Who is the world's top mathmatician and why ?

[Hal.]

Who is the world's top mathmatician and why ?

[DrRocket]

Who is the world's top mathmatician and why ?

 

There are some very good ones, Anyone who would unequivocably name the number 1 or even the top 10 doesn't understand mathematics very well.

[ajb]

There are some very good ones, Anyone who would unequivocably name the number 1 or even the top 10 doesn't understand mathematics very well.

 

One could rattle off famous people, but I agree it would be difficult to compare peoples' work and thus state who is top.

 

A better question could be who influences you the most?

 

For me I guess the list goes (in no particular order): Kontsevich, Schwarz, Manin, Stasheff, Voronov (Th. and A.), Roytenberg, Khudaverdian, Kosmann-Schwarzbach, (Janusz) Grabowski, Marmo and so on...

 

All the above have made contributions to the intersection of geometry and physics.

[baric]

There are some very good ones, Anyone who would unequivocably name the number 1 or even the top 10 doesn't understand mathematics very well.

 

Yes, what is more interesting is the most imaginary mathematician.

[DrRocket]

Yes, what is more interesting is the most imaginary mathematician.

 

All mathematics is, virtuallly by definition imaginative.

 

I like ajb's modification to the question.

 

One could rattle off famous people, but I agree it would be difficult to compare peoples' work and thus state who is top.

 

A better question could be who influences you the most?

 

For me I guess the list goes (in no particular order): Kontsevich, Schwarz, Manin, Stasheff, Voronov (Th. and A.), Roytenberg, Khudaverdian, Kosmann-Schwarzbach, (Janusz) Grabowski, Marmo and so on...

 

All the above have made contributions to the intersection of geometry and physics.

 

Not being a supermanifolds guy, my list is more conventional, older and more staid (also many of these guys are now deceased)

 

Kakutani, Lou Auslander, Pontryagin, Katznelson, Rudin, Laurent Schwartz, Gelfand, Kirillov, Weiner

 

These guys have made major contributions to harmonic analysis, differential equations, Banach algebras, operator theory and representations of Lie groups.

 

 

Years ago in grad school I was in an AMS meeting listening to Harry Furstenberg talk about some topic in ergodic theory. He had pretty much lost me. But there was an older oriental gentleman sitting beside me who was not only asking good questions, but seemed to be a step or two ahead of Furstenberg. After the session my advisor came by the room, and I indicated the oriental fellow and asked something like "Who is that masked man ?" His reply -- "Oh, that is Kakuntani !". That explained it all.

[ajb]

I like ajb's modification to the question.

 

Cheers.

 

 

 

Gelfand I of course know of due to his work in Banach algebras and in particular the GNS construction and the GN theorem in C*-algebras. One needs to know a little C*-algebra when thinking about noncommutative geometry and constructive field theory.

 

 

Kirillov I know of from the "Poisson-Lie-Konstant-Kirillov-Berezin" bracket (or some variant there of) on the dual of a Lie algebra. I generalised this to [math]L_{\infty}[/math]-algebras. There is also the related Kirillov method of coadjoint orbits; I have no idea if one can generalise this to [math]\infty[/math]-groups. Any way , I digress.

[baric]

All mathematics is, virtuallly by definition imaginative.

 

Yes, but I was suggesting that perhaps we not restrict ourselves to the set of real mathematicians, but perhaps include imaginary mathematicians as well. That would make the study more complex and would at least allow us to root out the negative mathematicians.

[DrRocket]

Cheers.

 

 

 

Gelfand I of course know of due to his work in Banach algebras and in particular the GNS construction and the GN theorem in C*-algebras. One needs to know a little C*-algebra when thinking about noncommutative geometry and constructive field theory.

 

 

Kirillov I know of from the "Poisson-Lie-Konstant-Kirillov-Berezin" bracket (or some variant there of) on the dual of a Lie algebra. I generalised this to [math]L_{\infty}[/math]-algebras. There is also the related Kirillov method of coadjoint orbits; I have no idea if one can generalise this to [math]\infty[/math]-groups. Any way , I digress.

 

You are probably familiar with the theorem that shows that the dual space of the continuous functions vanishing at infinity on a locally compact Hausdorff space is the set of regular (signed) Borel measures on that space. That is the Riesz-Markov-Kakutani theorem. The Daniel integral takes that as a starting point to define an integral and works backward to arrive at the idea of a measure.

 

You might know Lou Auslander's book, with McKenzie, on differentiable manifolds. He was a student of S.S. Chern and did a lot of work on the representations of solvable and in particular nilpotent Lie groups. That is the setting in which Kirillov's orbit method works (There is an exposition in Pukansky's Lecons sur les representations des groupes -- a book by a polish mathematician, in Pennsylvania, written in French !!!).

