In my experience there’s an issue of Less Wrongers being unusually emotionally damaged (e.g. relative to academics) and this gives rise to a lot of problems in the community. But I don’t think that the emotional damage primarily comes from the weird stuff that you see on Less Wrong. What one sees is them having born the brunt of the phenomenon that I described here disproportionately relative to other smart people, often because they’re unusually creative and have been marginalized by conformist norms
Quite frankly, I find the norms in academia very creepy: I’ve seen a lot of people develop serious mental health problems in connection with their experiences in academia. It’s hard to see it from the inside: I was disturbed by what I saw, but I didn’t realize that math academia is actually functioning as a cult, based on retrospective impressions, and in fact by implicit consensus of the best mathematicians of the world (I can give references if you’d like) .
I was disturbed by what I saw, but I didn’t realize that math academia is actually functioning as a cult
I’m sure you’re aware that the word “cult” is a strong claim that requires a lot of evidence, but I’d also issue a friendly warning that to me at least it immediately set off my “crank” alarm bells. I’ve seen too many Usenet posters who are sure they have a P=/!=NP proof, or a proof that set theory is false, or etc. who ultimately claim that because “the mathematical elite” are a cult that no one will listen to them. A cult generally engages in active suppression, often defamation, and not simply exclusion. Do you have evidence of legitimate mathematical results or research being hidden/withdrawn from journals or publicly derided, or is it more of an old boy’s club that’s hard for outsiders to participate in and that plays petty politics to the damage of the science?
Grothendieck’s problems look to be political and interpersonal. Perelman’s also. I think it’s one thing to claim that mathematical institutions are no more rational than any other politicized body, and quite another to claim that it’s a cult. Or maybe most social behavior is too cult-like. If so; perhaps don’t single out mathematics.
I’ve seen a lot of people develop serious mental health problems in connection with their experiences in academia.
I question the direction of causation. Historically many great mathematicians have been mentally and socially atypical and ended up not making much sense with their later writings. Either mathematics has always had an institutional problem or mathematicians have always had an incidence of mental difficulties (or a combination of both; but I would expect one to dominate).
Especially in Thurston’s On Proof and Progress in Mathematics I can appreciate the problem of trying to grok specialized areas of mathematics. The terminology and symbology is opaque to the uninitiated. It reminds me of section 1 of the Metamath Book which expresses similar unhappiness with the state of knowledge between specialist fields of mathematics and the general difficulty of learning mathematics. I had hoped that Metamath would become more popular and tie various subfields together through unifying theories and definitions, but as far as I can tell it languishes as a hobbyist project for a few dedicated mathematicians.
I’m sure you’re aware that the word “cult” is a strong claim that requires a lot of evidence, but I’d also issue a friendly warning that to me at least it immediately set off my “crank” alarm bells.
Thanks, yeah, people have been telling me that I need to be more careful in how I frame things. :-)
Do you have evidence of legitimate mathematical results or research being hidden/withdrawn from journals or publicly derided, or is it more of an old boy’s club that’s hard for outsiders to participate in and that plays petty politics to the damage of the science?
The latter, but note that that’s not necessarily less damaging than active suppression would be.
Or maybe most social behavior is too cult-like. If so; perhaps don’t single out mathematics.
Yes, this is what I believe. The math community is just unusually salient to me, but I should phrase things more carefully.
I question the direction of causation. Historically many great mathematicians have been mentally and socially atypical and ended up not making much sense with their later writings. Either mathematics has always had an institutional problem or mathematicians have always had an incidence of mental difficulties (or a combination of both; but I would expect one to dominate).
Most of the people who I have in mind did have preexisting difficulties. I meant something like “relative to a counterfactual where academia was serving its intended function.” People of very high intellectual curiosity sometimes approach academia believing that it will be an oasis and find this not to be at all the case, and that the structures in place are in fact hostile to them.
This is not what the government should be supporting with taxpayer dollars.
Especially in Thurston’s On Proof and Progress in Mathematics I can appreciate the problem of trying to grok specialized areas of mathematics.
The latter, but note that that’s not necessarily less damaging than active suppression would be.
I suppose there’s one scant anecdote for estimating this; cryptography research seemed to lag a decade or two behind actively suppressed/hidden government research. Granted, there was also less public interest in cryptography until the 80s or 90s, but it seems that suppression can only delay publication, not prevent it.
