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 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
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.
(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.
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?
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
A company-branded t-shirt and jeans?
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 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'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.
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?
How can you possibly know this?
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).
> 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.
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.
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.
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.
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.
Rubbing elbows with rich investors and CEOs from affluent backgrounds is definitely more difficult for someone from a lower class background.
With maths, you can work as a professor or work in finance. Two domains with limited demands that are highly competitive.
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.
Impostor syndrome is a real thing, and just repeating the comparisons you used in the tone you used, does not help address it.
My thoughts exactly.
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.
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.
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.
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.
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.
In general I think placement into top math undergrad/PhD programs (e.g. Harvard) should be less focused on contest math.
See Srinivasa Ramanujan for reference.
Because of this, Princeton offered Manjul Bhargava (another Fields winner) a tenure job right away without putting on the rigma role of tenure-track.
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.
Maryam Mirzakhani has been the only female recipient. 
 https://economics.mit.edu/files/7598 (admittedly a bit old; maybe a lot has changed in ~10 years?)
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.
That would seem rather detached from reality.
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.
The sex ratio gets progressively more extreme as you go further out in the tails.
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
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...
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.
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.
What kind of ability? Mathematical? IQ?
I don't know how well done those studies are though.
EDIT: I doubt it is that big though.
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".
As politically difficult as it is to say, intelligence is NOT distributed randomly among all people.
Not by sex, not by race.
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?
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.
Unsure. But you're the one making the claim.
Is there any experimental support for such an assumption?
Lots of room for explanation from many angles here.
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.
> 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.
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.
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.
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.
This statement is wrong 2x.
1. Lyonization is a process of inactivation that happens early in embryotic development so only one X is dominant in all somatic cells.
2. The chromatin packed X is not completely inactive, so if the dominant X has a deleterious variant the other X can sometime confer protection. Without a good copy of an X allele men getting X-linked disorder is a foregone conclusion. Women on the other hand suffer from X-linked disorders approximately 50-25% as often.
Also there is no evidence linking any of this to math ability
Edit: You know, it occurs to me maybe you aren't trying to put together statements that make any sense, because when you said "1. Lyonization is a process of inactivation that happens early in embryotic development so only one X is dominant in all somatic cells," you were acting like that's a support for your argument when it's in fact just a description of X-chromosome inactivation. Unless you meant that all cells pick the same chromosome, in which case you're just wrong.
In any case I direct the readers to this New York Times article which has a picture of a slice of the brain with different X chromosomes inactivated. Readers can draw their own conclusion about how this affects the probability of being in the top 0.001% of ability at anything.
You are right. I was wrong.
I was taught that X inactivation happens so early in development (I think pre-neural tube, no?? if so, that's like what, 200 total cells?) that all neurons, or at least all neural subtypes (e.g. Purkinje, pyramidal, basket, etc) all have the same dominant X chr.
When I saw the picture in the NYT article you linked, I was immediately like- no. fucking. way! Well, anyway. I'm sorry about that; and I appreciate the enlightenment.
That said, you should check out figure 8 in the original article. I'd be interested to know what you think. Here's a direct link:
(the paragraph just above the figure is helpful to read)
That sounds like something has been severely misunderstood by someone, possibly even me. Are you a biologist?
Or, like the saying goes- a little knowledge is a dangerous thing.
Women are vastly underrepresented in math.
There lies the ultimate discrimination resolution—at the level of the individual.