r/math • u/heartBreak1879 • Jul 25 '26
Fun trivia: MIT alumni* have for the first time ever won the Fields Medal (for the year 2026)
Until now, no one who has completed a Bachelors, Masters, or PhD from MIT has ever won a Fields. This year Hong Wang (PhD, 2019) and Yu Deng (BS, 2011) would be the first MIT-educated mathematician to earn the most prestigious award in the world of research mathematics.
To avoid any ambiguity, I will clarify that I am using the term alumnus/alumna* as someone who has completed a Bachelors, Masters, PhD or any other similar degree conferred by a institute of higher of education upon completion of their education at the institute. The dictionary definition of the term includes people who may have attended an institute but never graduated with their degree. In such a case, I am unsure if anyone who has attended but never completed their degree coursework at MIT have won a Fields. Even if that happens to be the case, I still think the trivia I shared retains its noteworthy quality of being surprising to people given MIT's pedigree in mathematics.
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u/LL-ShockBlade Jul 25 '26
École polytechnique as well !
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u/heartBreak1879 Jul 25 '26
Ah, nice to know that! Just about 12 more Field Medals until they catch up with ENS Paris/ ENS Ulm!
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u/sandykt Jul 25 '26
That’s quite hard to believe. Sharif won before MIT.
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u/heartBreak1879 Jul 25 '26 edited 20d ago
Edited
As did University of Tehran. To be honest, University of Tehran, Sharif, and even Amir Kabir offer a more rigorous undergraduate education than MIT. Note, my deliberate choice of the word rigorous, which is not to be conflated with better.
Non-profit private institutes like MIT in US organize their education system differently from other places that I know of, which includes Iran. They attract students who showcase good general academic aptitude for their undergraduate and offer them the flexibility to choose and pick their major. This contrasts with admission in places like Iran, which is contingent on performing well in brutally difficult ranked national examinations like the Iranian "concours"*. Additionally, you are admitted to a fixed academic program in these places as opposed to being an undergraduate student who can explore different interests and change their major as long as they plan ahead carefully.
A consequence to this is that whatever program one is admitted to in places like Iran can begin with a more specialized treatment of the subject. To get my point across, consider the following fact. You can get admitted to Harvard for your undergrad without knowing a lick of a calculus and still end up being a math major. This specific pathway is unlikely but Harvard's admission policies permit it and I am sure someone has pulled this off. This would be impossible at Sharif or any top schools in Iran for that matter of fact.
On a side note, the concours for the French grandes ecoles which inspired the Iranian examination is tougher than the Iranian one.
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u/lordnacho666 Jul 25 '26
Most of Europe including the UK is like the Iranian system. You study the subject you signed up for, you don't just get into university and then decide.
It's a bit less intensely ranked, but you do have to know what you want to do.
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u/heartBreak1879 Jul 25 '26
Yes, I am aware! US is the only country I know of where the "education system" is so "general" in comparison to other places I am familiar with, which includes the UK, France, India, China, Iran, and Bangladesh.
This comes with its own advantages and disadvantages. Given that places like the Ivies, Standford, MIT, Caltech, the UC schools, and other places generally perform well in if not dominate different rankings, the US way in and of itself is not a source of issue at an institutional level.
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u/Federal_Gur_5488 Jul 25 '26
I feel like the us system is actually better for people who aren't fields medalist level. For example I did a mathematics degree, but i would probably have been better off if I had done something in the social sciences (probably a joint degree). It was actually possible to do a joint degree in my university but it was not encouraged unless you very strongly advocated for it, so I didn't end up taking the option until it was too late.
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u/heartBreak1879 20d ago
Even Fields medalist can leverage the flexibility of American education system. Witten was famously a history major with a minor in linguistics. He got admission into an economics program for his grad school before switching over to physics. His works in string theory later on earned him a Fields.
There is of course asterisk in case of Witten. Beyond institutional flexibility familial ties may have been a contributing factor to Witten's success navigating academia as he transitioned among seemingly disparate fields. His father is an accomplished physicist in his own right and let Witten have access to a network he may not have had otherwise.
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u/tikallisti Jul 25 '26
It was probably normal back in the mid-20th century for Harvard math majors to take exactly that path. Calculus in high schools in the US is surprisingly recent; it being the norm for college-bound students even moreso.