The real risk of suppression and exclusion both seem to be in permanently discouraging mathematicians who would otherwise make great breakthroughs, since affecting the timing of publication/discovery doesn’t seem as damaging.
This is not what the government should be supporting with taxpayer dollars.
I think I would be surprised if Basic Income was a less effective strategy than targeted government research funding.
What are your own interests?
Everything from logic and axiomatic foundations of mathematics to practical use of advanced theorems for computer science. What attracted me to Metamath was the idea that if I encountered a paper that was totally unintelligible to me (say Perelman’s proof of Poincaire’s conjecture or Wiles’ proof of Fermat’s Last Theorem) I could backtrack through sound definitions to concepts I already knew, and then build my understanding up from those definitions. Alas, just having a cross-reference of related definitions between various fields would be helpful. I take it that model theory is the place to look for such a cross-reference, and so that is probably the next thing I plan to study.
Practically, I realize that I don’t have enough time or patience or mental ability to slog through formal definitions all day, and so it would be nice to have something even better. A universal mathematical educator, so to speak. Although I worry that without a strong formal understanding I will miss important results/insights. So my other interest is building the kind of agent that can identify which formal insights are useful or important, which sort of naturally leads to an interest in AI and decision theory.
I would like to see some of those references (simply because I have no relation to Academia, and don’t like things I read somewhere to gestate into unfounded intuitions about a subject).
Quite frankly, I find the norms in academia very creepy: I’ve seen a lot of people develop serious mental health problems in connection with their experiences in academia. It’s hard to see it from the inside: I was disturbed by what I saw, but I didn’t realize that math academia is actually functioning as a cult, based on retrospective impressions, and in fact by implicit consensus of the best mathematicians of the world (I can give references if you’d like) .
I’ve only been in CS academia, and wouldn’t call that a cult. I would call it, like most of the rest of academia, a deeply dysfunctional industry in which to work, but that’s the fault of the academic career and funding structure. CS is even relatively healthy by comparison to much of the rest.
How much of our impression of mathematics as a creepy, mental-health-harming cult comes from pure stereotyping?
I was more positing that it’s a self-reinforcing, self-creating effect: people treat Mathematics in a cultish way because they think they’re supposed to.
For what its worth, I have observed a certain reverence in the way great mathematicians are treated by their lesser-accomplished colleagues that can often border on the creepy. This is something specific to math, in that it seems to exist in other disciplines with lesser intensity.
But I agree, “dysfunctional” seems to be a more apt label than “cult.” May I also add “fashion-prone?”
Finally, Alan Turing, the great Bletchley Park code breaker, father of computer science and homosexual, died trying to prove that some things are fundamentally unprovable.
This is a staggeringly wrong account of how he died.
I don’t have direct exposure to CS academia, which, as you comment, is known to be healthier :-). I was speaking in broad brushstrokes , I’ll qualify my claims and impressions more carefully later.
The top 3 answers to the MathOverflow question Which mathematicians have influenced you the most? are Alexander Grothendieck, Mikhail Gromov, and Bill Thurston. Each of these have expressed serious concerns about the community.
Grothendieck was actually effectively excommunicated by the mathematical community and then was pathologized as having gone crazy. See pages 37-40 of David Ruelle’s book A Mathematician’s Brain.
Gromov expresses strong sympathy for Grigory Perelman having left the mathematical community starting on page 110 of Perfect Rigor. (You can search for “Gromov” in the pdf to see all of his remarks on the subject.)
Thurston made very apt criticisms of the mathematical community in his essay On Proof and Progress In Mathematics. See especially the beginning of Section 3: “How is mathematical understanding communicated?” Terry Tao endorses Thurston’s essay in his obituary of Thurston. But the community has essentially ignored Thurston’s remarks: one almost never hears people talk about the points that Thurston raises.
I don’t know about Grothendieck, but the two other sources appear to have softer criticism of the mathematical community than “actually functioning as a cult”.
The links you give are extremely interesting, but, unless I am missing something, it seems that they fall short of justifying your earlier statement that math academia functions as a cult. I wonder if you would be willing to elaborate further on that?
The most scary thing to me is that the most mathematically talented students are often turned off by what they see in math classes, even at the undergraduate and graduate levels. Math serves as a backbone for the sciences, so this may badly undercutting scientific innovation at a societal level.
