# top 5 living mathematicians **URL:** \ **Category:** In My Humble Opinion\ **Created:** [March 4, 2013, 1:14am UTC](https://boards.straightdope.com/t/top-5-living-mathematicians/651954 "2013-03-04T01:14:14Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![bup](https://avatars.discourse-cdn.com/v4/letter/b/6bbea6/32.png) [@bup](https://boards.straightdope.com/u/bup)\ **Post date:** [March 5, 2013, 10:43pm UTC](https://boards.straightdope.com/t/top-5-living-mathematicians/651954/21 "2013-03-05T22:43:23Z")
Jordan Ellenberg, Noam Elkies, and Brian Hunt. They all have this in common - they’re American, they’re close to my age, and they were the most brilliant kids on the national level when I was at a high school math tournament or two. 😃 ---
**Author:** ![ftg](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ftg/32/2801_2.png) [@ftg](https://boards.straightdope.com/u/ftg)\ **Post date:** [March 5, 2013, 10:51pm UTC](https://boards.straightdope.com/t/top-5-living-mathematicians/651954/22 "2013-03-05T22:51:17Z")
No mention yet of John Conway? I’m a big fan. Not as high some others have mentioned, but I’m also a fan of Ron Graham (both he and Conway are good popularizers and do top work). ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [March 5, 2013, 11:56pm UTC](https://boards.straightdope.com/t/top-5-living-mathematicians/651954/23 "2013-03-05T23:56:34Z")
> [@ftg](#): > > No mention yet of John Conway? I’m a big fan. I was tempted to mention him. I’m not qualified to evaluate his (or anyone else’s) mathematical significance, but I do keep seeing references to all sorts of things he’s done. ---
**Author:** ![Jamaika\_a\_jamaikaiake](https://avatars.discourse-cdn.com/v4/letter/j/7993a0/32.png) [@Jamaika\_a\_jamaikaiake](https://boards.straightdope.com/u/Jamaika_a_jamaikaiake)\ **Post date:** [March 6, 2013, 5:29am UTC](https://boards.straightdope.com/t/top-5-living-mathematicians/651954/24 "2013-03-06T05:29:42Z")
Saharon Shelah has done seminal work in Logic, and has authored over 1000 papers. > **[Saharon Shelah](https://en.wikipedia.org/wiki/Saharon_Shelah)** > > Saharon Shelah (Hebrew: שהרן שלח; born July 3, 1945) is an Israeli mathematician. He is a professor of mathematics at the Hebrew University of Jerusalem and Rutgers University in New Jersey. > Shelah was born in Jerusalem on July 3, 1945. He is the son of the Israeli poet and political activist Yonatan Ratosh. He received his PhD for his work on stable theories in 1969 from the Hebrew University. > Shelah is married to Yael, and has three children. His brother, magistrate judge Hamman Shelah was ... shelah.logic.at ---
**Author:** ![Elmer\_J.Fudd](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/elmer_j.fudd/32/1211_2.png) [@Elmer\_J.Fudd](https://boards.straightdope.com/u/Elmer_J.Fudd)\ **Post date:** [March 6, 2013, 5:45am UTC](https://boards.straightdope.com/t/top-5-living-mathematicians/651954/25 "2013-03-06T05:45:01Z")
Other than that vampire on Sesame Street? I got nothin’. ---
**Author:** ![DragonAsh](https://avatars.discourse-cdn.com/v4/letter/d/db5fbb/32.png) [@DragonAsh](https://boards.straightdope.com/u/DragonAsh)\ **Post date:** [March 6, 2013, 10:47am UTC](https://boards.straightdope.com/t/top-5-living-mathematicians/651954/26 "2013-03-06T10:47:59Z")
> [@Elmer\_J.Fudd](#): > > Other than that vampire on Sesame Street? I got nothin’. Who sadly passed away recently, so he can’t be considered for the list of ‘top five living mathematicians’ in any event :dubious: > **[Voice of Sesame Street Count von Count dies aged 78](https://www.bbc.co.uk/news/entertainment-arts-19384794)** > > Jerry Nelson, the voice of Sesame Street's Count von Count, dies aged 78, the Sesame Workshop says. ---
**Author:** ![Maserschmidt](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/maserschmidt/32/18829_2.png) [@Maserschmidt](https://boards.straightdope.com/u/Maserschmidt)\ **Post date:** [March 6, 2013, 11:38am UTC](https://boards.straightdope.com/t/top-5-living-mathematicians/651954/27 "2013-03-06T11:38:57Z")
> [@DragonAsh](#): > > Who sadly passed away recently, so he can’t be considered for the list of ‘top five living mathematicians’ in any event :dubious: > > [Voice of Sesame Street Count von Count dies aged 78 - BBC News](http://www.bbc.co.uk/news/entertainment-arts-19384794) But does being undead make him a candidate for honorable mention? ---
