Who is the greatest mathematician of all time?

[bitwise]

A question: Why is Descartes considered so great? I can’t recall anything he did besides the famous coordinate system and the eponymous rule of signs. Perhaps, I am biased against him, because I was forced to read his “proof” of God’s existence.

[bonzer]

@Spiritus Mundi

Are you sure? I never spent much time on the history of mathematics, but back in the Dark Ages when I groked on numbers the “mathemeticians on the street” pretty much spoke of Newton’s “method of fluxions” as retarding the progress of British mathematics for most of a century.

While this is certainly a deeply entrenched perception of 18th century British mathematics, to quote myself from this recentish thread on Newton’s contributions to calculus:

The notion that Newton’s influence over his British successors put them at a disadvantage over their Continental colleagues in the years after his death is certainly something that’s often been repeated by writers on the history of mathematics. However, this has been questioned by specialists in recent years, notably by Niccolo Guicciardini in his The Development of Newtonian Calculus in Britain, 1700-1800 (Cambridge, 1989). The argument is that, rather than this being a period of stagnation as suggested in the conventional picture, a detailed look at it reveals lots of fruitful work being done. Guicciardini does accept that there was a crucial divergence between the British and French traditions, with the latter’s contributions going on to dominate 19th century developments, but dates this rather late in the 18th century and absolves Newton of the blame.

[antechinus]

@Spiritus Mundi

My contrarian vote goes to Cantor. But in my heart I know the answer is Gauss.

Napoleon ordered his troops to spare Gottingen in 1807 because “the greatest mathematician of all times is living there”.
Jacob Bernoulli invented statistical sampling, which has had a huge impact on society. And his nephew Daniel who defined a systematic process of risk measurement has to be seen as very influential as well. These discoveries are fundamental to the modern way of thinking.

What about Fermat?

[duffymo]

@tim314

I’m not sure if this constitutes a Great Debate, or what. But anyway . . . who do you think is the greatest mathematician of all time? (And why, i.e. what did they do that’s so impressive?) What about the greatest of the 20th century?

I’ve seen this question asked a lot more for physics, with the answer generally being either Newton (co-invented calculus, major contributions with regard to mechanics, gravitation, optics, etc.) or Einstein (special and general relativity, explained photoelectric effect and brownian motion, etc.). In math, I don’t know of any such concensus.

When he presented his famous paper outlining the 23 great unsolved problems in 1900, David Hilbert was the master of the field. You can make a strong case for him at the start of the century.

Kurt Godel is another great 20th century mathematician. His theorem tells us a great deal about what’s possible and what’s not with mathematics.

And why just Einstein and Newton on that list of physicists? Maxwell’s equations, and all they’ve made possible since, might have been the greatest 19th century insight.

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[astro]

@duffymo

When he presented his famous paper outlining the 23 great unsolved problems in 1900, David Hilbert was the master of the field. You can make a strong case for him at the start of the century.

Kurt Godel is another great 20th century mathematician. His theorem tells us a great deal about what’s possible and what’s not with mathematics.

And why just Einstein and Newton on that list of physicists? Maxwell’s equations, and all they’ve made possible since, might have been the greatest 19th century insight.

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As an interesting side note here is a list of the problems that have been solved (or not) in that list.

Hilbert’s problems

Hilbert’s problems are a list of 23 problems in (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics put forth by German mathematician (German mathematician (1862-1943)) David Hilbert in the (The capital and largest city of France; and international center of culture and commerce) Paris conference of the (Click link for more info and facts about International Congress of Mathematicians) International Congress of Mathematicians in 1900. The problems were all unsolved at the time, and several of them turned out to be very influential for twentieth-century mathematics. At this conference he presented 10 of the problems (1, 2, 6, 7, 8, 13, 16, 19, 21, and 22) and the list was published later

[Malodorous]

My Math prof used to joke that when our math texts said “one can show”, or “one can prove” it meant that someone had already proven it and that “one” usually ment Euler.

[duffymo]

@astro

As an interesting side note here is a list of the problems that have been solved (or not) in that list.

Hilbert’s problems

Great link, thanks.

Benjamin Yandell wrote a great book entitled “The Honors Class” about the problems and their solutions:

http://www.amazon.com/exec/obidos/tg/detail/-/1568812167/qid=1126365978/sr=2-1/ref=pd_bbs_b_2_1/102-6310953-2688115?v=glance&s=books

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[Saint_Cad]

@Alessan

What about Euclid? Chopped liver?

Close! Euclid was a math teacher who compiled “Elements” from established problems into a textbook for his students. While he clearly defined the structure of math books up through the modern day, this does not make him a great mathematician.

[Clothahump]

@bitwise

A question: Why is Descartes considered so great? I can’t recall anything he did besides the famous coordinate system and the eponymous rule of signs. Perhaps, I am biased against him, because I was forced to read his “proof” of God’s existence.

Because every time a carriage got stuck in the mud, they would send for old Rene to pull them out.

It was a matter of putting Descartes before the horse…
Thank you, thank you. Please don’t applaud, just throw money on the stage.

[migueljjr]

Myself.

[Jonathan_Chance]

migueljr,

Thank you for your post and welcome to the Straight Dope Message Board.

This is a very old thread and your post didn’t really contribute much new information. In general, we prefer that bringing zombie thread - which is what we call such things - is caused by another substantial post and not a drive by.

I’m going to lock this thread now. You are welcome to browse the forums and post. I hope you enjoy your time at the SDMB.

Jonathan Chance
Moderator
Great Debates