Greatest Mathematician of all time?

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xo503
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Greatest Mathematician of all time?

Postby xo503 » Thu Apr 30, 2015 7:02 am UTC

in your personal opinion, who would you consider the greatest mathematician of all time? and why

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Re: Greatest Mathematician of all time?

Postby Qaanol » Thu Apr 30, 2015 10:46 pm UTC

Hasn’t been born yet.
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Re: Greatest Mathematician of all time?

Postby Flumble » Thu Apr 30, 2015 11:08 pm UTC

Qaanol wrote:Has almost surely not been born yet.


Moreover, f you assume finite time, the chance that the greatest mathematician has been born is even nonzero (unless you have additional heuristics).

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Re: Greatest Mathematician of all time?

Postby Qaanol » Fri May 01, 2015 1:00 am UTC

Hey, I answered the question that was asked!

Pedantry aside, the greatest mathematician alive (by ability-thusfar-demonstrated) I’d say is Terry Tao.

The greatest of the past…there’s a lot of options. I’m a fan of Euler personally.
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Re: Greatest Mathematician of all time?

Postby doogly » Fri May 01, 2015 1:47 am UTC

Gauss will never be supplanted. The correct answer is Gauss.
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Re: Greatest Mathematician of all time?

Postby notzeb » Fri May 01, 2015 8:26 am UTC

Fermat: invented analytic geometry, the method of using derivatives to minimize/maximize functions, the principle of least time, proof by infinite descent, the theory of Pell equations, etc., all in his spare time and without any help from anyone else. Little known fact: Fermat is the only mathematician who has successfully fought and killed a dragon.
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Re: Greatest Mathematician of all time?

Postby jestingrabbit » Fri May 01, 2015 6:09 pm UTC

Big fan of Archimedes. Didn't have the tool of algebra, calculated and proved the area and perimeter of the circle and the volume and surface area of the sphere.
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Re: Greatest Mathematician of all time?

Postby cphite » Fri May 01, 2015 9:24 pm UTC

The greatest mathematician of all time was Euler. Dude was into just about every area of math, plus the ones he invented. His work forms the basis for modern math.

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Re: Greatest Mathematician of all time?

Postby doogly » Fri May 01, 2015 9:33 pm UTC

Look, we went over this six years ago.

Pathway wrote:You know, I can definitely see picking Euler over Gauss. You just have to have never heard of Gauss.


eta: I also fixed my link!
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Re: Greatest Mathematician of all time?

Postby exfret » Fri May 01, 2015 10:02 pm UTC

notzeb wrote:Fermat is the only mathematician who has successfully fought and killed a dragon.

I've killed a dragon. Just haven't become a mathematician yet.

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Re: Greatest Mathematician of all time?

Postby Qaanol » Fri May 01, 2015 10:21 pm UTC

doogly wrote:Look, we went over this six years ago.

Pathway wrote:You know, I can definitely see picking Euler over Gauss. You just have to have never heard of Gauss.

I fixed your link. But that previous discussion wasn’t limited to mathematics. If you include physics then sure, Gauss beats Euler. But then he also has to compete against Isaac Newton, Albert Einstein, and Emmy Noether. That is not a league Gauss can realistically expect to dominate.

Restricted to just mathematical considerations, Euler invented the very idea of a “function”, he introduced the exponential and logarithmic functions to calculus, and, well, Wikipedia has an entire page dedicated to the contributions of Leonhard Euler to mathematics.

No such page exists for Gauss, who, it should be noted, had the benefit of drawing on the results that Euler had achieved, what with the whole being-born-70-years-later and all.

It may be interesting to compare these Wikipedia pages though:
List of things named after Carl Friedrich Gauss
List of things named after Leonhard Euler
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Re: Greatest Mathematician of all time?

Postby xo503 » Wed May 06, 2015 6:02 am UTC

so if you were to ask a consensus among mathematicians around the world

the consensus would be Euler it seems? would that be accurate

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Re: Greatest Mathematician of all time?

Postby ConMan » Wed May 06, 2015 6:41 am UTC

I think an honourable mention must be made of Paul Erdos, the stimulant-powered, ever itinerant and eccentric Kevin Bacon of mathematical journals.
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Re: Greatest Mathematician of all time?

Postby Forest Goose » Wed May 06, 2015 7:11 am UTC

Maybe not the best, but Grothendieck should be somewhere in the top five, I'd say.
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Re: Greatest Mathematician of all time?