I honestly think that it would be an improvement on the status quo to stop teaching math classes entirely. Thurston characterized his early math education as follows:
I hated much of what was taught as mathematics in my early schooling, and I often received poor grades. I now view many of these early lessons as anti-math: they actively tried to discourage independent thought. One was supposed to follow an established pattern with mechanical precision, put answers inside boxes, and “show your work,” that is, reject mental insights and alternative approaches.
I think that this characterizes math classes even at the graduate level, only at a higher level of abstraction. The classes essentially never offer students exposure to free-form mathematical exploration, which is what it takes to make major scientific discoveries with significant quantitative components.
I distinctly remember having points taken off of a physics midterm because I didn’t show my work. I think I dropped the exam in the waste basket on the way out of the auditorium.
I’ve always assumed that the problem is three-fold; generating a formal proof is NP-hard, getting the right answer via shortcuts can include cheating, and the faculty’s time is limited. Professors/graders do not have the capacity to rigorously demonstrate to themselves that the steps a student has written down actually pinpoint the unique answer. Without access to the student’s mind graders are unable to determine if students cheat or not; being able to memorize and/or reproduce the exact steps of a calculation significantly decrease the likelihood of cheating. Even if graders could do one or both of the previous for a single student, they are not 30x or 100x as smart as their students, making it impractical to repeat the process for every student.
That said, I had some very good mathematics teachers in higher level courses who could force students to think, and one in particular who could encourage/demand novelty from students simply by asking them to solve problems that they hadn’t yet learned to solve. I didn’t realize the power of the latter approach until later (and at the time everyone complained about exams with a median score well under 50%), but his classes were always my favorite.
Thank you for all these interesting references. I enjoyed reading all of them, and rereading in Thurston’s case.
Do people pathologize Grothendieck as having gone crazy? I mostly think people think of him as being a little bit strange. The story I heard was that because of philosophical disagreements with military funding and personal conflicts with other mathematicians he left the community and was more or less refusing to speak to anyone about mathematics, and people were sad about this and wished he would come back.
Do people pathologize Grothendieck as having gone crazy?
His contribution of math is too great for people to have explicitly adopted a stance that was too unfavorable to him, and many mathematicians did in fact miss him a lot. But as Perelman said:
Of course, there are many mathematicians who are more or less honest. But almost all of them are conformists. They are more or less honest, but they tolerate those who are not honest.” He has also said that “It is not people who break ethical standards who are regarded as aliens. It is people like me who are isolated.
If pressed, many mathematicians downplay the role of those who behaved unethically toward him and the failure of the community to give him a job in favor of a narrative “poor guy, it’s so sad that he developed mental health problems.”
I’m sympathetic to everything you say.
In my experience there’s an issue of Less Wrongers being unusually emotionally damaged (e.g. relative to academics) and this gives rise to a lot of problems in the community. But I don’t think that the emotional damage primarily comes from the weird stuff that you see on Less Wrong. What one sees is them having born the brunt of the phenomenon that I described here disproportionately relative to other smart people, often because they’re unusually creative and have been marginalized by conformist norms
Quite frankly, I find the norms in academia very creepy: I’ve seen a lot of people develop serious mental health problems in connection with their experiences in academia. It’s hard to see it from the inside: I was disturbed by what I saw, but I didn’t realize that math academia is actually functioning as a cult, based on retrospective impressions, and in fact by implicit consensus of the best mathematicians of the world (I can give references if you’d like) .
I’m sure you’re aware that the word “cult” is a strong claim that requires a lot of evidence, but I’d also issue a friendly warning that to me at least it immediately set off my “crank” alarm bells. I’ve seen too many Usenet posters who are sure they have a P=/!=NP proof, or a proof that set theory is false, or etc. who ultimately claim that because “the mathematical elite” are a cult that no one will listen to them. A cult generally engages in active suppression, often defamation, and not simply exclusion. Do you have evidence of legitimate mathematical results or research being hidden/withdrawn from journals or publicly derided, or is it more of an old boy’s club that’s hard for outsiders to participate in and that plays petty politics to the damage of the science?
Grothendieck’s problems look to be political and interpersonal. Perelman’s also. I think it’s one thing to claim that mathematical institutions are no more rational than any other politicized body, and quite another to claim that it’s a cult. Or maybe most social behavior is too cult-like. If so; perhaps don’t single out mathematics.
