Greatest Mathematician

Here’s an interesting page I managed to Google up.

Hmm…Cantor definitely had one of the more important ideas in history, but as the page says, he didn’t do that much. Galois could’ve been a contender, if only he hadn’t gotten himself killed so young.

Euler. In my everyday work Richardson would follow him.

Great link, thanks.

As someone that uses this stuff on a fairly regular basis, I vote for Gauss. Where other’s have things attributed to them that make problems doable but still difficult, many of Gauss’ credits make things beautifully simple.

I loved Charles Babbage’s work, personally.

I guess that’s just because I love computers.

This guy. Not only a towering genius, but also the most interesting mathematician of all time.

-Apoptosis

I think Riemann deserves more credit than he gets here. Gauss, who was no easy man to please, gave Riemann a standing ovation for a talk on a topic in which he was not an expert. Why? Because Gauss himself had not had create success in that area.

However, I don’t think you can rank one great mathematician above another, any more than you can claim there is a single “greatest writer” (even if you just stick to English). Pretty much by definition, the greats did stuff that stopped the other greats. Consider that:

Newton was only a part time mathematician and physicist. He did some of his greatest work in a period of six months. He also once solved a problem that was posed to the greatest mathematicians in Europe. While the rest, including Leibniz, struggled, Newton purportedly took just one evening to solve it.

Gauss spent much of his best years doing astrodynamics. It took a genius like Jacobi, while perusing some of Gauss’ notebooks, to realize just how much the world missed.

Archimedes was also a part time mathematician. I honestly can’t say that I know how he influenced mathematics, so I can only say the experts say he was important.

Riemann died at a very young age, somewhere in his lower 30’s. Still, he earned Gauss’s admiration, and posed some of the most difficult questions we’ve ever thought of.

Maybe not from the perspective of career output, but no one’s mentioned Von Neumann yet…

von Neumann is less important as a mathematician and more as a computer guy. Still, in terms of the influence he had in that field, I can see your point.

Of course, greatness here has not been strictly defined. Cantor provided a number of amazing theoretical results and in the long term changed the way that the professional math community looked at the real numbers. However, the sum total of his work did not affect the types of practical results that could be achieved through math as much as Leibnitz, Newton, or Gauss.

For all time, there is no way to choose between Gauss and Euler. Gauss did a lot of stuff outside of mathematics, but there is something about Euler that is hard to beat. Riemann, Abel, and especially Galois all died too young to judge. Newton wasted too much time on alchemy, religion and other firvolous pursuits and his really great work was in physics.

For the last century, I don’t think Erdos is in the running. It is between Hilbert (who was partly 19th) and Grothendieck who revolutionized two different fields. Turing’s work, while important, is really not in the same class as Goedel’s. Then there are Serre, Emil Artin and a few others.

Archimedes is my vote simply because of the number of clever things that he did which were without precident, and which weren’t repeated for a long long time.

Gauss is often (and I think correctly) claimed to be the last mathematician to rise to the top in all areas of mathematics. Since him the field has grown too vast and mathematicians have had to specialise. Having said that, I think Riemann would have had the same claim made about him if he had lived longer. And some believe that Hilbert was the last allrounder.

My current favourite is Euler. Mostly because I understand his stuff. But he was an all-round nice guy. And he did maths for the fun of it. A lot of his proofs were not watertight, but he wasn’t interested in rigour as much as in pushing the boundaries. No one introduced more notation than Euler.

As for the Newton/Leibniz argument. Newton definitely had priority on the calculus, but didn’t publish because he hadn’t fully come to grips with the concept of limit. He was a man of rigour. Leibniz didn’t care about the finickity and elusive details the same way and so felt at liberty to publish and share his information. Which of course got Newton a bit upset. Personally, I think of Newton as a physicist.

I am surprised that hardly anyone has mentioned Godel so far. His proof would have to be among the most important ever. I don’t know what else he accomplished though.

What? No mention of John von Neumann?

There was a show called INFINITE SECRETS about a lost document by Archimedes saying he was working on calculus before 200 B.C. Maybe he should be raised in the ranks.

Dal Timgar

How much really seminal new mathematics has been done by mathematicans past the age of 35?

Can’t believe nobody’s mentioned this guy yet.

(erm…sorry. carry on with the serious intellectual discussion.)

Does anybody have a copy of Clifford Pickover’s Wonders of Numbers close to hand? There’s a list in there of the results of a survey among mathematicians of the ten greatest mathematicians of all time.

Will Hunting. Did you see him whip out that problem that was supposed to be oh-so-tough, just for the hell of it, then go right back to sweeping up?

Kidding. I’m a kidder.

astro writes:

> How much really seminal new mathematics has been done by
> mathematicans past the age of 35?

Well, just to mention the obvious case, Andrew Wiles proved Fermat’s Last Theorem at the age of 40. (At 41 if you consider the point when the proof was done to be when he and John Taylor announced a correction in the proof the next year.) The notion that first-rate mathematics is only done by young people is at least an exaggeration.

I do. His list:

  1. Newton
  2. Gauss
  3. Euclid
  4. Euler
  5. Hilbert
  6. Poincare
  7. Riemann
  8. Galois
  9. Descartes
  10. Pascal

Runners-up: Cardano, Godel, Cantor, Napier.

There are other cool Top n Lists in that book, including “10 most influential mathematicians alive today,” “8 most influential female mathematicians,” “5 strangest mathematicians who ever lived,” and “10 most difficult-to-understand areas of math.”