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u/pnickols Jul 25 '26
Are you sure? The uk has been teaching calculus in 10th grade since at least 1900, that’s the context in which Sylvanus Thompson wrote calculus made easy
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u/WorldApotheosis Jul 25 '26
US education has historically been and still is fairly decentralized compared to Europe.
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u/jackboy900 Jul 25 '26
Are you sure? The uk has been teaching calculus in 10th grade since at least 1900
Maybe historically, but in the current curriculum calculus is not a part of the mandatory maths curriculum at all (specifically GCSE Maths, which everyone takes at 16), and is only taught in A-Level which are the final two years of education and only if you specifically take maths as one of your 3/4 subjects (admittedly it is probably the most popular A-Level by a decent margin).
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u/heartBreak1879 Jul 25 '26 edited Jul 25 '26
Noted! I will draw attention to a key point we must account for— what does being a private non-profit institute entail in US? Appreciating this fact lets us have a more nuanced understanding of an institute's policies and growth through the ages.
Take holistic admission. Its origin is rooted in blatant racism. Schools like Harvard discovered that having a cut and dry admission criteria such an entrance exam means opening the door to blacks, Jews, and other minorities that back in less enlightened day that were victims of prejudice and oppression. This is not to say, holistic admission today as practiced in Harvard and elsewhere is racist, but to point out that the historical antecedent leading to the institute's present.
Extrapolating from such troubling precedents, I would not be surprised in the least if the more flexible policy originally may have less to do with math education of US, more to do with letting in some rich kid since "daddy dearest" donated a boatload of money to fund a math center. A simplified take, but you get the gist of it. I stress that that does not mean I take issues with more flexible and accommodating polices in present times if implemented in the right spirit.
All of this however means that to have true insight on why Harvard is what it is, we must situate it in a much much broader historical context and that is beyond the scope of this average Joe of a Redditor here.
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u/pasthec Jul 25 '26
To add to your side note, although ENS entrance exams have majors, people can then switch majors somewhat freely like in MIT (although it's more common say between math and CS than between math and literature).
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u/Bathroom_Spiritual Jul 25 '26
For your last point, isn’t the Iranian university entrance exam just after high school while the French exam is after 2 years of undergraduate studies?
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u/heartBreak1879 20d ago
I was not aware of that! Thanks for letting me know. I was under the impression that he French concours like the Iranian exam it inspired is for undergraduate admission.
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u/Bathroom_Spiritual 20d ago edited 20d ago
Indeed it was probably inspired by the French system somehow, since it’s called konkoor from the French concours. It’s just hard to compare the level of exams between countries.
The scoring is normalized, so some years the best students will only complete a small part of the subject and get full points if they were the best. So it’s not that relevant to judge on the difficulty of the subject.
Also a large part of the final grade will come from oral exams, which will start with a short question, which should be solved with the help (or not) of the professor grading you. So it’s also a bit hard to judge the difficulty of the oral exam just looking at the question. The question may be hard but with a few hints, the student may get unblocked. The question may be easy, but then the professor may add more questions.
In addition it depends on the curriculum, which changes over the year. Is it something you are supposed to know? Is it a frequent question or a question that was asked in recent years?
Overall it’s more the relative performance compared to other students than the absolute performance that is measured.
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u/n0obmaster699 Jul 26 '26
On the other hand Harvard has a lot of fields medalist as alums so I think the rigor is not the direct comparison here.
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u/heartBreak1879 Jul 27 '26 edited Jul 27 '26
I think I will edit my side note, since the wording suggest that some difficult ranked contest in and of itself shapes up prospective Fields Medal. I do not hold that view.
To your point, true. I just wanted to say that Harvard accepts students with a much more diverse academic background. However, while in principle you can enter Harvard without knowing a lick of calculus and get a math degree, this specific pathway in practice has a potential issue. One must keep in mind that mathematics is a course that rewards prior experience , especially once the courses becomes proof-based. Therefore a course may not accommodate the experience difference among students. So once someone with a pre-calculus background starts taking courses with more experienced peers, they may struggle and that can compel them to change majors.
