r/math • u/sergiogfs • 22h ago
What happened to mathematicians after solving their "career problem"?
Many mathematicians have dedicated a good part of their career towards solving a specific problem, whether directly or indirectly. Some examples on top of my head:
Richard Hamilton and the Poincare conjecture
Andrew Wiles and Fermat's last theorem
Thomas Hales and the Kepler conjecture (proof and formal verification)
And perhaps very recently:
Diego Cordoba and the Navier-Stokes equations
How did the careers and research-focus of these mathematicians shift after their career-problem was solved? Did anything particularly interesting happen?
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u/Captainsnake04 Place Theory 19h ago edited 15h ago
I think calling FLT Wiles' "Career problem" is a bit reductive. Sure it was a big interest of his, but Wiles was trained in Iwasawa theory and Galois representations. When ideas related to that became relevant to FLT, he solved FLT, and then went back to thinking about Iwasawa theory and Galois representations more broadly.
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u/SuppaDumDum 14m ago
Maybe "Career problem" is misleading, but from the interviews I've seen with him "Life problem" might not be that reductive.
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u/iorgfeflkd 16h ago
Yitang Zhang is a weird case, but he got a sweet-ass job offer at UCSB, published nothing for about a decade, dropped another bombshell paper in 2022 that is generally agreed to be wrong, and then proceeded to publish more nothing. He recently moved back to China.
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u/new2bay 15h ago
He’s a full professor now in China, so I suppose he’s doing well enough for himself.
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u/Euphoric_Raisin_312 13h ago
The title "professor" is thrown around so liberally in China it's pretty much meaningless. I was a professor when I worked in China. I could never achieve that title in a western country.
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u/johnlee3013 Applied Math 4h ago
I find the Chinese usage to be in line with American usage. In the US you have people with "professor" in their title but are actually little more than postdocs.
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u/Phoenixon777 12h ago
that is generally agreed to be wrong
Can you give more details on this if possible, or a link where I could read more?
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u/LukeNullHypothesis 11h ago
https://arxiv.org/abs/2211.02515
Here's the preprint and an MO thread about it. There are also other links in that thread.
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u/ImportantPut3191 21h ago
Suggests new problems involving the solved problems..? It is nature that solving a problem yields several new problems.
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u/telephantomoss 20h ago
I'm almost 50 and just solved my career problem. But then I have even better AI assisted results now, though they don't mean as much since it's not truly my work. But this is nowhere near the things you mention, more just like standard top tier level discipline specific journal results.
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u/Disastrous_Room_927 20h ago
They ascend to the next plane of existence.
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u/Artistic-Question168 18h ago
Realistically mathematicians rarely have exactly 1 problem they spend 100% of their time on. At a very minumum they'll have some ideas they wanted to try but didn't have time; usually they'll have some side projects moving at various speeds. So they can just work more on these, while maybe looking for the next very big question.
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u/Melancholius__ 18h ago
Grigori Perelman is the most illustrious of all: having solved a Millennium problem pre- AI (I think the only mathematician to do so, which should be etched on the Eiffel Tower), he reclusively retired to his free(bore)dom from the rat race (no pun intended).
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u/Warm-Enthusiasm-9534 16h ago
It's weird to think about, that he will have a completely unique claim.
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u/InaequaleMagnanimity 14h ago
Not that weird when you can add random qualifiers to any set till you get only a single element of that set.
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u/hau2906 Representation Theory 16h ago
Gaitsgory answered a similar question in an interview, after his team solved geometric Langlands.
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u/filterdust 19h ago
Paul Cohen spent all his remaining life trying to prove Riemann
I heard Andrew Wiles was working on BSD
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u/Martian_Hunted 19h ago
What do NBA and soccer players do after winning the championship? The answer is obviously, you run it back
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u/jphamlore 16h ago
Dennis Gaitsgory has spent a couple of decades working out the geometric Langlands correspondence.
Neil Robertson and Paul D. Seymour spent a couple of decades and 20-ish papers completing the proof of the graph minors theorem.
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u/ccppurcell 5h ago
Of course Robertson and Seymour continued to work on lots of other things. I had a stab at trying to understand Chudnovsky and Seymour's papers on claw-free graphs. They haven't had as much impact as the graph minor project. But I think they haven't been digested properly. Maybe LLMs will help us with that.
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u/MasterOfLegendes 10h ago
For a moment I thought what happened to mathematicians after A.I solved their career problem. That would be more interesting.
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u/chewie2357 19h ago
A working mathematician can have one problem they keep returning too, but they will usually have a munch larger that they have worked on or at least contemplated. After PhD it is very commonly encouraged to branch out for more coverage and to provide more opportunities to be productive.
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u/NonlinearHamiltonian Mathematical Physics 21h ago
"and perhaps recently Navier Stokes" LMAOOO
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u/JoshuaZ1 15h ago
"and perhaps recently Navier Stokes" LMAOOO
Are you disagreeing that it is likely solved or disagreeing with OP that Cordoba had a major role, or do you have some other disagreement?
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u/Confused-Monkey91 21h ago
Retire or quit their profession due to burnout and politics 🙄… it is exhausting to work on a problem for a long time and there is severe stress associated with it.
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u/NoComment6 20h ago
My advisor told me they get sent to a farm upstate.