Who are the Top Mathematicians of All Time?

[Stephanus]

Was the calculation correct? Just curious, of course I trust all waiters.

I just laughed when he counted. I don't know. We were 7 then, when he produced some number below $30 rate, I just paid. But I think he was. Because he was featured on TV once. Btw, he couldn't subtract. If you made a mistake listing your finished order, such as "On no, it wasn't fried chicken, it's fried duck" He could get into trouble subtracting fried chicken price and replace it with fried duck price. . But he was a phenomenon at that area

 

[Let'sthink]

Yes. I was going to do so, but I did not know exactly how to describe Newton. I also have the same problem with Leibniz. Possibly both should be called polyhistors (jack of all trades)?

today you may say Rieman is better than Newton, But without Newton/Leibniz discovery/invention of Calculus, there could not be any differential Geometry at all. Similarly QM and QED have taken birth from Classical Mechanics which founded in principle by Newton\, Lagrange and Hamilton.

 

[QuantumCurt]

I think it's 100 meter, not 1000 meter. .

I paused for a second when I wrote that post to think about which it was. Good thing I'm not an athlete. I'd hit the 100 meter mark and just keep running (yeah right).

 

[mathwonk]

the following article desribes some of Euler's many accomplishments:

http://www-history.mcs.st-and.ac.uk/Biographies/Euler.htmlI rather like his computation of the values of the zeta function at even integers e.g. Sum 1/n^2 = π^2/6, and the solution of Fermat's last theorem for n=3, not to mention the Euler equation in the calculus of variations, as discussed in Courant's Calculus vol. 2. His clever method of tweaking the series for arctan to estimate π to a large number of digits is also explained in Courant, vol.1. Gauss also thought highly of him and described some of his own work as achieving "almost all of the results of the illustrious Euler", but in a simpler way. Euler in the theory of surfaces, e.g. proved that the normal curve sections of a surface through a given point, achieve maximal and minimal curvatures in mutually perpendicular directions. His explanation of the Cardano formula for aolving cubics in his algebra book is so clear that it enabled me to understand that formula simply for the first time, even after a whole career spent teaching and writing about it in graduate courses. After reading Euler I was able to teach it to (very bright) 10 year olds.

Here is a nice excerpt from that biography involving another very clever and interesting formula:

"In 1737 he proved the connection of the zeta function with the series of prime numbers giving the famous relation

ζ(s) = ∑ (1/n^s) = ∏ (1 - p^-s)^-1

Here the sum is over all natural numbers n while the product is over all prime numbers."Perhaps most impressive of all is the euler formula v-e+f=2, for facets of a convex polyhedron. In spite of all the attention these polyhedra received for 2,000(?) years, it is astonishing then to observe something this simple and basic. To me this alone would justify Euler's fame. This is impressive to me because it has so many generalizations. After the discovery of cohomology and the fact that v-e+f equals the alternating sum of the ranks of the cohomology groups of the surface, this type of "euler characteristic" is one of the most universal of all invariants. The Hirzebruch Rieman Roch formula is a computation of the "euler characteristic" of a line bundle on a smooth projective variety. The fact that such alternating sums are topological invariants, when none of the individual terms are, seems to me perhaps the most fundamental discovery in mathematics.

 

[atyy]

Perhaps most impressive of all is the euler formula v-e+f=2, for facets of a convex polyhedron. In spite of all the attention these polyhedra received for 2,000(?) years, it is astonishing then to observe something this simple and basic. To me this alone would justify Euler's fame. This is impressive to me because it has so many generalizations. After the discovery of cohomology and the fact that v-e+f equals the alternating sum of the ranks of the cohomology groups of the surface, this type of "euler characteristic" is one of the most universal of all invariants. The Hirzebruch Rieman Roch formula is a computation of the "euler characteristic" of a line bundle on a smooth projective variety. The fact that such alternating sums are topological invariants, when none of the individual terms are, seems to me perhaps the most fundamental discovery in mathematics.

I read a nice popsci book about this: Euler's Gem by David Richeson. https://www.amazon.com/dp/0691154570/?tag=pfamazon01-20

 

[tommyxu3]

Why is Euler considered so great? Is it because of exp(ix) = cos(x) + isin(x)?

Euler had lots of dedication on a variety of mathematic fields. The beautiful of the mergence of the sin and cos functions is just a little bit of his great works.

 

[cpsinkule]

no one is going to mention sophus lie?...alright then...sophus lie.

 

[Svein]

no one is going to mention sophus lie?...alright then...sophus lie.

As long as you are thinking of Norwegian mathematicians - Niels Henrik Abel.

 

[gleem]

Niels Abel is considered one of the greatest mathematical geniuses of all time, although living only 27 years . C Hermite said "Abel has left mathematicians enough to keep them busy for five hundred years" Abel only worked for seven years but accomplished an astonishing amount which was recognized in his time. Asked how he did it, Abel responded. "By studying the masters, not their pupils.".

 

[Tech1]

Lists like these are difficult. But in terms of historic influence, we'd have to put people like Descartes, Archimedes, Newton, Euler, Galois, Riemann, Gauss and Poincare very high. In recent times Grothendieck really stands out in my opinion. I may be biased, but he must be the greatest mathematical genius of the 20th century. I would hesitate at putting Einstein high on a list of influential mathematicians. While surely a good mathematician, he did not revolutionize mathematics like the others.