The Fields Medal should return to its roots | Hacker News Reader

The Fields Medal should return to its roots

nature.com

122 pointsadenadel129 comments

Committee members started talking about criteria such as age and fields of study, even before suggesting nominees. Most thought that focusing on specific branches of mathematics was inadvisable. They entertained a range of potential age considerations, from an upper limit of 30 to a general principle that nominees should have made their mark in mathematics some time since the previous ICM in 1936. Bohr cryptically suggested that a cut-off of 42 “would be a rather natural limit of age”.

By the time the first set of nominees was in, Bohr’s cut-off seemed a lot less arbitrary. It became clear that the leading threat to Bohr’s designs for Schwartz was another French mathematician, André Weil, who turned 43 in May 1949. Everyone, Bohr and Morse included, agreed that Weil was the more accomplished mathematician. But Bohr used the question of age to try to ensure that he didn’t win.

Why let the committee argue whether the nuclear reactor needs to be built, when you can get them to argue about the color of the bikeshed. Stuff like that makes you wonder about the true significance of academic accolades.

This is not an example of bikeshedding. Bikeshedding is fighting over trivial details in order to delay or avoid a decision (perhaps subconsciously)

This is an example of gaming the system in order to steer a decision in a particular direction. It is an example of organizational politics - perhaps even of corruption

I think the age limit for the Fields medal reinforces this idea that "mathematics is a young mans game." It's one of many reasons why I got discouraged into entering mathematics when I was young because of this and math competitions.

When I was younger , I would visit websites such as AOP , and ask questions and then be treated in a condescending way by students who were my age or younger who would then boast about their scores on Contests such as AMC. This just reinforced me that I probably shouldn't waste time pursuing mathematics as a career because I felt that I was drastically behind them, and I would be competing with them for positions that they could take.

It took some time for me to realize that having encouraging parents who are academics/engineers helps significantly in guiding you in a career such as mathematics.

> When I was younger , I would visit websites such as AOP , and ask questions and then be treated in a condescending way by students who were my age or younger who would then boast about their scores on Contests such as AMC.

(Assuming you mean AoPS) As someone who was relatively active in that scene back then, but not nearly good enough to brag about their score, I find the reason behind this to be relatively obvious. It’s not that they’re trying to put you down because of your age; rather, they’re teenagers being told that they’re the best at math in the country. It’s easy to let that get to your head.

From my experience in my friends that have pursued math degrees is that the job market is extremely competitive to become a professor. You either attempt to cash out in finance after learning how to code or start working for the local community college. Even if you do try to get a tenured track position you will be an assistant professor or worse unless you do everything perfectly.

This will come across as harsh, but that isn't my intention. My intent is to explore ideas, so I apologize in advance.

Are your friends aware that scientific breakthroughs have not typically come with rewards to the observer/identifier/mathematician? If so, they likely selected for a role that benefits the other humans but not themselves; if not, perhaps they are unrealistic about expectations as a thinker.

We all seem to love new thinkers so much, but telling people what they've built is incorrect has rarely been personally profitable. Outside of the maths/sciences, hell, they freaking crucified Jesus for his social policies.

The entire structure of human civilization suggests its unprofitable to tell people they're wrong. It requires that wrongness to "create new paradigms". People who buy into the system are unlikely to overturn it, so the complaints become less "they dont like me for my ideas because they're recolutionary" and more "they don't like me because my ideas aren't as mainstream as theirs".

If your metric is the latter, can you help me understand what the problem is?

But "disruptive" tech is like that, but rather than tell the old guard that they are wrong, you just try to displace them..

> It took some time to realize that having parents who are academics/engineers helps significantly in guiding you in a career such as mathematics.

This is true of every good job.

I'm trying to get hired at big 4 tech right now. Every person interviewing me is a rich kid. All of my competition is rich kids.

Touring these big tech companies was discouraging. They're all very diverse. Rich white kids. Rich Asian kids. Rich female kids. Rich European kids. Rich Indian kids.

I'm not sure there's anything I can ever do to make it past the social/socioeconomic judgment round of these interviews.

These interviews make me feel like Red at a parole hearing in Shawshank Redemption.

This isn't meant to question your experiences, but to provide an alternative story, just for the sake of readers who might feel discouraged.

I'm a senior SWE at a major tech company. My background is definitely toward the lower end of the middle: my family went without health insurance at times, we passed down clothes from sibling to sibling, and most nights of the week our usual meal was pasta with canned sauce or hot pockets (we never went to bed hungry, so we were privileged in that respect). I went to public school and got subsidized lunches. I got a full ride on need-based aid for college, and I didn't get a BS in CS. I'm smart, but far from brilliant.