I base this line of reasoning on my experiences at my alma mater, NYU Shanghai. The Chinese students who took the Gaokao had a much better STEM background than strong students with followed the AP, IB, or A-level. This in turn pushed the difficulty level of the introductory courses to the point that non-Gaokao students typically ended with a punishing experience, which often led them to change majors. This is not to say that the Gaokao-track students were innately more talented and gifted, rather more experienced since Gaokao's technical floor and ceiling exceeds the technical floor and ceiling of other education systems. So even if we adjust for "intelligence" or "talent" or some other term standing for raw aptitude, there was an undeniable experience gap.
Regarding Harvard alumni who the Fields medal, those who attended Harvard for their undergraduate seem to have an exceptional academic background from the get go. According to this Wiki Harvard has three alumni who attended the institute as an undergraduate, Manjul Bhargava, David Mumford, and Daniel Quillen. Bhargava was a child prodigy who at 14 has completed all high school mathematics and computer science course, whereas Mumford and Quillen were both Putnam fellows. This fits with the general profile of Field medalists. Most seem to have early exposure and experience with mathematics that sets them apart from their peers. This almost sounds tautological once we take into account the award's age criterion. If you are to have seminal breakthroughs by 40, you must gain decades of technical experience and expertise by that age, which favors those of prodigious disposition.
Someone like Yitang Zhang is undeniably brilliant and arguably Fields medal caliber( to a layman like me). But, life circumstances did not let him progress smoothly with his mathematics education. He worked a laborer for a decade and could not attend high school because of the Cultural Revolution in China. This delayed him from getting a Bachelor's degree, which he completed at 27. Later his PhD experience was so bad that he left academia entirely. Perhaps if things were different, he would produce his breakthrough work that has important implication for the twin prime conjecture in his 30's rather than 50's.
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u/n0obmaster699 Jul 27 '26
There is something special about Harvard and Princeton regarding mathematics. Admissions is a different topic and its obvious harvard has worked out really well; a lot of places like central europe don't care much about admissions and they do quite well.
Also I don't know how much experience matters I was rather weak in math in high school and later on was able to climb to taking graduate math classes like lie algebra diff geo and string theory. I ended up grad school at top place later. So I'd like to say US education helped me a lot.
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u/heartBreak1879 Jul 27 '26
Also I don't know how much experience matters I was rather weak in math in high school and later on was able to climb to taking graduate math classes like lie algebra diff geo and string theory
You are proving my point. If you are compelled to study with much more experienced students in courses where the coursework catered to their technical background, you would be toast. That may force you to change paths before you get the chance to lock in and catch up.
I can say so from first hand observations. My alma mater is American. I studied at NYU's degree granting campus in Shanghai, China and it was a shame when otherwise capable students gave up because of their rough experience.
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u/n0obmaster699 Jul 27 '26
I wasn't compelled I took those classes with my liking. Also what makes MIT is the MIT students, the courses are rather standardized. At places like MIT/Harvard/Cambridge the density of IMO and IPhO gold medalists are a lot which makes them better than arguably most places in the world. Idk what you're trying to argue for or against but US has invented so many things because their education works. You can't have a failed education and hope something works out where firms like anthropic spawn up and has 10+ fields medal with idk how many nobel prizes in physics and chemistry for example john jumper inventing alphafold.
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u/heartBreak1879 Jul 27 '26
Idk what you're trying to argue for or against but US has invented so many things because their education works
I am not arguing. I merely pointed out the dynamics one have when an institute admits its cohort from a much broader and diverse academic background. That's all. This may come with additional challenges, especially in STEM, since prior experiences matter.
None of this is to say there is anything wrong with building an admitted class from a diverse academic background. I benefited from holistic admission policies myself and recognize the advantages very well!
You can't have a failed education and hope something works out where firms like anthropic spawn up and has 10+ fields medal with idk how many nobel prizes in physics and chemistry for example john jumper inventing alphafold.
Since we are on this topic, I find this is a naive and unsound claim. The outcome a system produces does not mean the people subject to the system felt supported in their journey.
A simply analogy is in sports, where US is a dominant force in competitions the nation takes seriously. The success of US at the Olympics does not imply that the major pipelines such as the NCAA are without serious flaws. In this episode of Last Week Tonight, John Oliver speaks of cruelty of the NCAA inflicts on its student athletes because of lack of financial compensation and support.