Postby xo503 » Wed May 06, 2015 7:21 am UTC

Forest Goose wrote:Maybe not the best, but Grothendieck should be somewhere in the top five, I'd say.

Grothendieck was widely considered the greatest mathematician of the 20th century right?...man was a genius

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Re: Greatest Mathematician of all time?

Postby mathmannix » Wed May 06, 2015 12:21 pm UTC

the first one.
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Re: Greatest Mathematician of all time?

Postby Qaanol » Wed May 06, 2015 7:20 pm UTC

xo503 wrote:so if you were to ask a consensus among mathematicians around the world

the consensus would be Euler it seems? would that be accurate

No, the consensus would be that the question is neither meaningful nor well-defined.
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Re: Greatest Mathematician of all time?

Postby xo503 » Wed May 06, 2015 7:48 pm UTC

Qaanol wrote:
xo503 wrote:so if you were to ask a consensus among mathematicians around the world

the consensus would be Euler it seems? would that be accurate

No, the consensus would be that the question is neither meaningful nor well-defined.

I know the question is vague...but still who do you think would come out on top if a vote happened?

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Re: Greatest Mathematician of all time?

Postby Tirian » Wed May 06, 2015 8:33 pm UTC

cphite wrote:The greatest mathematician of all time was Euler. Dude was into just about every area of math, plus the ones he invented. His work forms the basis for modern math.


I don't know exactly what you think modern math is, but I think its basis was formed by Cantor, Frege, Dedikind, Russel, and that gang. And that's "modern math" as in 150 year-old math, good enough to teach to undergraduates in math.

It's just plain a useless question. What if you asked all athletes who was the greatest athlete of all time or all actors who the greatest actor of all time? You wouldn't get an answer, you'd get a discussion, just like you're getting now.

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Re: Greatest Mathematician of all time?

Postby xo503 » Wed May 06, 2015 9:26 pm UTC

Tirian wrote:
cphite wrote:The greatest mathematician of all time was Euler. Dude was into just about every area of math, plus the ones he invented. His work forms the basis for modern math.


I don't know exactly what you think modern math is, but I think its basis was formed by Cantor, Frege, Dedikind, Russel, and that gang. And that's "modern math" as in 150 year-old math, good enough to teach to undergraduates in math.

It's just plain a useless question. What if you asked all athletes who was the greatest athlete of all time or all actors who the greatest actor of all time? You wouldn't get an answer, you'd get a discussion, just like you're getting now.


i think the guys you mentioned did more for logic, more so then pure math

but your right, a discussion is probably more appropriate for this topic then an outright question

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Re: Greatest Mathematician of all time?

Postby doogly » Wed May 06, 2015 10:05 pm UTC

The greatest athlete was Jesse Owens, greatest actor was Marlene Dietrich, and Gauss is still the correct answer to the original question. If you have further questions, just let me know.
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Re: Greatest Mathematician of all time?

Postby lorb » Wed May 06, 2015 10:11 pm UTC

Greatest by work actually achieved/done or by talent/potential?
I nominate Galois as the greatest Mathematician measured by talent.
Would you even know Gauss or Euler had they been shot at the age of 20?
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Re: Greatest Mathematician of all time?

Postby Flumble » Wed May 06, 2015 10:15 pm UTC

jestingrabbit wrote:Big fan of Archimedes. Didn't have the tool of algebra, calculated and proved the area and perimeter of the circle and the volume and surface area of the sphere.

I wonder what that must've been like: being the best mathematician of your time without even having the concept of algebra, positional notation or calculus. Or maybe I'm just blabbering and people at the time could conceive it. Either way, at least they had basic logic.

doogly wrote:The greatest athlete was Jesse Owens, greatest actor was Marlene Dietrich, and Gauss is still the correct answer to the original question. If you have further questions, just let me know.

Isn't it easier to fill in Gauss for every entry? You'll be wrong no matter what you choose.

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Re: Greatest Mathematician of all time?

Postby WibblyWobbly » Wed May 06, 2015 11:31 pm UTC

Flumble wrote:
doogly wrote:The greatest athlete was Jesse Owens, greatest actor was Marlene Dietrich, and Gauss is still the correct answer to the original question. If you have further questions, just let me know.

Isn't it easier to fill in Gauss for every entry? You'll be wrong no matter what you choose.

Seriously. I hope that Jesse Owens bit is your well-attested sarcasm, because Jim Thorpe.