**Author:** ![Wendell\_Wagner](https://avatars.discourse-cdn.com/v4/letter/w/8491ac/32.png) [@Wendell\_Wagner](https://boards.straightdope.com/u/Wendell_Wagner)\ **Post date:** [March 6, 2013, 12:58pm UTC](https://boards.straightdope.com/t/top-5-living-mathematicians/651954/28 "2013-03-06T12:58:04Z")
So Shelah is now pushing Paul Erdős for having the most co-authors on papers. He has 220, while Erdős had 511. And Shelah has some time yet to catch up with Erdős, since he’s a mere lad of 67, while Erdős lived to be 83. Soon we’ll be able talk about Shelah numbers in addition to Erdős numbers. ---
**Author:** ![President\_Johnny\_Gentle](https://avatars.discourse-cdn.com/v4/letter/p/5f9b8f/32.png) [@President\_Johnny\_Gentle](https://boards.straightdope.com/u/President_Johnny_Gentle)\ **Post date:** [March 6, 2013, 2:11pm UTC](https://boards.straightdope.com/t/top-5-living-mathematicians/651954/29 "2013-03-06T14:11:08Z")
I have to second Serre (for those who don’t know, his thesis “Homologie singulière des espaces fibrés” was published when he was 25 and completely revolutionized algebraic topology.) > [@Itself](#): > > - Alexander Grothendieck. He went crazy, unfortunately, but he pretty much invented modern algebraic geometry from scratch. All the categorial language and the setting of schemes are due to him. Is it known for sure that Grothendieck is still alive? ---
**Author:** ![Wendell\_Wagner](https://avatars.discourse-cdn.com/v4/letter/w/8491ac/32.png) [@Wendell\_Wagner](https://boards.straightdope.com/u/Wendell_Wagner)\ **Post date:** [March 6, 2013, 6:33pm UTC](https://boards.straightdope.com/t/top-5-living-mathematicians/651954/30 "2013-03-06T18:33:23Z")
All anyone can say is that since there has been no announcement that he has died, then he must still be alive: > **[Alexander Grothendieck](https://en.wikipedia.org/wiki/Alexander_Grothendieck)** > > Alexander Grothendieck (/ˈɡroʊtəndiːk/; German pronunciation: \[ˌalɛˈksandɐ ˈɡʁoːtn̩ˌdiːk\] (listen); French: \[ɡʁɔtɛndik\]; 28 March 1928 – 13 November 2014) was a German-born mathematician who became the leading figure in the creation of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory, and category theory to its foundations, while his so-called "relative" perspective led to revolutionary advan Gro... [http://boxen.math.washington.edu/home/wstein/www/sga/circle/pragacz.pdf](http://boxen.math.washington.edu/home/wstein/www/sga/circle/pragacz.pdf) ---
**Author:** ![hogarth](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hogarth/32/1773_2.png) [@hogarth](https://boards.straightdope.com/u/hogarth)\ **Post date:** [March 6, 2013, 7:19pm UTC](https://boards.straightdope.com/t/top-5-living-mathematicians/651954/31 "2013-03-06T19:19:54Z")
> [@Wesley\_Clark](#): > > At that kind of level of academic ability, can people really even tell the difference? If a mathematician opens up a whole new field of study that is still popular decades later, then it’s pretty clear that he (or she, I guess) did something important. Milnor, Serre and Atiyah are living legends, although I don’t know how prolific they are nowadays. ---
**Author:** ![thanatic](https://avatars.discourse-cdn.com/v4/letter/t/97f17d/32.png) [@thanatic](https://boards.straightdope.com/u/thanatic)\ **Post date:** [March 7, 2013, 2:35am UTC](https://boards.straightdope.com/t/top-5-living-mathematicians/651954/32 "2013-03-07T02:35:10Z")
this Milnor guy must be pretty important can someone tell me more about him ---
**Author:** ![Wendell\_Wagner](https://avatars.discourse-cdn.com/v4/letter/w/8491ac/32.png) [@Wendell\_Wagner](https://boards.straightdope.com/u/Wendell_Wagner)\ **Post date:** [March 7, 2013, 4:02am UTC](https://boards.straightdope.com/t/top-5-living-mathematicians/651954/33 "2013-03-07T04:02:29Z")
Well, here’s the Wikipedia entry: > **[John Milnor](https://en.wikipedia.org/wiki/John_Milnor)** > > John Willard Milnor (born February 20, 1931) is an American mathematician known for his work in differential topology, algebraic K-theory and low-dimensional holomorphic dynamical systems. Milnor is a distinguished professor at Stony Brook University and one of the five mathematicians to have won the Fields Medal, the Wolf Prize, and the Abel Prize (the others being Serre, Thompson, Deligne, and Margulis). > Milnor was born on February 20, 1931, in Orange, New Jersey. His father was J. Willard M... One interesting fact not mentioned there is that if the movie _A Beautiful Mind_ had been more accurate, Milnor would have been a character in it, since he and John Nash were fellow grad students and shared an apartment one summer. ---
