I’m sure Euclid, Archemedes and Newton are in the top 5, but who would you choose as the all time greatest mathematician. A good buddy of mine, a PhD in math, always said he would choose Gauss.
Gauss is the obvious answer. Or, you could just follow Eric Bell:
“Archimedes, Newton, and Gauss, these three, are in a class by themselves among the great mathematicians, and it is not for ordinary mortals to attempt to range them in order of merit.”
E. T. Bell, Men of Mathematics, Ch. 14
I think I would have to find a place in the top 10 for Cauchy, Riemann and Cantor.
For what the world was before him and what the world was after, and what he did to change it, you really can’t hold a candle to Isaac Newton.
The problem I always had with Newton was the Libnitz published some of the same ideas at roughly the same time. I always wondered who was the Microsoft and who was the Apple. 
(I suppose from the tales of history Newton had the be the Apple because one fell on his head. Right? HA!!!)
I’m not a mathematician, but I would agree that Gauss belongs and we mustn’t forget Leonhard Euler.
Newton. Definitely Newton.
ccwaterback wrote
One of my favorite books is The 100: A Ranking of the Most Influential Persons in History. A very good read; I recommend it. Obviously, there is plenty of debate about who belongs in the book, and in what order, but in general, I agree with their assessments. They put Isaac Newton at the second most influential person in the history of the world. Higher than Jesus Christ. Higher than Albert Einstein. And reading their assessment, I have to agree. There’s a small chapter about him; I’ll quote a paragraph:
I agree.
If I disagree about Newton, strictly as a mathematician, it is so that some of our mathematicians can straighten things out.
Newton was transcendent as a thinker and in applying mathematics to physical problems.
However, I do believe that it took mathematicians quite a few years to put the integral calculus on a sound mathematical basis after he and Leibnitz started the ball rolling.
I think I would have to agree, Mr. Newton was the greatest scientist of all time. But I was thinking more along the lines of strictly mathematics. We can argue Descartes was the greatest philosopher of all time, and a pretty nifty mathematician too. But as far as pure mathematical accomplishments and revolutionary ideas, I’m not sure Newton would be number one. Let me add, if he isn’t number one, it would be difficult to find someone to beat him out for the number two spot.
I was watching a show the other night about Archemedes. The only known copy of his greatest work was discovered somewhere in the Mideast. During the middle ages, a monk ran out of paper so he white-washed Archemedes book and wrote over the pages. They are currently in the processes of restoring what they can of his work. Very interesting.
Bill H., I’m curious. Who was the number one most influential person? It wasn’t Jesus? Hmmm … let me think … Copernicus?
ccwaterback, it was Muhammad. Which struck me as strange the first time I read it, but I’ve come to think it’s a good call. There were a couple reasons he was placed above Jesus. First, he was more directly responsible for Islam than Jesus was for Christianity. Without St. Paul (who likely never even met Jesus), there wouldn’t have been Christianity. St. Paul was the main developer of Christian theology, its principal proselytizer, and the author of a large portion of the New Testament. Muhammad on the other hand was responsible for both the theology of Islam and its main ethical and moral principles, plus he played a key role in proselytizing and estabilishing the religious practices and wrote the Koran. (well, dictated it; he was illiterate). Also, he was not just a religious leader, but also a very powerful secular leader. He was the driving force behind the Arab conquests, and even putting aside his religion, these conquests may have placed him as the most influential leader.
After reading the book’s rational, I think I agree with his placement. For the record, I’m an atheist.
Upon reading the thread title, the name that immediately popped in my head was Gauss. I just saw a special on Archemedes, where they have discovered some of his “lost” works. If they had known of these works right after he wrote them, we would be light years ahead of where we are now. He also had thought of the basic framework of calculus. Those are definately the top two. Newton is top 10, but strictly math wise, he is not the greatest.
I might be talking out of my ass here, but I think in a few more years, Stephen Hawking will be up there among the greats.
Newton, Euler and Euclid are the three that immediately spring to mind.
He’s not a mathematician he’s a cosmologist.
I vote for Euler & Gauss. I’m partial to Euler. I don’t know why.
This site has all the biographies (in a nutshell):
http://www-history.mcs.st-andrews.ac.uk/history/Indexes/Full_Alph.html
That was done by Euler:
Euler’s work in mathematics is so vast that an article of this nature cannot but give a very superficial account of it. He was the most prolific writer of mathematics of all time. He made large bounds forward in the study of modern analytic geometry and trigonometry where he was the first to consider sin, cos etc. as functions rather than as chords as Ptolemy had done.
He made decisive and formative contributions to geometry, calculus and number theory. He integrated Leibniz’s differential calculus and Newton’s method of fluxions into mathematical analysis. He introduced beta and gamma functions, and integrating factors for differential equations. He studied continuum mechanics, lunar theory with Clairaut, the three body problem, elasticity, acoustics, the wave theory of light, hydraulics, and music. He laid the foundation of analytical mechanics, especially in his Theory of the Motions of Rigid Bodies (1765).
http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Euler.html
I think everyone is leaving one out.
*He’s reclusive- sequestered in a castle while he works.
*His singular pursuit of mathematical excellence as it describes the world around him is legendary.
*Most importantly, he has probably had more influence (mathematically) over two generations of the world’s youth than anyone in his field.
*He’s purple and he has fangs.
I believe you know by now that I’m talking about none other than THE COUNT.
Archimedes, Newton, and Gauss are definitely the big three. Euler’s up there, but not quite on their level.
I think that in a hundred years Turing, Gödel, Erdos (don’t know the accents), and possibly Chaitin will be counted as the 20th century’s greatest mathematicians.