As for mathematicians, I'm going to throw in some love for W. R. Hamilton. You may say "but he's a physicist, mostly." I say a physicist is just a mathematician who knows what he wants to do when he grows up.

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Re: Greatest Mathematician of all time?

Postby doogly » Thu May 07, 2015 12:04 am UTC

Jim Thorpe is correct. Jesse Owens is dope but you are right.

lorb wrote:Would you even know Gauss or Euler had they been shot at the age of 20?

Look it's not asking for much for you to read the wikipedia article, but I will help by pasting the link:
http://en.wikipedia.org/wiki/Carl_Fried ... arly_years
His fame would probably be more limited to number theory and geometry but those are still big deals.
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Re: Greatest Mathematician of all time?

Postby Tirian » Thu May 07, 2015 12:13 am UTC

doogly wrote:The greatest athlete was Jesse Owens, greatest actor was Marlene Dietrich, and Gauss is still the correct answer to the original question. If you have further questions, just let me know.


Turns out the best athlete was Bo Jackson. Inorite? Google it.

But yeah. We say Gauss was standing on Euler's shoulders, but we might as well say that Euler picked all the low-hanging fruit and Gauss would have been able to do most of it in his head had Euler not been there. How amazing would Galois or Abel have been had they lived a full life? What would Ptolemy have accomplished if he had had access to the Internet instead of the Library at Alexandria? (Maybe he would have invented some quirky science about cat photos instead of astrology, so maybe we're better off the way it turned out.)

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Re: Greatest Mathematician of all time?

Postby doogly » Thu May 07, 2015 12:26 am UTC

Ptolemy, I dunno. Archimedes was probably a Roman sword away from the complete integral calculus though.
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Re: Greatest Mathematician of all time?

Postby Cauchy » Thu May 07, 2015 4:41 am UTC

I'm always a fan of Cauchy. (obviously)

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Re: Greatest Mathematician of all time?

Postby xo503 » Wed May 13, 2015 2:40 am UTC

if we were talking in terms of 20th century...who would it be, i think Ramanujan?

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Re: Greatest Mathematician of all time?

Postby jestingrabbit » Wed May 13, 2015 2:47 am UTC

xo503 wrote:if we were talking in terms of 20th century...who would it be, i think Ramanujan?


A lot of people would join you on that bus, but there's other contenders. Alan Turing for instance.
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Re: Greatest Mathematician of all time?

Postby Forest Goose » Wed May 13, 2015 3:51 am UTC

I'm not sure if I'd list him as one of the greatest mathematicians (top 3) of the 20th century, maybe one of the greatest talents. I think a bunch of others (Hilbert, Grothendieck, Serre, Shelah, Atiyah, Deligne, Fefferman, Milnor, Tate, etc.) are easily contenders, and the list can go on quite a bit. I'm not really sure the question can be answered any better than, here's a list of great people (not top 3, but highly superlative/up there - he definitely makes that list). It probably depends a lot of what you consider important too - Grothendieck and Hilbert would make most lists, Shelah is someone I would list, but I'm not sure others would agree, same for so many others (I'd want to list Woodin as somewhere in there because Omega Logic and Large Cardinals, but I doubt others would, even for this century).
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Re: Greatest Mathematician of all time?

Postby Cleverbeans » Wed May 13, 2015 5:18 am UTC

So to ensure that we have a supremum on the set of famous mathematicians it's going to require some ordering so we can define "greater than". It's natural to use lexigraphic ordering, but that still leaves the arbitrary choice of which end is "greater" than the other. Since we know apriori that the answer should probably be from the subset Archimedes, Euler, or Gauss we should choose the first alphabetically to be the greater so that Archimedes becomes the correct answer once we enlarge to set to include others since he retains his dominance. Therefore, we must conclude that Archimedes is the greatest mathematician of all time. QED.
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Re: Greatest Mathematician of all time?

Postby xo503 » Wed May 13, 2015 5:57 am UTC

I notice Archimedes many times...it's really interesting to see an Ancient Mathematician mentioned when this question occurs within the same ranks as guys like Euler and Gauss

but can we even say Archimedes was the greatest mathematician pre-modern/ancient history, when there are guys like Aryabhata, Bharmagupta, al-Khowârizmi, Al-Haytham
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Re: Greatest Mathematician of all time?

Postby Forest Goose » Wed May 13, 2015 5:58 am UTC

One should strive for more intrinsic properties, a name is a parent-dependent condition, but birthdate is invariant under calendromorphisms. Since later dates are greater, Gauss is the proper choice.
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Re: Greatest Mathematician of all time?

