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.
I’m interested to know at what sort of level people here would place Srinivasa Ramanujan? Do you think he would make the top hundred mathematicians of all time?
Well, perhaps the other people ultrafilter quoted were active in a broader variety of areas, whereas so far as I know Euclid’s work (at least his surviving work) is mainly just geometry (plus a bit of astronomy, optics, and number theory.) Also, I’m not sure if we know just how much of Euclid’s Elements was his own original work and how much was a compilation of previous results.
Archimedes and Newton aren’t noted so much for their breadth as the fact that they more or less invented what we consider fundamental nowadays. Gauss and Euler were probably the two most prolific mathematicians of all time; Euler with his published works and Gauss with his notebooks.
And yes, I’m aware of the Newton vs. Liebnitz issue. Common opinion has come down on the side of Newton.
AFAIK, Ramanujan is considered more of a curiosity than an important mathematician. I don’t know of any of his work that would be considered influential. But I could be wrong.
Right on, although many people might put Euler a notch below the others. Regardless, all these gentlemen made profound advances in all of the many areas of math they touched (especially Gauss ) That is not the case with folks like Ramanujan or Lobachevsky.
I don’t know from math, but I find Pythagoras and Descartes to be the most useful on a day-to-day basis, followed closely by Hipparchus and Newton/Leibnitz.
Although just because a certain person’s name is attached to something doesn’t necessarily mean that person deserves all the credit. Not much is known for sure about Pythagoras, including exactly what he had to do with the Theorem that bears his name. And the Cartesian coordinate system commonly used today doesn’t look like what Descartes originally dreamed up (IIRC he didn’t assume that the axes would be parallel and didn’t use negative coordinates).
I don’t see Newton as being one of the top five mathematicians of all time; top 10, maybe. But I don’t see in Newton the breadth of mathematical accomplishment to rank him in the same company as Gauss and Euler. After those two, the next name on my short list would be Augustin-Louis Cauchy.
In Clifford Pickover’s book Wonders of Numbers, he lists “A Ranking of the 10 Most Influential Mathematicians Who Ever Lived” (based, if I understand correctly, on surveys and interviews with mathematicians). His list:
Newton
Gauss
Euclid
Euler
Hilbert
Poincare
Riemann
Galois
Descartes
Pascal
(runners-up Cardano, Godel, Cantor, and Napier).
It’s debatable to what extent “greatest” = “most influential” (which may be why Archimedes, for example, didn’t make the list while Euclid did).
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. Modern analysis is certainly based upon the notations and approach of Liebniz. Whomever may have “invented” calculus first, Liebniz did it better. (or at least more usefully).
My contrarian vote goes to Cantor. But in my heart I know the answer is Gauss.
) That is not the case with folks like Ramanujan or Lobachevsky.