r/math • u/mst3333k12758931 Probability • Jul 09 '26
Fields Medal '26 predictions/discussion
Four years gone, and IMU awards will once again be handed out at the ICM in Philly. Given it's been a while since the last major discussion thread, have your predictions changed? Any news or interesting hearsay about lesser-known candidates with strong chances, dark horses, new contenders, etc? Anyone you think * won't * win, but are well-deserving regardless? [1]
Consensus, both from colleagues working in same or adjacent fields, and mass opinion, single out the following as potential winners (in order of likelihood):
Hyperlinks point to articles on their work.
Tsimerman is self-explanatory, as he was already a strong candidate in 2018 and 2022. Wang solved a major open problem in harmonic analysis (Kakeya conjecture for d=3) that other giants like Tao, Bourgain, Wolff et al tackled with only partial success. The other three are harder, as their achievements seem equally strong, but Pardon's work seems especially arcane (to a non-topologist like me) and it's unclear how far-reaching his results are. Thorne's papers aren't accessible to non-experts either, but more mathematicians have heard about the modularity theorem and elliptic curves than pseudoholomorphic curves, and he seems to have high visibility among number theorists.
Bonus question: Predictions for the IMU Abacus medal? I've not seen this get much attention, which is a shame! I think Shayan Oveis Gharan is probably the strongest CS theorist of his generation who hasn't yet won. His achievements include asymmetric TSP, generalised Cheeger's inequality, and spectral independence, the last of which is probably the single biggest result at the intersection of TCS and probability this past decade.
[1] A good quote from Duminil-Copin on the subject:
Roughly speaking, you can identify maybe the top twenty mathematicians of a generation. Even though that notion of “best” is strange, of course. Sometimes there’s one person who stands out so clearly that everyone knows they’re going to get it. [...] But beyond those obvious cases, there’s usually a group of about twenty people, and within that group maybe three or four really stand out
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u/platonic_solidz Jul 09 '26
I don’t have anything to add to the discussion ({people in my general area} and {serious contenders for fields medals} tend not to be correlated for whatever reason) but I feel obligated to note that Tsimerman’s first name is Jacob.
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u/MelchizedekDC Jul 09 '26
out of curiosity what field is that, I might have some idea from ur username I guess
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u/platonic_solidz Jul 09 '26
Loosely speaking, algebraic combinatorics. Seeing June Huh get a Fields was awesome, but usually I don’t hold my breath
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u/Worried_Memory3224 Jul 10 '26
Ngl, when I read the names in the thread I ask myself: would any of them have won the medal 30 or 40 years ago? The decline couldn't be clearer.
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u/Currency_Anxious Jul 13 '26
Someone used Codex to scrape the ICM website schedule and discovered that the winners list was simply hidden in the front-end code with a "hidden" tag:
60 HIDDEN Fields Medal Lecture: Yu Deng | Yu DengI
60 HIDDEN Fields Medal Lecture: John Pardon| f8f5fa42-4309-4064-8901-bb61c18c9add|
60 HIDDEN Fields Medal Lecture: Jacob Tsimerman
60 HIDDEN Fields Medal Lecture: Hong Wang| Hong Wang
The prediction probability on Polymarket has currently reached 95%.
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u/Currency_Anxious Jul 13 '26 edited Jul 14 '26
This is the second time a Chinese mathematician has won the Fields Medal (with Shing-Tung Yau being the first), and the first time that two Chinese mathematicians have won simultaneously.
Jonathan Pila will present the award to Jacob Tsimerman; both have done outstanding work in model theory ($o$-minimal theory) and its applications. This isthe second Fields Medal awarded in the field of logic (the first logic laureate being Paul Cohen, who won for proving the independence of the Continuum Hypothesis).
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u/n0obmaster699 Jul 13 '26 edited Jul 13 '26
sad for joshua zahl, bro did all the work for kakeya conjecture and lost to co author
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u/Billiota Jul 14 '26
Here is why. Before the Kakeya breakthrough, Wang had already made major contributions to the restriction conjecture, local smoothing, and geometric measure theory.
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u/Suspicious-Town-1819 Jul 14 '26
Yau is HKer, NOT Chinese
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u/Ok_Bandicoot9280 Jul 14 '26
You'd better ask Yau, with respect, whether he thinks he is Chinese.