**Author:** ![drew870mitchell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/drew870mitchell/32/3946_2.png) [@drew870mitchell](https://boards.straightdope.com/u/drew870mitchell)\ **Post date:** [March 7, 2013, 5:26am UTC](https://boards.straightdope.com/t/top-5-living-mathematicians/651954/34 "2013-03-07T05:26:11Z")
[http://academic.research.microsoft.com/RankList?entitytype=2&topDomainID=15&subDomainID=0&last=0&start=1&end=150](http://academic.research.microsoft.com/RankList?entitytype=2&topDomainID=15&subDomainID=0&last=0&start=1&end=150) ---
**Author:** ![Itself](https://avatars.discourse-cdn.com/v4/letter/i/d07c76/32.png) [@Itself](https://boards.straightdope.com/u/Itself)\ **Post date:** [March 7, 2013, 6:28am UTC](https://boards.straightdope.com/t/top-5-living-mathematicians/651954/35 "2013-03-07T06:28:33Z")
> [@](#): > > this Milnor guy must be pretty important > > can someone tell me more about him He’s a brilliant topologist who’s done a lot of work on knot theory, singularities, K-theory, and surgery theory. The two most readily identifiable (which is not the same as significant or deep) results of his are the explicit construction an exotic S^7 and the construction of the higher K-groups, along with their calculation in certain cases. The former is a manifold that homeomorphic but not diffeomorphic to the 7-sphere S^7; it was the first manifold for which that was known to hold. The latter is harder to describe, but it’s some high-powered machinery that describes things like equivalence classes of vector bundles modulo stabilization; that’s useful and interesting on its own, but it turns out that a bunch of surgery obstructions live in K-theory, and you actually get a full cohomology theory out of it rather than just the ground level K\_0. (Wikipedia has more details and background material on all the stuff I mentioned above.) ---
**Author:** ![thanatic](https://avatars.discourse-cdn.com/v4/letter/t/97f17d/32.png) [@thanatic](https://boards.straightdope.com/u/thanatic)\ **Post date:** [March 7, 2013, 6:29am UTC](https://boards.straightdope.com/t/top-5-living-mathematicians/651954/36 "2013-03-07T06:29:32Z")
> [@Itself](#): > > He’s a brilliant topologist who’s done a lot of work on knot theory, singularities, K-theory, and surgery theory. The two most readily identifiable (which is not the same as significant or deep) results of his are the explicit construction an exotic S^7 and the construction of the higher K-groups, along with their calculation in certain cases. The former is a manifold that homeomorphic but not diffeomorphic to the 7-sphere S^7; it was the first manifold for which that was known to hold. The latter is harder to describe, but it’s some high-powered machinery that describes things like equivalence classes of vector bundles modulo stabilization; that’s useful and interesting on its own, but it turns out that a bunch of surgery obstructions live in K-theory, and you actually get a full cohomology theory out of it rather than just the ground level K\_0. (Wikipedia has more details and background material on all the stuff I mentioned above.) would you consider him the top mathematician in america… ---
**Author:** ![Wendell\_Wagner](https://avatars.discourse-cdn.com/v4/letter/w/8491ac/32.png) [@Wendell\_Wagner](https://boards.straightdope.com/u/Wendell_Wagner)\ **Post date:** [March 7, 2013, 7:06am UTC](https://boards.straightdope.com/t/top-5-living-mathematicians/651954/37 "2013-03-07T07:06:19Z")
That question is unanswerable, just as the question in the OP is unanswerable. Naming the five best living mathematicians in the world is as hard as naming the five best living novelists in the world. I pick that as an example because I believe that there are approximately as many mathematicians in the world as there are novelists in the world. Let me define a mathematician as someone who either (a) has at