I'm acutely aware of class in a way most of my colleagues aren't. But most aren't from "rich" backgrounds: I'd say the most typical background is upper-middle, with at least one parent who's a working professional.

Have I had to work "harder" than most? Probably, but it seems like a really messy and ill-posed question. Getting a job at one of the big tech companies is a combination of preparation and luck of the draw. It's easy to read conspiracy into the fact that most people from poor backgrounds get rejected, but the reality is that most people from rich or middle class backgrounds also get rejected.

Everyone brings a different set of privileges into the job hunting process. But you have as much agency as anyone, and you're doing yourself a disservice if you trade that sense of agency in for despair or bitterness.

>most typical background is upper-middle

To someone who grew up working class or working poor, upper-middle is "rich".

I suspect that when the OP said "rich kids" they were referring to upper-middle class kids.

As a self taught, working class rural European white kid with a fairly successful career at one of the big four, I can tell you that this is simply not generally true. Sure, a lot of my peers come from financially well off families who sent them to prestigious universities, but many others had to make their own way. On top of that, I consider many of the "rich" kids pretty open minded, they're sure accepting of me and let me tell you I do not fit the standard mold.

Interviewing is a game in its own, but if you show that you're a problem solver who can work in team, and that you have done your homework, and that you can display some sort of passion for the job you're hiring for, you have a high chance of passing the interview.

Wow. Lots to digest here, and I think I detect some strong frustration. My sympathies on that.

I have worked at the big 4 (MS) but I'm a consultant now. I do a fair bit of interviewing and what I propose is that you don't actually have a clue what the finances of your interviewers are like, and you don't actually have a clue what the finances of your competitors are like. You would be far better served putting it out of your mind and focus on just trying to be a good engineer (presuming that's what you are trying to be) and enjoying it.

The reason being is that, not only are you almost certainly wrong, but it doesn't matter. Interviewers don't care about how much money the candidates have because...

1. they get a perk if you get hired and retained regardless, so they're incentivized to place anyone that can do the job

2. the competition often doesn't exist: the big 4 will often just hire anyone and everyone who fit their criteria (high turnover and need leads to a few hundred engineers starting each week)

3. the job has a pay band, and if you're currently making low or nil, then you're far more likely to HAPPILY fit into the lower segment of the band

BTW: The other interviewers and I can tell when the candidate is crusty and/or resentful during the interview, and it reflects negatively on their performance.

> you don't actually have a clue what the finances of your interviewers are like, and you don't actually have a clue what the finances of your competitors are like

The point isn't about the wealth of these people, it's about their background, and the resulting confidence and comfort with which they can negotiate the social structure of interview and employment at these companies.

> The other interviewers and I can tell when the candidate is crusty and/or resentful

Like that, for example.

>The point isn't about the wealth of these people, it's about their background, and the resulting confidence and comfort with which they can negotiate the social structure of interview and employment at these companies.

This is simply not true, and imagined. You've been biased by a small subsample of the industry I believe. Programming is one of the few white collar industries that can be entered without a degree. Those rich kids you're interacting with are less likely to have been rich before their tech jobs than those in most other industries.

I personally know multiple self taught "rich kid" programmers who lived in third world countries and dirt floors as children.

The big company is half of rich privileged kids and half of people who just moved in to the most expensive city in the world and don't know if they can pay rent the next month.

You'll meet both types of people in the interview panel.

Interviewers are just people who happen to be here at the moment, they have nothing special. They have the power to grant you the job or not but that doesn't mean anything about their personal life.

> The reason being is that, not only are you almost certainly wrong, but it doesn't matter.

I've noticed that, in this field at least, everyone does come from a much more wealthy background than I do. I once talked about my experience of working at McDonald's as a youth once and got a lot of weird stares. Kids of doctors, professors, etc...I think it is mostly because they went to good schools in the first place, there aren't that man poor kids that go to CMU or Stanford. Heck, it is much worse at the PhD level.

The other points are valid: given the talent shortage in our field, they mostly don't care about your background. It is much more relevant during promotions in dysfunctional orgs.

>> Interviewers don't care about how much money the candidates have because...

No, hang on, I get what the OP says and it's a reasonalbe assumption. In large companies with rigid hierarchies, people will often be sort of subtly flash (!) with their money, because it basically marks their position in the hierarchy. You can see this in the clothes people wear, their cars obviously, their phones also obviously, the other tech they proudly display, discussions about where they're going for holidays, or for the weekend etc etc.

If you're getting hired in a company with that sort of culture as a recent graduate, say, coming from a less affluent background, then it's easy to feel somewhat excluded.

> No, hang on, I get what the OP says and it's a reasonalbe assumption.

It's definitely an assumption, which is a problem to begin with, and it's not a reasonable one. Interviewers often go through training to avoid pre-judging candidates, and candidates would be wise to do the same.