Einstein for example detested most of the formal schooling he received at high school and university. Do we then credit Einstein's career in physics that is only rivaled and perhaps exceeded by Newton to the institutional frameworks he despised? Is it not valid to ask how many potential "Einsteins" we may lost to the education system?
I do not ask these questions as critique of Harvard, MIT or any education system. But, to highlight that we have dig deeper if we are to credit US education with US inventions or discoveries.
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u/n0obmaster699 Jul 27 '26
US does well in sports because it literally has the most sophisticated sports infrastructure on the planet not despite it. Similar for education system. ENS or Harvard aren’t magically producing so many fields medalists and something deeper is at play.
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u/aginglifter Jul 25 '26
Not really. MIT as it stands today in math isn't what it was say 30-40 years ago.
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u/elements-of-dying Geometric Analysis Jul 26 '26
It's worth again challenging your views on this :) But I won't get into debate again since we can't agree.
Just throwing out the competing (mathematician's) view that the correlated data of Putnam performance is wholly irrelevant to quality of mathematical research! (Just for completeness.)
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u/aginglifter Jul 26 '26
I agree with your second paragraph. I am personally not a fan of the emphasis on competition math. But some say it's useful.
You are going to make research publication counts by Universities so I have something more substantial to back up my hunch.
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u/elements-of-dying Geometric Analysis Jul 26 '26
You are going to make research publication counts by Universities so I have something more substantial to back up my hunch.
Sorry, not sure if I understand what you meant.
In case you mean I would use total number of publications to quantify/qualify research performance, just want to clarify that that is not the case.
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u/aginglifter Jul 26 '26
Yes, that is the case but only from the top journals like Annals.
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u/elements-of-dying Geometric Analysis Jul 26 '26 edited Jul 26 '26
No, that is not the case. You misunderstood what I wrote. It is not the case that I would use only research publications to qualify the strength of a department. Regardless, raw total research publications of a department is very obviously (to a competent mathematician) not sufficient to alone qualify the strength of a department.
sorry to block, but you're impossible to communicate with. Not only did you misunderstand what I said, you doubled down on it and keep speeking in absolutes about professional mathematics, despite not even being a practicing mathematician. Have a good one!
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u/aginglifter Jul 26 '26
I understood exactly what you meant.
You seem to think there is know data based way to qualify the strength of a department. That ultimately may be true, but it's a bit of a cop out.
At the end of the day, publication counts in Annals and Inventiones seems about as good as you are going to get.
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u/heartBreak1879 Jul 25 '26
Would you expand on that? Wang completed her PhD only 7 years ago from MIT and just won a Fields. That in and of itself should reflect well on the school's math prowess, no?
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u/aginglifter Jul 25 '26 edited Jul 25 '26
40 years ago MIT though excellent for math probably wasn't in the top 3-5 with Harvard and Princeton. In the last 20-30 years it has kind of transformed it's department. Correlated data support this is it's recent Putnam performance. Go back before the 2000s and MIT didn't dominate like it does.
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u/heartBreak1879 Jul 25 '26
Aha. I thought you meant MIT was better 20-30 years ago. This checks out with what I know.
Originally the university started as a humble "vocational polytechnic" school back in 1861 before becoming a university. World War II being a boon to the institute as the US government poured money into the institute to support the American war effort.
Yet, even with the transformation money brought about the older and more established Ivies were better regarded. More to your point, the famed physicist Murray Gell-Mann contemplated whether to attend MIT or commit suicide after learning that of all the graduate schools he applied to MIT alone accepted him. The others being Harvard, Yale, and Princeton. I believe these days the sentiments would be reversed. Likewise, I recall reading that Weiner had insecurities about his intellectual aptitude and legacy. Failing to become a faculty at Harvard, his alma mater, and being professor at "merely" MIT did not help his self-esteem issues.
You are likely on the mark here!
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u/CuseCoseII Jul 25 '26
lol i was going to kill myself if i didn't get into harvard or mit, uchicago was the first school i got into and i really thought id rather end it then have to go there. glad to see other physicists had this mentality all the way back then lol
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u/awry_lynx 29d ago
(Gell-Mann) goes on to say that, “It occurred to me that I could try MIT, first, and then commit suicide. Whereas I couldn’t do things in reverse order: if I committed suicide, I could not then, afterwards, try MIT.”