I question the direction of causation. Historically many great mathematicians have been mentally and socially atypical and ended up not making much sense with their later writings. Either mathematics has always had an institutional problem or mathematicians have always had an incidence of mental difficulties (or a combination of both; but I would expect one to dominate).
Especially in Thurston’s On Proof and Progress in Mathematics I can appreciate the problem of trying to grok specialized areas of mathematics. The terminology and symbology is opaque to the uninitiated. It reminds me of section 1 of the Metamath Book which expresses similar unhappiness with the state of knowledge between specialist fields of mathematics and the general difficulty of learning mathematics. I had hoped that Metamath would become more popular and tie various subfields together through unifying theories and definitions, but as far as I can tell it languishes as a hobbyist project for a few dedicated mathematicians.
Thanks, yeah, people have been telling me that I need to be more careful in how I frame things. :-)
The latter, but note that that’s not necessarily less damaging than active suppression would be.
Yes, this is what I believe. The math community is just unusually salient to me, but I should phrase things more carefully.
Most of the people who I have in mind did have preexisting difficulties. I meant something like “relative to a counterfactual where academia was serving its intended function.” People of very high intellectual curiosity sometimes approach academia believing that it will be an oasis and find this not to be at all the case, and that the structures in place are in fact hostile to them.
This is not what the government should be supporting with taxpayer dollars.
What are your own interests?
I suppose there’s one scant anecdote for estimating this; cryptography research seemed to lag a decade or two behind actively suppressed/hidden government research. Granted, there was also less public interest in cryptography until the 80s or 90s, but it seems that suppression can only delay publication, not prevent it.
The real risk of suppression and exclusion both seem to be in permanently discouraging mathematicians who would otherwise make great breakthroughs, since affecting the timing of publication/discovery doesn’t seem as damaging.
I think I would be surprised if Basic Income was a less effective strategy than targeted government research funding.
Everything from logic and axiomatic foundations of mathematics to practical use of advanced theorems for computer science. What attracted me to Metamath was the idea that if I encountered a paper that was totally unintelligible to me (say Perelman’s proof of Poincaire’s conjecture or Wiles’ proof of Fermat’s Last Theorem) I could backtrack through sound definitions to concepts I already knew, and then build my understanding up from those definitions. Alas, just having a cross-reference of related definitions between various fields would be helpful. I take it that model theory is the place to look for such a cross-reference, and so that is probably the next thing I plan to study.
Practically, I realize that I don’t have enough time or patience or mental ability to slog through formal definitions all day, and so it would be nice to have something even better. A universal mathematical educator, so to speak. Although I worry that without a strong formal understanding I will miss important results/insights. So my other interest is building the kind of agent that can identify which formal insights are useful or important, which sort of naturally leads to an interest in AI and decision theory.
I would like to see some of those references (simply because I have no relation to Academia, and don’t like things I read somewhere to gestate into unfounded intuitions about a subject).
I’ve only been in CS academia, and wouldn’t call that a cult. I would call it, like most of the rest of academia, a deeply dysfunctional industry in which to work, but that’s the fault of the academic career and funding structure. CS is even relatively healthy by comparison to much of the rest.
How much of our impression of mathematics as a creepy, mental-health-harming cult comes from pure stereotyping?
Jonah happens to be a math phd. How can you engage in pure stereotyping of mathematicians while you get your PHD?
I was more positing that it’s a self-reinforcing, self-creating effect: people treat Mathematics in a cultish way because they think they’re supposed to.
I don’t believe there’s any such thing, on the general grounds of “no fake without a reality to be a fake of.”
Who do you mean when you say “people”?
For what its worth, I have observed a certain reverence in the way great mathematicians are treated by their lesser-accomplished colleagues that can often border on the creepy. This is something specific to math, in that it seems to exist in other disciplines with lesser intensity.
But I agree, “dysfunctional” seems to be a more apt label than “cult.” May I also add “fashion-prone?”
Er, what? Who do you mean by “we”?
The link says of Turing:
This is a staggeringly wrong account of how he died.
Hence my calling it “pure stereotyping”!
I don’t have direct exposure to CS academia, which, as you comment, is known to be healthier :-). I was speaking in broad brushstrokes , I’ll qualify my claims and impressions more carefully later.