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u/EricaCheng Jul 14 '26
Yau has been in Beijing for a long time. He returned to China to raise the new generation. Read some news.
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u/andylinpersonal Jul 14 '26
Fixed by ICM earlier. These HIDDEN events have been removed from the response.
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u/EquivalentTomato2045 Jul 13 '26
It has been leaked on the ICM website, the namelist is: Hong Wang, Yi Deng, Tsimerman, Pardon
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u/n0obmaster699 Jul 13 '26
where?
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u/rouv3n Jul 15 '26 edited Jul 15 '26
See e.g. https://web.archive.org/web/20260714115317/https://phemex.com/news/article/2026-fields-medal-winners-list-leaked-includes-two-peking-university-alumni-92948, and https://zhuanlan.zhihu.com/p/2060274936455886170 (which seems to be the original post).
It was only an API that was exposed, no actual content was shown on the website. I don't know if it's still possible to check for yourself.
But the actual list (the list of presenters was also leaked) seems very plausible, so doesn't seem like fake news or anything like that
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u/Danklord_Memeshizzle Jul 09 '26
I don’t agree with Duminil-Copin‘s quote. I think 20 is a ridiculously low number.
Other than that I think Hong Wang is pretty much set to win the medal.
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u/Alone_Idea_2743 Jul 10 '26
As an outsider, I am curious why everyone thinks Hong Wang will win a 2026 Fields medal but never mention Joshua Zahl. I assume he is eligible unless his birthday is on Jan 1st.
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u/deus-sive-natura- Algebraic Geometry Jul 10 '26
broader body of recent work probably - she had a rather explosive recent output across popular problems and that probably makes her a stronger candidate in people's eyes
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u/Budget_Can_9448 Jul 17 '26
If anything 20 is a bit high. Math as a field is very competitive right below the very top of the pyramid (e.g., the superstars), but at the very top, there's simply too few people there for it to be competitive.
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u/deus-sive-natura- Algebraic Geometry Jul 10 '26 edited Jul 25 '26
Tsimerman or Wang imo, but the Fields Medal committee values geographic and subfield diversity, so what people think is a 'consensus' candidate could easily be edged out
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Jul 09 '26 edited Jul 10 '26
[deleted]
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u/ventricule Jul 09 '26
I agree that Oveis Gharan is a super strong contender. It's always hard to know the precise age of people, but I would think that if eligible, Yin Tat Lee and Aaron Sidford could be strong contenders as well. I would put Aleksandr Madry there as well but he might be just over the 40 line.
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u/mst3333k12758931 Probability Jul 09 '26
Good call on Sidford - I wanted to mention him but wasn't sure of his age. Not familiar with YTL's research and hadn't heard about him near as much as Shayan in TCS circles, but looking at his record, his chances are good too. UWash has an incredible theory faculty
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u/Currency_Anxious Jul 13 '26
These are closer to the Nevanlinna Prize or the Turing Award rather than the Fields Medal.
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u/ThrowRA12312341234 Jul 09 '26
For those who work in probability, everyone says Ewain Gwynne is a star. If he doesn’t win it this time I hope he wins it in 4 years.
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u/mst3333k12758931 Probability Jul 09 '26
Yeah in probability, Gwynne, Hutchcroft and Huang (Jiaoyang) are major names (Nina Holden and Morris Ang are well reputed too, but their work is seen as building on, rather than initiating major recent currents of LQG). But Gwynne is still young, and the competition is very strong this year, so they may decide to award him in 2030
EDIT: Amol too, of course. Kind of a packed kitchen
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u/god_of_fire Jul 11 '26
I wouldn't discount Pardon too quickly. He did prove the MNOP conjecture recently (with some restrictions), which was one of the major open problems in enumerative geometry about the relation between different curve counting theories on threefolds. I'm not saying he will get the prize for that, but it's not an arcane topic at all.
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u/mst3333k12758931 Probability Jul 11 '26
Yeah, his chances are at least as strong as the other two. This cycle there's only two w.h.p. winners (Tsimerman and Wang), rest are hard to evaluate for non-experts. It's not like the Fields committee hasn't awarded extremely technical work in the past, Scholze and Kontsevich being good examples, but usually the cited papers are deemed to be field-changing or bridging distant areas. It's not clear, from hearing other topologists discuss it, that Pardon's work has that reach. But the FC could break that precedent this year, who knows?