An interview candidate gets to talk to a couple of recruiters and have at most 2 conversations with 3-6 engineers at most. I would be pretty suspicious if any of those conversations were about the interviewer in any significant way to begin with, let alone about what they drive, where they're going on vacation, or what they make.

So I get what you're saying, and there's certainly people like that anywhere that pays their people exceptionally well, but making assumptions about the character of your future-coworkers before you've actually gotten to know them is a recipe for a bad time.

>> You can see this in the clothes people wear

A company-branded t-shirt and jeans?

Some of my coworkers have this disgusting habit of putting where they’re going for vacation in the shared Outlook PTO calendar.

He’s talking about culture fit.

Where does your average Stanford, Berkeley, MIT grad come from? A: A collection of a couple hundred high schools. Those schools aren’t where middle America comes from.

From what I can see, the Valley kicks that up a notch. I considered working for a big 4 after seeing what seemed like a fantastic salary offer. Then I started looking at the cost side of the equation. Forget it — unless you have cash, it does not compute.

I read the problem as being a cultural one, not a financial one.

Interviewers get a perk? That's news to me. I can see recruiters getting a perk, but wouldn't it be a perverse incentive to give interviewers a perk?

My last interview was with a big 4 and every single one of my interviewers was from a different country (China, India, somewhere in Eastern Europe). I bring that up only because I know they grew up there and didn't study in the US, so they probably weren't as privileged as me or you.

I wouldn't read too much about class into it. Prestige (of college, other places you've worked) is definitely important for getting the interviews, but it's at best only a proxy for wealth, and it doesn't help you navigate the interviews themselves IMO.

I'm not really sure how exactly you think SES/class plays into big 4 interviews, honestly. At my interviews my interviewers were mostly wearing jacket+tshirt+jeans, most of the other interviewers were wearing about the same thing, and I wore sweater+collared shirt+khakis, which was also fine (I got the job). The only time SES came up is when I brought up how my background coming from a more rural/poorer area could help me provide unique perspectives about users and how they might interpret the products that I contribute to.

I was in a similar position for a long time but then I found once you make it into one of the circles all of the others open up. It’s dumb. There’s so much untapped talent out there because tech giants are relying on “namebrand” schools or other companies to do their recruiting filters for them.

I have no direct knowledge of academic careers like mathematics.

I'm white, but I came from a lower middle-class background in a rural area. My parents were barely supportive of me going to the university. I'm a real-life redneck.

I eventually made millions in Silicon Valley and retired at age 40.

One of the best pieces of advice I received in life was this: don't sell yourself short. Try, strive, and then let other people reject you. But never reject yourself. And if others reject you, stand up and try again. If they hit you harder, then get up quicker and hit back harder.

Perhaps you'll find that you're not really all that you thought. Or perhaps you'll find that with each small success, your odds increase in the next round because you learned something important from your failure in the previous round. If you don't stand up and fight the next round, you'll never know the true answer.

> One of the best pieces of advice I received in life was this: don't sell yourself short. Try, strive, and then let other people reject you. But never reject yourself. And if others reject you, stand up and try again. If they hit you harder, then get up quicker and hit back harder.

This is great advice and it's been how I live my life, and it's revealed so many opportunities to me that I never thought I would have.

With these big 4 and unicorn onsites, though, that attitude didn't reveal new opportunities to me. It confirmed all of my worst suspicions about how people behave and how big tech companies operate. People actually are going to discriminate against me. These big companies actually are a socioeconomic monoculture. The circumstances of my birth actually will cause people to deny me opportunities regardless of how hard I work to prove them wrong. There actually is a glass ceiling.

I guess I had to get here eventually. It just feels terrible. I spent 8 months preparing for these interviews while working full-time, I aced Facebook and Instacart, aced 4/5 at Google, and got 5 rejections and 0 offers.

The engineer I ate lunch with at Facebook went to a top school. He literally told me that when he interviewed for his internship, he was asked only 1 coding question. It was Three Sum, which is a very well-known and easy question. That got him inside and he converted it to a full-time offer.

Why does he get in based on 1 easy question, but I get asked ~7 algorithms questions, write asymptotically perfect solutions to all of them, and get rejected?

The most frustrating thing about this is all the sacrifices I make in life preparing for this and trying to break through, despite truly not knowing whether it's even possible for me to get accepted by these people.

If they are discriminating, they don't say "we're literally never going to hire you and it's for reasons you can't ever change, so you're free to give up." I would feel better about that because at least I would get my evenings and weekends back. But they would never say that, they'll just keep encouraging me to sacrifice all my evenings and weekends for the rest of my life until I give up and blame myself.