least a master’s degree in math or (b) has published a paper in a refereed mathematical journal or © works at a job where their title is mathematician or mathematics professor. Let me define a novelist as someone who has published a fictional work of at least 40,000 words in printed form that has sold at least one copy. Then I suspect that there are several hundred thousand mathematicians in the world and several hundred thousand novelists in the world. Now, if you were to ask someone with some thorough knowledge of current mathematics who the best living mathematicians were, their answer wouldn’t be random. They would be unlikely to name any of the 90% of mathematicians whose work is very minor. They would be likely to name some of the twenty or so mathematicians who are usually accepted as being top mathematicians. But it’s quite unlikely that the list of the five best living mathematicians that one knowledgeable person comes up with is the same as the list that another person comes up with. The same is true of novelists. If you were to ask someone with some thorough knowledge of current fiction who the best living novelists were, their answer wouldn’t be random. They would be unlikely to name any of the 90% of novelists whose work is very minor. They would be likely to name some of the twenty or so novelists who are usually accepted as being top novelists. But it’s quite unlikely that the list of the five best living novelists that one knowledgeable person comes up with is the same as the list that another person comes up with. This is partly because it’s impossible for anyone to know the entire field of current mathematics, just as it’s impossible for anyone to know the entire field of current fiction. This is also because there is a certain amount of personal taste in what constitutes top-notch mathematics, just as there is a certain amount of personal taste in what constitutes top-notch literature. In any case, no, it’s not possible to say who the top mathematician in the U.S. is with any certainty. ---
**Author:** ![Itself](https://avatars.discourse-cdn.com/v4/letter/i/d07c76/32.png) [@Itself](https://boards.straightdope.com/u/Itself)\ **Post date:** [March 7, 2013, 4:37pm UTC](https://boards.straightdope.com/t/top-5-living-mathematicians/651954/38 "2013-03-07T16:37:35Z")
> [@](#): > > would you consider him the top mathematician in america… No. He’s 82. As for the top American mathematician of his generation, the question isn’t readily answerable. He’s definitely in the top tier, but sorting that that tier is more a matter of personal taste than any mathematical judgment. ---
**Author:** ![thanatic](https://avatars.discourse-cdn.com/v4/letter/t/97f17d/32.png) [@thanatic](https://boards.straightdope.com/u/thanatic)\ **Post date:** [March 7, 2013, 4:50pm UTC](https://boards.straightdope.com/t/top-5-living-mathematicians/651954/39 "2013-03-07T16:50:17Z")
i also here that this french guy serre, is legendary as well ---
**Author:** ![RTFirefly](https://avatars.discourse-cdn.com/v4/letter/r/c77e96/32.png) [@RTFirefly](https://boards.straightdope.com/u/RTFirefly)\ **Post date:** [March 7, 2013, 6:10pm UTC](https://boards.straightdope.com/t/top-5-living-mathematicians/651954/40 "2013-03-07T18:10:28Z")
> [@Wendell\_Wagner](#): > > That question is unanswerable, just as the question in the OP is unanswerable. Naming the five best living mathematicians in the world is as hard as naming the five best living novelists in the world. It’s actually a good deal harder to pick the five best living mathematicians than the five best living novelists. After all, anyone can read the work of those novelists that has been translated into their language, and once one has done that, one can compare and contrast the work of different novelists. But in order to do the same with different mathematicians working in different fields, one has to have a sufficient understanding of each field to be able to appreciate the quality of each mathematician’s contributions to his/her field. IOW, you’d need a PhD-level grasp, or close to it, of all the major areas of mathematics. [Previous page](https://boards.straightdope.com/t/top-5-living-mathematicians/651954.md?page=1) [Next page](https://boards.straightdope.com/t/top-5-living-mathematicians/651954.md?page=3)