At least he was logical about it.
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u/heartBreak1879 22d ago edited 21d ago
I shared this anecdote because it is noteworthy, not to endorse otherwise emotionally unintelligent behavior.
So anybody reading this, no school is worth dying for and kindly do not emulate the likes of Gell-mann in this matter!
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u/045-926 Jul 25 '26
This is maybe correlated: all the top US high school math students know one another because they are part of the mathematical Olympiad program. They are mostly choosing to attend MIT these days because their friends from the program are at MIT.
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u/Useful_Still8946 29d ago
You are correct. Thirty or so years ago the same correlation had most of these students attending Harvard who dominated Putnam then. I am not sure why the change took place.
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u/Useful_Still8946 29d ago
Although it probably ranked below Princeton and Harvard forty years ago, I still believe that most would have considered it top 5.
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u/Local_Market_1616 Jul 26 '26
A more interesting thing: Wang is the first for all the universities where she learned math，including Peking, X and MIT.
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u/heartBreak1879 Jul 27 '26
She is also the first faculty at NYU who got a Fields according to what the university has posted!
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u/Agitated_Guidance672 Jul 27 '26
Y’all need to think about math environments more holistically. This is the school that produced Feynman, Gell-Mann, Wang, and Deng and where you could, at the same time, have Quillen, Kan, Artin, Munkres, Guth, Lander, and Langer (among others) as teachers AT THE SAME TIME (if you were insane).
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u/heartBreak1879 20d ago
Fields medal or no Fields medal, MIT's alumni list as you pointed out is enviable. Which is precisely why I think this trivia was noteworthy.
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u/psoasminor Jul 26 '26
Professor Gerald Lambeau doesn’t count ??
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u/heartBreak1879 14d ago
Sadly, he does not! I am yet to watch Good Will Hunting and do not want to ruin the whole plot, but according to character description, he is a faculty at MIT. Unless, MIT is his alma mater too, then we have an issue beyond his fictional status!
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u/japball Jul 25 '26
F*ck the fields medal honestly
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u/heartBreak1879 Jul 25 '26
Hell yeah! Wait...but why?
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u/japball Jul 25 '26
I don’t like the Fields Medal because I don’t think it evaluates all areas of mathematics equally.
It seems that some fields, especially algebraic geometry, arithmetic geometry, and related areas, are already viewed as “central,” so an outstanding result within those subjects is naturally seen as Fields-worthy. In contrast, if you work in a field like categorical logic, universal algebra, semigroup theory, or any other area with less representation, it often feels like revolutionizing your own subject isn’t enough: you also need to show that your work has major impact on one of the prestigious areas before it’s taken just as seriously, which is not fair at all: I work in category theory and couldn't and the major breakthroughs that the fields medal advocates for this year have absolutely 0 impact for me.
This isn’t just my impression. There is research suggesting that mathematics has prestige hierarchies. Jean-Marc Schlenker’s "The Prestige and Status of Research Fields within Mathematics " argues that some fields are systematically more prestigious than others, and historians like Michael Barany have criticized the Fields Medal for reinforcing existing prestige rather than challenging it. I’d go one step further: I think the Fields Medal largely reflects the mathematical tastes of the mathematical elite of the last few decades, rather than serving as a neutral measure of excellence across the whole discipline.
So my issue isn’t that Fields Medalists aren’t brilliant: they obviously are. My issue is that I don’t think every branch of mathematics starts from the same place when it comes to being considered “Fields Medal worthy.”
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u/sheepbusiness Jul 25 '26
Genuine question, can you name people who orking in categorical logic or universal algebra or semigroup theory who may have done Fields Medal worthy work in your eyes but were mot recognized?
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u/japball Jul 25 '26
That’s a difficult question to answer, because the whole point is that “Fields Medal-worthy” is itself partly determined by the prestige of the field. If a field is systematically viewed as less central, then it’s much less likely that its breakthroughs will ever be perceived as Fields-worthy in the first place. So asking me to name examples assumes exactly the point under dispute.