So I'll never receive any signal for when I should stop. I'm just perpetually stuck in this mode of having my entire personal life on hold trying to get into companies that simply don't hire people like me regardless of technical performance or merit.

I've spent 30 unpaid hours per week over the last 8 months studying for this and I have nothing to show for it. It's not like knowing how to invert a binary tree on a whiteboard is transferrable and benefits me elsewhere in life, this is completely trivial and useless knowledge for me. It's not worth anything to me anymore, it's a thousand hours of unpaid overtime devoted to passing technical interviews that I then pass and still get rejected anyway.

And I honestly don't know what else to do now other than to continue giving unpaid 30-hour weeks to Google and Facebook's recruiting processes. What else am I supposed to do? That's where all the advancement is, what else is there for me to do?? Am I supposed to just accept my lot in life like a pauper in feudal Europe? Where is there any happiness to be found in just accepting this?

"I aced Facebook and Instacart, aced 4/5 at Google"

How can you possibly know this?

This is pretty much unrelated to the original topic, but on the off chance that it will help you in your career, I'll do my best. I've done a lot of hiring in my career. I've encountered a lot of people who come to interviews with the same kind of attitude that you express in your messages. I realise your interview-face and your complaining-on-the-interview-face are different, but I've never met you and I have no way of giving you good advice based on who you actually are, so this will have to do.

Trying to get a job at a big 4 or unicorn: my first question for you (which you don't have to answer out loud) is why? Why would you go after that job? What makes you think this is the best for your career? If you were interviewing with me, you are already on the back foot. The reality of the situation is that these places are not any better than anywhere else. In fact, you have a much better chance of getting a crap job in one of these behemoths than in a small, focused, unknown company -- because there is no way to hire X-thousand good people. Internal infighting and politics means that entire divisions will be rotting away. To be fair, there are going to be gems inside those big, rich companies and those gems will be very bright, indeed. But unless you are being headhunted for those departments, you are unlikely to get in. You are better off making your name elsewhere. That you don't know this, makes me think that you are young, naive and lack real world experience. It makes me think that if you get a job in one of these famous places you will be unsatisfied because your internal view of them is completely out of whack. Remember -- I don't know you and I'm extrapolating dangerously from what you have written. But also remember that an interviewer is doing exactly the same thing with the hour that they have to chat with you.

The fact that you spent 30 hours a month studying to get into these companies makes me question your motivations even more. If you had said, "I spent 30 hours a month learning cool stuff", or "working on an awesome side project", or pretty much anything else that could also make people interested in you I would have been impressed. I would also be happy for you because you would have something that nobody can take away. Instead you wasted your time doing things that are trivial to you. You lack good judgement. If you write asymptotically perfect solutions for 7 algorithm questions and don't display a completely nerdy love of algorithms, then that's going to be a massive knock against you.

Look, I could go on, but that would just be kicking someone when they are down. That's not my intention. I don't know how many programmers there are in the "big 4", but we're talking about tens of thousands. There are millions upon millions of programming jobs in the world.

Programming is a boring, stressful, thankless job. People who have no idea what you do are going to yell at you for being slow, stupid, and incompetent. Manipulative, self-important sociopaths are going to blame you for all of their mistakes. You will make 2-3 times the wage of a firefighter, nurse, teacher or insert-ridiculously-difficult-job-that-actually-saves-peoples-lives-here and you will be spending your time wresting with CSS to make a bloody column line up (because if you don't get it done by Monday, the whole company is going under). And despite making ridiculous wages compared to the rest of the population it will never be enough to "put up with this crap". Trust me!

If you don't do this job because you love it, then you will be miserable. If your goal in life is to get status, or make money, then find a job more in keeping with that goal. But if you want to be a programmer, than find something you love and do it. Be the best you can possibly be. Be happy. And, strangely, at that point I think you will find the big 4 (or whatever) will be beating down your door to scoop you up.

And to answer your question: Why do those other people get scooped up right out of school. Mainly because they are easy going, confident and look like they will be super fun to work with. Nobody hires new grads because they are "good" (because, with very few exceptions, they aren't).

Thank you.

Your comment exhibits a lot of disdain. Sorry to hear about the interviewing trouble.

> I'm trying to get hired at big 4 tech right now. Every person interviewing me is a rich kid. All of my competition is rich kids.

Touring these big tech companies was discouraging. They're all very diverse. Rich white kids. Rich Asian kids. Rich female kids. Rich European kids. Rich Indian kids.

I'm not sure there's anything I can ever do to make it past the social/socioeconomic judgment round of these interviews.

Is your primary issue that everyone interviewing you is much younger than you are, or that they have more money? If the latter, is it because they presently have more money or because they had a better socioeconomic upbringing?

