Which are the greatest mathematicians of all times?

[Dr Sardonicus]

Originally Posted by jwaltos

<snip>
“When you have eliminated all which is impossible, then whatever remains, however improbable, must be the truth.” ~ Arthur Conan Doyle, The Case-Book of Sherlock Holmes.
<snip>

BZZZZT!

"You will not apply my precept," he said, shaking his head. "How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth? We know that he did not come through the door, the window, or the chimney. We also know that he could not have been concealed in the room, as there is no concealment possible. When, then, did he come?"

-- Sherlock Holmes, to Dr. Watson, in The Sign of the Four by Arthur Conan Doyle (Chapter 6)

I'd say Archimedes is definitely in the running.

There is a property of real numbers named for him (the "Archimedean property"): If x is a positive real number, there is a positive integer n such that n*x > 1.

He made any number of geometric discoveries. He came very close to inventing calculus. He found formulas for the volume and surface area of a sphere.

In physics, he discovered the concept of the center of gravity, the principle of buoyancy ("Eureka!"), and the use of pulleys and of the lever and fulcrum to move massive objects with small forces. ("Give me a place to stand, and I will move the Earth.")

Though he lived long before Arabic numerals were invented, he was able to devise a way to describe very large numbers ("The Sand-reckoner"). He was able to prove that the number is greater than 223/71 and less than 22/7.

[EdH]

. . . When, then, did he come?"

I think it is:

. . . Whence, then, did he come?"

Spell checker trouble?

[Dr Sardonicus]

Originally Posted by EdH

I think it is:

Spell checker trouble?

"When, then, did he come?" is how it was printed. Since The Sign of the Four was first published in 1890, I think we can rule out spell checker trouble.

[rudy235]

Ok . Very good replies. Thank you.

I will answer them going from the trivial to the sublime. Pythagoras goes after Poincaré. Yes, Sir!

Why not Capitalize Isaac? Paraphrasing Freud, "sometimes a typo is just a typo".

Is Hypatia just there just for female representation? I don't really know. But she has a cool name and that should count for something.

Ramanujan and Galois died too young and they could have produced much more. Yes, absolutely. I call them The rookies of the Century.(XX and XIX)

Joseph-Louis Lagrange, Emmy Noether and John von Neumann are notable omissions so far,

Probably. But this is not supposed to be exhaustive list. It is mainly declarative more than enumerative.

Enumerative definitions are only possible for finite sets and only practical for relatively small sets.

Now, to my input on the main question (and with the caveat that I am more partial to Number Theory , than Group Theory, Topology, Set Theory for example).

Tied for First Place. Leonhard Euler and Carl Friedrich Gauss. (alphabetized)
Non-number theory first Place Georg Cantor (mistakenly called Greg in the OP)

I might elaborate more on the "why?' later on.

[Uncwilly]

We have had some visitors to the forum over the years that believe or state that they should be on such a list.

[EdH]

Originally Posted by Dr Sardonicus

"When, then, did he come?" is how it was printed. Since The Sign of the Four was first published in 1890, I think we can rule out spell checker trouble.

Was this in the original book? In the versions I've read, on line freebies of late, whence was used, which makes more sense with the rest of the context. They're wondering how the perpetrator got in, not when he was there.

“How came he, then?” I reiterated. “The door is
locked, the window is inaccessible. Was it through
the chimney?”

“The grate is much too small,” he answered. “I
had already considered that possibility.”

“How then?” I persisted.

“You will not apply my precept,” he said, shak-
ing his head. “How often have I said to you that
when you have eliminated the impossible what-
ever remains, however improbable, must be the truth?
We know that he did not come through the door,
the window, or the chimney. We also know that he
could not have been concealed in the room, as there
is no concealment possible. Whence, then, did he
come?”

“He came through the hole in the roof,” I cried.

Sign of the Four - Arthur Conan Doyle

This is of interest to me. Have you the original? I might have a printed version of some type somewhere, but not at all handy. And, all the online versions I've just checked (Gutenberg, etc.) have whence.

[xilman]

Originally Posted by retina

The time span of ~2600 years makes comparisons difficult.

If a Pythagoras equivalent was born in this era could (s)he make any contribution today?

Also Ramanujan and Galois died far too early IMO. I'm sure there could have been a lot more from them.

Why does isacc not get a capital I?

Ditto Abel, who should also make the cut IMAO

Hendrik Lenstra is in the running, perhaps?

[masser]

I don't believe Godel has been mentioned yet.

[firejuggler]

Terence Tao, for the modern time?
https://en.wikipedia.org/wiki/Terence_Tao

[xilman]

Originally Posted by masser

I don't believe Godel has been mentioned yet.

Well, if you are going to bring in logicians, I would raise you Russel and Whitehead.

Hardy anyone?

[rudy235]

Originally Posted by masser

I don't believe Godel has been mentioned yet.

Right. You beat me to the punch..

Originally Posted by Uncwilly

We have had some visitors to the forum over the years that believe or state that they should be on such a list.

I would like to think I am one of those.. but alas! I'm not worthy!

Girolamo Cardano, Leonardo de Pisa, Bertrand Russell, Hilberth, de La Vallée Poussin, Legendre, Laplace, Pascal, Poissan, Gögel, Tao .... are a few example of names. You could easily double the size of the list. I haven't gone too much into the late XX, early XXi Century, but of course, at least, we could consider four or five.

Definitely the guy or gal that proves the Riemann Hypothesis (or conversely disproves it) will deserve a place. Of course it could be Gögel Undecidable too. Which would mean it is true!


I will just give a few highlights of one of the achievement of the first ONE (ALPHABETICALLY) of my two choices Leonhard Euler [ˈɔʏlɐ]

Prolific 60 to 80 volumes or work. His work has not yet been completely transcribed yet. Up to date there are 78 volumes although the work was started 111 years ago.
Moved around a lot. Basel, Berlin, Saint Petersburg..
Breath of work : Mechanics, Optics, Astronomy, Analysis, Geometry, Calculus, Trigonometry, Algebra, Number Theory, Physics, Set Diagrams,some people believe that he is the inspiration of the game Sudoku.

The Euler Number. e =2.7182818...

EULOGY OF EULER

.
.
.Excerpt of the Eulogy of Euler. (it is very long. Took me three separate readings to finish it!)

...and took a few cups of tea, when all of a sudden the pipe that he was smoking slipped from his hand and he ceased to calculate and live.