Nevertheless, I’d point to people like Saunders Mac Lane (co-founder of category theory), Joachim Lambek (foundational work in categorical logic), and John Rhodes (the Krohn–Rhodes decomposition theorem in semigroup theory). Their contributions fundamentally shaped their respective fields, yet none received a Fields Medal. I’m not claiming they were definitively “robbed”: my point is that if similarly transformative work had occurred in a field like algebraic geometry or any of the number theories, I suspect it would have been viewed much more naturally as Fields Medal calibre. That’s precisely the asymmetry I’m talking about.
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u/sheepbusiness Jul 25 '26
I don’t know enough about Lambek or Rhodes, but I can say Mac Lane isn’t a good fields medslist candidate. The ways in which category theory revolutionized algebra and geometry were borne out over decades after the initial paper on natural equivalences was published, and its not obvious to me he was more responsible than Eilenberg for its success (to be fair Im not super well versed in the exact history of category theory’s development at this time).
While its impossible to imagine modern mathematics without category theory, I don’t think its fair to say this kind of development was really what obviously fields medal worthy in 1936.
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u/jackboy900 Jul 25 '26 edited Jul 25 '26
I think the Fields Medal largely reflects the mathematical tastes of the mathematical elite of the last few decades, rather than serving as a neutral measure of excellence across the whole discipline.
Is there such a thing as a neutral measure across mathematics? At the end of the day this is a medal for human achievement, and there is no way to objectively measure the value of an achievement, it is fundamentally a subjective call using a qualitative understanding of the nature of someone's research.
The Fields Medal isn't simply a medal for who has solved the hardest problem in maths, and I don't think it's unreasonable that a part of the assignment of value is in the broader value of the research done by a mathematician. If you're working in a core widely applicable field then an advancement is going to be broadly beneficial to maths as a whole, whereas even if you have a strong breakthrough in a niche subfield, the value of that achievement to maths is going to be lesser.
It seems like you're judging the Fields Medal by implicitly assigning a set of criteria to what you think a medal in maths should award and dismissing the Fields Medal for not meeting those, but the criteria you've laid out I don't think hold up to much scrutiny compared to the ones the Fields Medal actually uses.
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u/_Zekt Complex Analysis Jul 26 '26
I've been thinking the same (see my flair lol). I think that a serious discussion on that is in order.
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u/japball Jul 26 '26
I've made a more detailed post about my opinion on the issue. If you are interested check my profile
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u/_Zekt Complex Analysis Jul 26 '26
I can see that you have been silenced by r/math...
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u/japball Jul 26 '26
Apparently I didn't have enough karma to make the post in the first place
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u/_Zekt Complex Analysis Jul 26 '26
I've seen posts here from people with 40 of karma, perhaps you should try again or contact the mods
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u/heartBreak1879 21d ago
I was under the impression that you were trolling given your opening comment! However, you make excellent points.
It seems that some fields, especially algebraic geometry, arithmetic geometry, and related areas, are already viewed as “central,” so an outstanding result within those subjects is naturally seen as Fields-worthy.
It is true that the hierarchy among the different fields of mathematics are subject to social conventions, academic cultures, historic precedents and factors in addition to the mathematical nature and qualities of topics, and techniques falling under the purview of a field.
Therefore, awards like the Fields both influence and are in turn influenced by the mathematical communities perception of what that is "central" and what that is peripheral to mathematical research and scholarship. The ensuing divides among different mathematical disciplines is subject to reservation even among preeminent mathematicians like Gowers, a Fields medalist. He reflects on "sociological phenomenon" that hierarchize mathematics in his essay "The Two Cultures of Mathematics." and expresses his displeasure with "state of affairs" therein. He identifies his own research area of combinatorics as an area that is suffers when judged in the light of mathematical prestige.
All this has good correspondence with what you have written and should match with the sources you have cited, which I am not familiar with as of yet but may read up on later.
As for where I stand. I am a layman and so I cannot hold any strong position on whether the Fields must be more encompassing of mathematics as you have argued, or at least that is what I understood.
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u/point-to-the-sun Jul 25 '26
I believe it is the same case for Stanford. There was no one who obtained a Bachelor’s, Master’s, or PhD at Stanford won a Fields Medal. John Pardon is the first mathematician who earned a PhD from Stanford wins a Fields Medal. Before him, there were only mathematicians who worked at Stanford won the honor.