I’m not trying to invalidate your experience, just understand it. But unless you specifically mean ageism, I don’t see how you could clearly link prejudices in these interviews to a difference of wealth.

I’m not the previous commenter, but I’ll share my thoughts on this as someone from a lower-middle-class background.

Having to support yourself financially while going to college makes it far more difficult to meet the standards that top firms demand. Extracurriculars? Tough to justify when you’re already working 40+ hours a week while taking a full-time courseload. Good GPA? A lot harder to keep up when you get called into work when you’re supposed to be doing homework or studying. Internships? You have to start applying at the start of your junior year nowadays, which is when a lot of students are transferring from community college to 4-year schools. So no recommendations from professors, limited relevant coursework, and limited access to a (competent) career center. And you wouldn’t believe some of the looks I got from interviewers when I told them I went to a mediocre public school instead of my state’s flagship school because I couldn’t afford the latter, even with student loans. As if it’s inconceivable that I couldn’t afford an extra $4,000/year out of pocket while working in a warehouse.

So yeah, after I got a job in my field in spite of all of that, it’s hard not to resent coworkers who had easier paths because they had better support networks. This is unfounded personal bias, but I also can’t help but think of those coworkers as less capable than the minority who put themselves through school independently like I did. But mostly it’s a general sense of frustration with the difficulty of getting into competitive jobs without a significant support network.

Honest question: How do you estimate family financials of people interviewing you? Judging by the school they graduated or from the comments they make during the interview?

Shirt, watch, haircut, jewelry, manicured nails, cleaner pressed pants, designer bag:glasses:whatever, favorite restaurants, shoes, phone, vacation stories, fraternity/sorority mentions, accent, colloquialisms, alma matter, hobbies, connections, and other off hand comments. The formerly poor are very attuned to it. We don't always know, but sometimes it's obvious.

Since IQ, education and wealth are all positively correlated, it's true that any group of smart highly-educated people is likely to come from privileged backgrounds, but that's not why they are being selected.

A lot of those immigrants you talk about will actually be middle class people that had to work twice as hard to get hired in a foreign country.

I went to Cambridge University, UK and got a first in maths. I have friends who did to. Those of us who came from poor backgrounds had real difficulties getting a good job. We just weren't a "good fit". One of my friends with a 2.1 Cambridge maths degree was a waitress for 3 years after graduating.

Perhaps this is more of the case in the UK where class is more of a salient aspect of life than in the US?

Class is profoundly salient in the United States. Unless you've been on the outside it's very difficult to see, because the gradations are more subtle, but they run no less deep.

It's worth noting the distinction between social class and socioeconomic class/status. Socioeconomic status plays a larger role in United States relative to the UK. Social class refers to one's fixed sociocultural background and plays a far larger role in the UK compared to the US.

I've been outside the US. People care much less about where you've come from than in the places I've been (in Asia and Europe).

Of course class exists in the US, but if you're able to move up in a tax bracket people won't judge you for having come from a lower tax bracket.

People don't judge you openly or likely even consciously. But fitting in is fairly difficult.

Rubbing elbows with rich investors and CEOs from affluent backgrounds is definitely more difficult for someone from a lower class background.

I think the issue of the original poster was being a math graduate. Little to do with class or social economic background.

With maths, you can work as a professor or work in finance. Two domains with limited demands that are highly competitive.

How do you know the people interviewing you are rich kids? I work at a big 4 company and I grew up in a low-middle class household.

You gave up Maths because you felt you couldn't win the Fields medal?

Do you also not cook, since you won't be Ramsay? Or not swim since you won't be Phelps? You must do nothing but contemplate the void, then.

HN usually is trying to uphold a tradition of addressing the strongest, not the weakest, interpretation of others' arguments. I believe this is why you are downvoted.

Impostor syndrome is a real thing, and just repeating the comparisons you used in the tone you used, does not help address it.

He should institute a Barany medal instead. It's an interesting idea, but the Fields medal is what it is at this point. It would be very slow to change, and even though his article is well researched, it's a bit idealistic and the interpretation of the original intent isn't black & white.

> He should institute a Barany medal instead.

My thoughts exactly.

I am not sure awarding someone a prize 20 years after their work like the Nobel, would achieve the goal of 'encouragement'. It may be ageist due to that goal but that was the intent of Fields.

I don't think this article is arguing that the Fields medal should imitate the Nobel prize. Rather, it argues that the Fields medal should return to its early selection criteria: mathematicians who have 1. done good work, 2. look like they will do more good work/positively impact math, and 3. would find the Fields medal's recognition and prestige useful in doing future good work (e.g. in getting them collaborators or funding)

The article argues that the <=40 cutoff is a poor proxy for points 2 and 3, and also seems to make a separate point that the habit of awarding mathematicians who are already professors at top institutions means point 3 may not be addressed well either.