 

I am sure you have run across Pontryagin. He is the Pontryagin of Pontryagin classes in topology, and also the inventor of the idea of the "dual group" of a locally compact abelian group that is the starting point for the general theory of the Fourier transform.

 

Laurent Schwartz is the Schwartz of Schwartz distributions which are critical in harmonic analysis and partial differential equations. He was one of Grothendieck's thesis advisors.

 

I was a bit surprised that you did not name Alain Connes. He has not influenced me, largely because I know nothing about non-commutative geometry -- which is probably why I don't know the people on your list.

 

Yes, but I was suggesting that perhaps we not restrict ourselves to the set of real mathematicians, but perhaps include imaginary mathematicians as well. That would make the study more complex and would at least allow us to root out the negative mathematicians.

 

Excellent.

[ajb]

I am sure you have run across Pontryagin. He is the Pontryagin of Pontryagin classes in topology, and also the inventor of the idea of the "dual group" of a locally compact abelian group that is the starting point for the general theory of the Fourier transform.

 

Yes, especially to do with topology.

 

Laurent Schwartz is the Schwartz of Schwartz distributions which are critical in harmonic analysis and partial differential equations. He was one of Grothendieck's thesis advisors.

 

Grothendieck is one of the main forces in establishing modern algebraic geometry, so he has been influential to me in a general sense.

 

I was a bit surprised that you did not name Alain Connes. He has not influenced me, largely because I know nothing about non-commutative geometry -- which is probably why I don't know the people on your list.

 

I thought about adding Connes as his C*-algebra approach to NCG is one well established approach. I seem more influenced by the approach of Manin on quantum spaces and the associated quantum groups (Hopf algebras) of Drinfeld and Jimbo. I guess this is because it looks a lot closer to classical and super geometry than Connes spectral triples, which are a NC generalisation of a Riemannian manifold via a Dirac-like operator.

 

Quantum spaces are a weak form of noncommutativity, for example the quantum plane is understood of polynomials in two variables (x,y) subject to the relation xy= q yx. Such "spaces" have the coaction of a quantum group upon them. Also, it is quite easy to add extra gradings into this and have quantum superspaces.

 

In physics the most common approach to NCG is to use the Moyle star product. This you can also generalise to being over a supermanifold (and I assume also a graded manifold?). Gauge theories over noncommutative spaces are usually of this type and this is motivated by the kind of noncommutative geometry suggested by string theory. There is a lot more to be said about this, but really these are things I am only just starting to work on.

 

I should also include Berezin and Leites who are the founders of supergeometry as being very influential on me.

 

Dirac I should also include. Really his confidence in his mathematics to predict a whole family of undetected particles is inspirational.

Edited June 16, 2011 by ajb

[baxtrom]

My list would include Laplace, Lagrange and Lasagne, HA HA HA! _{Hrrrmm. he.}

 

Ok, seriously. What about that guy who proved Fermat's theorem? Wiles? And that russian guy who's apparently sitting in some datcha refusing to accept both money and prestigious positions..

[ajb]

What about that guy who proved Fermat's theorem? Wiles?

 

Andrew Wiles.

 

And that russian guy who's apparently sitting in some datcha refusing to accept both money and prestigious positions..

 

Grigori Perelman?

[khaled]

My list is different, because I'm in Computer Sciences and Logic ...

 

My list contains: Thales, Aristotle, Euclid, Pythagoras, Al-Khawarizmi, Al-Kindi, Euler, Hamiliaton, Sigmund Freud, Einstein, Turing, Godel, Post ...

Edited July 23, 2011 by khaled

[ajb]

My list contains: Thales, Aristotle, Euclid, Pythagoras, Al-Khawarizmi, Al-Kindi, Euler, Hamiliaton, Sigmund Freud, Einstein, Turing, Godel, Post ...

 

Any contemporary mathematicians influence you?

 

Given you say logic, then maybe Alex Wilkie? (I don't really know many logic people.)

[random]

I'd have to say Hugh Hefner anyone surrounded by that many gorgeous women who still has money has got to be good with numbers

[ajb]

I'd have to say Hugh Hefner anyone surrounded by that many gorgeous women who still has money has got to be good with numbers

 

But mathematics is much more than just numbers

[khaled]

well Alex Wilkie worked in Model theory and First-order logic, but I'm more interested in Artificial Intelligence and Algorithms, thus, I'd say Godel

 

.. although Godel said "A formal system can not prove all true statements." based on his Incompleteness theory, I agree with him, but I'm still not good enough in mathematics that I currently have a bachelor degree, I need to learn more to be able to work on a research I started long time ago for a new type of logic, one that does not seem logical !

Edited July 23, 2011 by khaled