I don’t really understand what you mean about math academia. Those references would be appreciated.
The top 3 answers to the MathOverflow question Which mathematicians have influenced you the most? are Alexander Grothendieck, Mikhail Gromov, and Bill Thurston. Each of these have expressed serious concerns about the community.
Grothendieck was actually effectively excommunicated by the mathematical community and then was pathologized as having gone crazy. See pages 37-40 of David Ruelle’s book A Mathematician’s Brain.
Gromov expresses strong sympathy for Grigory Perelman having left the mathematical community starting on page 110 of Perfect Rigor. (You can search for “Gromov” in the pdf to see all of his remarks on the subject.)
Thurston made very apt criticisms of the mathematical community in his essay On Proof and Progress In Mathematics. See especially the beginning of Section 3: “How is mathematical understanding communicated?” Terry Tao endorses Thurston’s essay in his obituary of Thurston. But the community has essentially ignored Thurston’s remarks: one almost never hears people talk about the points that Thurston raises.
I don’t know about Grothendieck, but the two other sources appear to have softer criticism of the mathematical community than “actually functioning as a cult”.
The links you give are extremely interesting, but, unless I am missing something, it seems that they fall short of justifying your earlier statement that math academia functions as a cult. I wonder if you would be willing to elaborate further on that?
I’ll be writing more about this later.
The most scary thing to me is that the most mathematically talented students are often turned off by what they see in math classes, even at the undergraduate and graduate levels. Math serves as a backbone for the sciences, so this may badly undercutting scientific innovation at a societal level.
I honestly think that it would be an improvement on the status quo to stop teaching math classes entirely. Thurston characterized his early math education as follows:
I hated much of what was taught as mathematics in my early schooling, and I often received poor grades. I now view many of these early lessons as anti-math: they actively tried to discourage independent thought. One was supposed to follow an established pattern with mechanical precision, put answers inside boxes, and “show your work,” that is, reject mental insights and alternative approaches.
I think that this characterizes math classes even at the graduate level, only at a higher level of abstraction. The classes essentially never offer students exposure to free-form mathematical exploration, which is what it takes to make major scientific discoveries with significant quantitative components.
I distinctly remember having points taken off of a physics midterm because I didn’t show my work. I think I dropped the exam in the waste basket on the way out of the auditorium.
I’ve always assumed that the problem is three-fold; generating a formal proof is NP-hard, getting the right answer via shortcuts can include cheating, and the faculty’s time is limited. Professors/graders do not have the capacity to rigorously demonstrate to themselves that the steps a student has written down actually pinpoint the unique answer. Without access to the student’s mind graders are unable to determine if students cheat or not; being able to memorize and/or reproduce the exact steps of a calculation significantly decrease the likelihood of cheating. Even if graders could do one or both of the previous for a single student, they are not 30x or 100x as smart as their students, making it impractical to repeat the process for every student.
That said, I had some very good mathematics teachers in higher level courses who could force students to think, and one in particular who could encourage/demand novelty from students simply by asking them to solve problems that they hadn’t yet learned to solve. I didn’t realize the power of the latter approach until later (and at the time everyone complained about exams with a median score well under 50%), but his classes were always my favorite.
Thank you for all these interesting references. I enjoyed reading all of them, and rereading in Thurston’s case.
Do people pathologize Grothendieck as having gone crazy? I mostly think people think of him as being a little bit strange. The story I heard was that because of philosophical disagreements with military funding and personal conflicts with other mathematicians he left the community and was more or less refusing to speak to anyone about mathematics, and people were sad about this and wished he would come back.
His contribution of math is too great for people to have explicitly adopted a stance that was too unfavorable to him, and many mathematicians did in fact miss him a lot. But as Perelman said:
Of course, there are many mathematicians who are more or less honest. But almost all of them are conformists. They are more or less honest, but they tolerate those who are not honest.” He has also said that “It is not people who break ethical standards who are regarded as aliens. It is people like me who are isolated.
If pressed, many mathematicians downplay the role of those who behaved unethically toward him and the failure of the community to give him a job in favor of a narrative “poor guy, it’s so sad that he developed mental health problems.”
What failure? He stepped down from the Steklov Institute and has refused every job offer and prize given to him.
From the details I’m aware of “gone crazy” is not a bad description of what happened.