An example of the kind of person this might help is Yitang Zhang, who made substantial progress on the Twin Primes conjecture in his 50s after a relatively quiet math career as an untenured lecturer beforehand. Granted, his result was big enough to get him a MacArthur and a professorship at his university, so he may not need extra recognition. But perhaps there are similar, less-lauded cases.

I think the equivalent of the Nobel prize for Mathematics is the Abel prize not the Fields Medal. The former rewards lifetime achievement.

Totally agree, but it should be pointed out that unlike the Fields Medal, the Abel Prize is relatively new, and perhaps intentionally set up in a way to invite comparison to the Nobel (whereas the Fields wasn't).

Credentials and prizes are heading the way of the dodo because we're slowly realising that while neither knowledge nor significance can be measured our opinions can be swayed by prestige and politics.

I would say charisma.. that gets people before they think about any of those things

Ok so what awards ceremony selection process isn’t political?

Any guess on who is in consideration of the 2018 prize? I imagine those under consideration are already at top tier institutions.

Is no noteworthy mathematics being done at less prestigious institutions? (Loaded question I know) but it would be cool to see some undiscovered mathematician doing ground breaking stuff at a lesser known university.

(Professional mathematician here, indeed one at a less prestigious institution.)

I would argue that medalists' universities have been reasonably diverse. For example, in the US since 1990, medals have gone to mathematicians from Rutgers and three separate University of California campuses. These are prestigious universities to be sure, but it's not like all the medalists are from the same two or three places.

> it would be cool to see some undiscovered mathematician

I think "undiscovered mathematicians" are very rare, for the reason that mathematics is an inherently social activity. We are constantly reading each other's papers, visiting each others' universities to give talks, and meeting each other at conferences. If you do excellent work, then in general your peers will learn about it and spread the word.

> Is no noteworthy mathematics being done at less prestigious institutions?

People with high-potential are detected early on and can choose to work in the most prestigious institutions.

It's like a pro-athlete. You don't expect Michael Jordan to be playing with a small local team.

I think people are psychologically averse to acknowledging this level of "filtering" even though it's mostly true, because it suggests an uncomfortable level of inequality.

However I do think that there might be just a little too much focus on contest-math when it comes to identifying the country's best mathematicians. It's easily seen that the best contest mathematicians usually become the best professional mathematicians. In aggregate, though, most contest-math participants come from a very particular demographic (i.e. they live in big cities in wealthy areas, have very supportive/tiger parents (this is the key), go to magnet schools, obviously practice a lot, etc.). These people are still probably much more likely than average to become professionals, but it filters out a lot of bright people from less wealthy families or areas, or in regions where culturally math competitions are barely even a thing.

That's not that true. Plenty of non IMO/Putnam people have won Fields Medals.

I think you may have misinterpreted my comment, because I'm really in agreement with what you just said: placing near the top in prestigious math contests indicates that you'll probably be a good professional mathematician, but not having top contest-math scores does not preclude you from being a good professional mathematician.

In general I think placement into top math undergrad/PhD programs (e.g. Harvard) should be less focused on contest math.

> It's like a pro-athlete. You don't expect Michael Jordan to be playing with a small local team.

See Srinivasa Ramanujan for reference.

But how many other examples do we have? It's a rarity to see such an occurrence. That's why Yitang Zhang's work was such a surprise.

That's like saying how many examples of great black American presidents do we have? If these people are systemically barred from these communities then it should be no wonder why we have so few.

Ciprian Manolescu or Peter Scholze (perhaps he is too young for it for this year).

I would be shocked if Scholze didn't win this year.

https://www.quantamagazine.org/will-peter-scholze-win-the-fi...

Like Grigori Perelman did?

It appears that Grigori Perelman was a well-known mathematician even before his work on the Poincare conjecture. He proved the wonderfully named "soul conjecture" almost a decade beforehand.

Even though he proved "soul conjecture", no university in the US wanted to give him a tenure job. Instead, they offered him a tenure track position. Once he proved the Poincare, every one wants him on their faculty.

Because of this, Princeton offered Manjul Bhargava (another Fields winner) a tenure job right away without putting on the rigma role of tenure-track.

How about: https://en.wikipedia.org/wiki/Yitang_Zhang

I think this overlooks the fact that mathematics is very specialised, segmented. Enormous talent in one strain of maths does not mean that anybody, following a slightly different course, would recognise the talent.

So, being an arbiter always means disappointing someone.

I suggest several micro-Fields medals, each arbitrated by the cross-cut of the nebulously defined experts of this field.