Postby Flumble » Wed May 13, 2015 9:46 am UTC

While moment of birth is easily measured, it's only slightly correlated to greatness. Today's newborns have a greater birth moment, but I think you won't consider them greater mathematicians than anyone mentioned in this topic.

greatness(m) ≡ log(|{body of knowledge before birth of m} ∪ {knowledge added by m}|)-log(|{body of knowledge before birth of m}|)
which is isomorphic to greatness'(m)=|{knowledge added by m}|/|{body of knowledge before birth of m}|
Calculating the sizes of the sets is left as an exercise for the reader.

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Re: Greatest Mathematician of all time?

Postby xo503 » Mon Jun 08, 2015 3:34 am UTC

all time- Gauss

20th century- Grothendieck

would this be accurate?

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Re: Greatest Mathematician of all time?

Postby Wildcard » Wed Jun 10, 2015 8:14 am UTC

xo503 wrote:all time- Gauss

20th century- Grothendieck

would this be accurate?
Well, hey, what's your opinion? I mean, you now have a hefty list of contenders as well as access to the internet (obviously), so you should have read up a bunch on Wikipedia by now.

Personally, I would vote for either Euler or Gauss.

There is one mathematician I haven't seen mentioned here, and while I certainly wouldn't call him the "greatest of all time", I personally find quaternions fascinating, especially their (asserted) connection/relation to space-time. Hamilton, I would love to discuss relativity with you and see what you would think of it.
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Re: Greatest Mathematician of all time?

Postby tarascon » Wed Jun 10, 2015 3:06 pm UTC

Wildcard wrote:Personally, I would vote for either Euler or Gauss.


Certainly would agree with those two lads. And which of the two would cross the finish line as the greatest? I would say Gauss though if Zeno's paradox of the Tortoise and Achilles applies I'd say that line might never be crossed.

I'm smitten with the work of Bernhard Riemann and Georg Cantor--why is a topic for later because I have to rush off to work--and of these two my favorite is Cantor because I love the deep imagination inducing science fiction-like realm of Transfinite numbers (and Set Theory in general). That and the fact that during his final institutionalization, Cantor decided to spend the rest of his time writing about Shakespeare. I guess he took Hamlet's line to heart: "I could be bounded in a nutshell and count myself a king of infinite space..."
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Re: Greatest Mathematician of all time?

Postby quintopia » Fri Jun 26, 2015 12:13 am UTC

Having read about a lot of mathematicians in the last few days, I add one vote for Cauchy

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Re: Greatest Mathematician of all time?

Postby f5r5e5d » Fri Jun 26, 2015 8:48 pm UTC

There is one mathematician I haven't seen mentioned here, and while I certainly wouldn't call him the "greatest of all time", I personally find quaternions fascinating, especially their (asserted) connection/relation to space-time. Hamilton, I would love to discuss relativity with you and see what you would think of it.


you could look at Crowe's "A History of Vector Analysis" book, and related article: https://www.math.ucdavis.edu/~temple/MA ... ectors.pdf

I believe the position is that Hamilton did include a lot of "philosophical speculation" in trying to justify Quaternions as a then novel Algebra - how to "explain" the real/scalar component when the 3 component "pure Quaternion" that he called the vector part seemed should be sufficient for "a 3D algebra" - after all the "method of Cartesian Triples" was well established
but I don't think science history scholars see any real meat in Hamilton's associating the real part of Quaternions with "time" other than coincidence, seen in hindsight from today

Grassman buried his vector algebra under apparently even more impenetrable philosophical musings so his system which was much closer to the modern view and predated Hamilton never caught on

Clifford saw how Grassman's work could include Quaternions, explored metrics in a way that more scholars believe could have had his work anticipate Special Relativity if he hadn't died at 34


I am a fan of David Hestenes' modern reboot of Clifford Algebra under the "Geometric Algebra" name used by both Grassman and Clifford

I'm pretty convinced GA is the better way to do what Quaternions do, understand them and today's Cartesian Vectors, Gibbs/Heaviside Vector Algebra playing together in one algebraic system for applied math in physics, vision, robotics

the Wikipedia page is getting fairly good https://en.wikipedia.org/wiki/Geometric_algebra

and of course you can search for GA and Quaterions with results like: http://www.geometricalgebra.net/quaternions.html


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