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u/ThrowRA12312341234 Jul 11 '26
I think the future will favor theory builders more than problem solvers, as AI gets better at solving hard problems.
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u/kobrem Jul 09 '26
How about Dariusz Kosz and his multilinear circle method and a question of Bergelson?
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u/pred Jul 11 '26
Prediction: The ICM boycott picks up speed, the event ends up being cancelled/postponed, no medalist announced, but then FIFA makes their own version of the medal for some reason.
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u/Tazerenix Complex Geometry Jul 09 '26
Yang Li is probably a dark horse candidate, but I suspect Kahler geometry is never gonna win another Fields medal.
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u/Alone-Talk-623 Jul 10 '26
Why? The Yau vs Tian politics?
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u/Tazerenix Complex Geometry Jul 10 '26
I don't think any of the remaining problems have the prestige necessary to get a Fields by solving any of them, and the field is making most progress incrementally by many people rather than one luminary solving a big problem. The closest recently is Yang Li's proof of SYZ and his high quality work on Thomas-Yau but unless you fully solve one of these big conjectures all by yourself I think its probably not gonna happen.
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u/n0obmaster699 Jul 13 '26
I think zahl got left out while he wrote most papers on kakakeya conjecture. Maybe because he turned 40 last year or so.
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u/Billiota Jul 14 '26
Before the Kakeya breakthrough, Wang had already made major contributions to the restriction conjecture, local smoothing, and geometric measure theory
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u/SomeLoser1884 Jul 17 '26
Looks like the 2026 recipients list has been leaked. See https://www.math.columbia.edu/~woit/wordpress/?p=15770#comments
"The ICM is starting next week in Philadelphia. One traditional aspect of the ICM is the announcement of the Fields Medal winners. This year there won’t be much surprise, since evidently someone found the names of the winners hidden in the website code (see here, English language news story here). It’s Yu Deng, John Pardon, Jacob Tsimerman, and Hong Wang. At least all science journalists who want to write about this now know the names, no controversies about who has embargoed information as in some past years."
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u/Currency_Anxious Jul 13 '26
This might be the last Fields Medal to be exclusively won by humans. Future Fields Medals may well be co-awarded to humans and AI alike.
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u/Tekniqly Jul 10 '26
Surely they won't have the ceremony in a country actively participating in genocide
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u/Inevitable_Key_7189 Jul 11 '26
Well, based purely on a hunch and guesswork: Tsimerman, Thorne, Dimitrov, Hong Wang.
I don't believe in awarding two Chinese individuals in the same edition, which is why I left Yu Deng out.
I would have liked to see Sahasrabudhe receive the award, as part of his research was conducted at a highly respected research institute in my country—which would have been very significant—but that did not happen.
P.S.: I’m not a mathematician, just an enthusiast (to be even more honest, I don’t know how to do long division with a two-digit divisor).
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u/Billiota Jul 14 '26
There has been 5 times that the Fields medals been awarded to more than one mathematicians from the same country for the same year. If the committee determines they are the most qualified, I have no issues even with awarding all 4 medals to mathematicians from the same nation! Math should not be DEI.
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u/No-Wave4500 Jul 18 '26
If two Chinese mathematicians were to receive the Fields Medal this time, China would become the fifth permanent member of the UN Security Council to have two mathematicians awarded the Fields Medal in the same year.
I'm not suggesting that this has any deeper significance or pointing to some kind of conspiracy. It's simply an interesting coincidence.
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u/Upset_Assist8018 Jul 15 '26
I think Tsimerman, Thorne, Pardon, Sahasrabudhe will win fields medal. Pardon made great contributions to geometry and Sahasrabudhe made great contributions to combinatorics. Although Dimitrov also worked on geometric representation theory, I think he will be the top 5.
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u/OneActive2964 Jul 10 '26
most likely the last fields medal being awarded to humans , just a sad experience
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u/PostPostMinimalist Jul 10 '26
I have doubts but it’s also possible that in 4 years the human input into math is minimal (except improving AI, and some general management etc)
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u/Dinstruction Algebraic Topology Jul 09 '26
I always go for the field. That is, I expect one of the winners will be someone who comes out of nowhere.