I recently got to meet a fields medalist who will remain nameless but he mention a really really interesting statistic. No Field’s medalist has ever been the mentor to another Field’s medalist. I (my opinion here not his) think that this glorifies these young mathematicians who never go onto mentor or yield another similarly gifted mathematician. We should be finding great mathematicians who discover great math collaboratively.

Quibbling about the Fields Medal mentoring claim: Schwartz -> Grothendieck -> Deligne is a counterexample.

Also Avila & Yoccoz: https://en.wikipedia.org/wiki/Artur_Avila and https://en.wikipedia.org/wiki/Jean-Christophe_Yoccoz.

Also Atiyah supervised Donaldson (albeit jointly with Hitchin), Mirzakhani was supervised by McMullen and others I'm sure.

Shocking that 55/56 Fields Medals have been awarded to men.

Maryam Mirzakhani has been the only female recipient. [0]

[0] https://www.nytimes.com/2017/07/16/us/maryam-mirzakhani-dead...

It's disappointing, but you'd have to have been living under a rock for two thousand years to find it shocking.

putting an age limit of 40 is probably skewing the result as women who want to have children have a biological constraint to have them in their 20s or 30s when their fertility is higher.

why is it shocking?

If you accept the idea that a penchant for math is randomly distributed among all people, then the odds of 55/56 men winning by chance are very, very, very low.

That gap also exists in the middle-school and high-school levels [0] (at least in the US), so it fully reduces to the simpler question of why that's true. We should be able to agree that by the time we're discussing professional mathematics there's no expectation that it would be randomly distributed among genders.

[0] https://economics.mit.edu/files/7598 (admittedly a bit old; maybe a lot has changed in ~10 years?)

Still true globally at the high school level. Found some quora answers with perspectives on IOI(programming olympiad) and IMO(math olympiad) which both have low single digit percentage female participants:

https://www.quora.com/Why-are-there-few-females-in-competiti...

https://www.quora.com/Why-do-boys-outperform-girls-in-math-c...

All it would require is just that the standard deviation for math ability in men (whether by nature or nurture, I am making no judgment either way) is only very slightly higher than for women. Since we are looking at the tail of the distribution, the result would not be surprising.

That hypothesis got Larry Summers in a lot of trouble.

https://en.wikipedia.org/wiki/Lawrence_Summers#Differences_b...

As Helena Cronin noted of men: "more dumbbells but more Nobels" [1].

[1] https://www.edge.org/annual-question/2008/response/10670

I once did some calculations to explore the expected effect of that difference in standard deviation: https://news.ycombinator.com/item?id=14997524

I'm on my phone right now and can't redo it for the gender ratio of Fields medalists, but I expect that the effect would cover most of the difference, since the cutoff for the award does seem quite high.

> If you accept the idea that a penchant for math is randomly distributed among all people

That would seem rather detached from reality.

Maybe he meant "Even if" ?

> penchant for math is randomly distributed among all people

Fields medals are not awarded based on "penchant for math" though. And it surely isn't exactly fault of the prize committee that there aren't very many female mathematicians to choose from.

Note: I don't know if 55/56 is "correct" from the point of the actual numbers.

For the last 30 years over 40% of graduating math majors where where women. That drops to 15% of tenure track mathematicians being women, but again that's a long way to sub 2%.

This is the exactly the pattern you would expect to see though if the variance of mathematical ability is higher in men than in women, even if mean ability is precisely identical.

The sex ratio gets progressively more extreme as you go further out in the tails.

Not really, you get a fat tail effect at extreme ability reducing the differences. A more likely cause are highly capable women bailing on the field.

EX: Women live significantly longer on average and the oldest women lived 6 years longer than the oldest man. Yet, the 16th oldest person was a man and 6% of oldest 100 people where men. And 6% of the top 100 living people are men https://en.m.wikipedia.org/wiki/List_of_oldest_living_people

I'm not sure what you mean—why would you assume there is a fat tail expect in the first place, and not something approximating a normal distribution?

And even if you presume something like a Pareto distribution, the likelihood ratio between two distributions grow through the tails if their variance is not identical.

edit: I see you bring up longevity, but I don't see why this is relevant to a discussion about variance in mathematical ability or intelligence? See: https://www.sciencedirect.com/science/article/pii/S019188690...

Based on a wide range of ability testing we see fat tails (edit: more black swans than expected), it would be more surprising if they where skinny.

Granted, we can't measure very high ability very well due to sampling bias. I am simply saying even if there is a modest bias that's not enough it would have to be huge to account for these numbers.

So, I am bringing up something else with the kind of distribution we are talking about which has more accurate data. Women live ~ 5% longer both looking at the average lifespans and oldest examples which is a very significant difference. Yet, the oldest population has more men in it than you would think.

Edit: Math: 6 year longer lifespan + 50% risk of death per year = you would expect ~1% of top 100 oldest people to be men.

