some underlying principles with the Cognitive Theoretic Model of The Univerise [CTMU] which was created by one with an IQ of about 195) does not imply that he was unintelligent. Especially when one looks at his biography and other work (in general the former is a much better one for assessing intelligence).
Richard Feynmann's alleged IQ of 127 or so does not come from a reliable source. Arthur Jensen, a famous psychologist, mentions that "famously reported" IQs are not something he at all takes seriously, and are often fictious and made in an attempt to putdown IQ. Sir Francis Cricke (the individual who discovered the structure of DNA) was also alleged to have an IQ of 115. All of these reported IQs are ridiculous and trying to use them as evidence that IQ has no applications is even more so. Most mathematicians with a PhD have IQs of about 140 (with doctors and lawyers at about 127); I'm quite suspect of your friend's score of 105 than; perhaps he didn't take a professional IQ test or equivalently wasn't measured thoroughly (a single IQ test only provides a rough estimate). Isaac Newton was by no means unintelligent; his early childhood is obvious evidence of this, as he built sun dials, waterclocks, tables, wildmills and various other contraptions after drawing blue prints and diagrams for them. Newton's estimate was one standard deviation below Leibniz on the Weschler intelligenec scale or StanfordBinet tests above the fourth version (190, although it should be noted that Newton's coefficient of the reliability of the data was lower as well, which sometimes condensed the estimate).
Understanding the intelligence of eminent figures has many applications. For one it allows us to relate if there is a correlation between genius and intelligence (apparently there is to a degree, but not as much as one would expect). Proving the Riemann hypothesis doesn't have many applications (nor the Goldbach's conjecture), but mathematicians are still trying to do it anyway.
If you'd like to get a greater appreciation for the concept of IQ (and intelligence) as a whole than I'd recommend you read Bell Curve: Intelligence and Class Structure by Hernnstein, Bias in Mental Testing by Dr. Arthur Jensen as well as The g Factor: The Science of Mental Ability, also by Dr. Arthur Jensen.
I'd also like to make a few points on Newton's contributions that you name: most of it relates to physics; there is no argument here, Newton contributed to physics much more than Leibniz and perhaps any other human being (although Archimdes and Einstein are also honrable mentions), being Chancellor of the Exchequer doesn't mean much; he was also president of the Royal Society; Leibniz was also president of Berlin's Society of Sciences. Newton's true contribution to pure mathematics relates almost entirely to calculus (inventing it). Even here, Leibniz's notation is adopted today. The Bernoulli brothers both advanced calculus more so than Newton and Leibniz as well. I'm not trying to put Newton down, but I also don't believe, with all of immensley hard working mathematicians there are in history and their love for mathematics in contributing to the field as they did, that somebody who invented a very important branch of it than stayed away from it for most of the rest of his life and had a main interest in physics and theology should deserve the title. Leibniz on the other hand, in addition to inventing calculus, found a proof for Fermat's Little Theorem, refounded the Leibniz series for finding one fourth of pi, discovered the Leibniz Harmonic Triangle, found a formula for finding the determinant of a square matrix, and made large advanced in diagrammatic reasoning.
No doubt Gauss would be my pick. His extraordinary abilities in the field of maths and physics left mathematicians mourning at his death and at the death of his direct students when " the last link to the great Gauss was lost". :(
'Originally Posted by newton
Who said the "last link to the great Gauss was lost'
In under 5 minutes I found a direct academic descendant of Gauss who received a degree in 2007. In this particular case it was Mathew Miller, University of Oregon. I am sure there are others. I pursued only one path from Gauss.
http://genealogy.math.ndsu.nodak.edu/id.php?id=110272
Gauss is shown as having 47371 descendants.
It turns out that John Archibald Wheeler is traceable to Gauss as well. He had many student, including Richard Feynman, Kip Thorne, Charles Misner, and Wightman. among Wightman students were Jerry Marsden, Arthur Jaffe, and Bary Simon, all of whom are still alive and all of the whom have had many students.
I'm not a mathematician, but I vote for Gauss.
If nothing else, I love the story about him adding the numbers from 1 to 100 in primary school.
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