Life span here is interesting.

If it’s affected by things like work place deaths because men are more likely to take on dangerous jobs, e.g. sea fisherman, military service, etc. would that overlap with the section of the population likely to be working on pure mathematics?

Suicide, another cause of that difference in average life span, would overlap though I guess.

It would be worth properly investigating as I suspect there’s a lot of complexity hidden here.

> Based on a wide range of ability testing we see fat tails

What kind of ability? Mathematical? IQ?

IQ, memory etc, in uncalibrated tests you see something close to a bell curve in raw scores but more people score very high 180+ than you would get from an actual bell curve. So, many tests are given a max score or compressed at the high end.

One argument that some have is that men have a more extreme distribution of IQ and mathematical ability and when it comes to things like the Fields medal it is the few extreme ones that make an impact.

I don't know how well done those studies are though.

EDIT: I doubt it is that big though.

I used to believe this, but now I think a confounding factor here is that girls are socialized away from extremes in general.

Ok, I can get you can somehow socialize a person to pretend be dumber than they are, but how do you socialize someone away from being dumb? And why does that not work for boys?

I think poor achool performance is more a function of behavioral issues than "being dumb" -- not because everyone is smart, but because the bar in your average American school is more about following directions than anything else. Boys lagging behind girls in social development is well-documented, right?

And at the Fields medal level it's less about "pretend you're not smart" and more about "we just don't think it's a good idea for you to skip grades".

> a penchant for math is randomly distributed among all people

As politically difficult as it is to say, intelligence is NOT distributed randomly among all people.

Not by sex, not by race.

Characterizing something as "politically difficult" is no evidence for a claim.

There's tons of evidence. You can google as easily as I can.

The hard part is not the evidence, it's dealing with the social result. Do we as a culture decide "Yes, it might be true, but it's too harmful, so we will act as if it's false?"

Give extra tutoring to those lower on the scale, and withhold it from those higher, to try to even the balance?

Give special advantage to those lower? Is there a way to do that without disadvantaging others? What sort of advantage?

Something else?

Each of those options has pros and cons.

It should be discussed, but like I said, it's politically difficult, so people try not to talk about it.

> You can google as easily as I can.

Unsure. But you're the one making the claim.

> If you accept the idea that a penchant for math is randomly distributed among all people

Is there any experimental support for such an assumption?

If.

You also need the assumption that the judges are unbiased and that people have equal opportunities.

Lots of room for explanation from many angles here.

The penchant for math is probably randomly distributed between men and women.

But all that is overshadowed by the fact that culturally and societally women are heavily discouraged from entering and succeeding in fields like math. This begins right from childhood, where an abacus may make a good toy for a boy, while the appropriate toy for a girl would be a mini kitchen set.

Fortunately a lot of this is changing, however, the benefits of no longer discouraging 50% of the population from entering science/engineering won't be felt for another couple of generations.

  > The penchant for math is probably randomly distributed
  between men and women.

Source?

  > But all that is overshadowed by the fact that culturally and
  > societally women are heavily discouraged from entering and succeeding
  > in fields like math.

Source?

  > This begins right from childhood, where an abacus may make a good toy for a boy, 
  > while the appropriate toy for a girl would be a mini kitchen set.

This is often repeated, but I doubt that's true.

> Source?

You mis-quoted; the original comment said:

> If you accept the idea that a penchant..

which was a response to:

> why is it shocking?

i.e. It answers the question, "Why might [someone] find this shocking?" - Note that user 'Hasz' was not the user that found it shocking.

If you think about it, a 55/56 ratio (.98) is only commensurate with a distribution of mathematical talent by which the vast majority of women can't add 2 and 2 together.

Like, it would not even justified by women being "somewhat" less good at maths at the high level than men. Women would have to be really, really bad at maths for that to be a natural result.

To see why this is not true think about the average difference in men and women’s height and the relative prevalence of men and women among people 1.6, 1.7, 1.8, 1.9m tall, etc.

The difference with height is that you can train mathematical skill. For women to be trying, presumably as hard as the men, to become good enough to be elligible for a Fields medal, but (almost) never achieving it- they have to really suck at maths to begin with.

Mathematical skill can be trainable without a huge difference in male/female representation implying women are unable to add two and two, your original bar for sucking at math.

There are many, many obviously trainable skills where the best men are very obviously superior to the best women, sports and athletics providing endless examples. I would be very happy just to finish a marathon but the Irish men’s world record is almost ten minutes faster than the woman’s world record.

Malright. That was a dumb argument. Mine I mean.

Nature vs nurture.

I meant shocking as in causing dismay, not surprising.

Women are vastly underrepresented in math.

50/56 is more likely. To get to 55/56 is quite an outlier.

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