6 ms·

It's not mathematics that you need to contribute to (2010)

187 points by susam 3y ago

susam 3y ago
Some background about the author of this MathOverflow answer: > William Paul Thurston (October 30, 1946 – August 21, 2012) was an American mathematician. He was a pioneer in the field of low-dimensional topology and was awarded the Fields Medal in 1982 for his contributions to the study of 3-manifolds. Source: https://en.wikipedia.org/wiki/William_Thurston https://en.wikipedia.org/wiki/William_Thurston
- KnobbleMcKnees 3y ago
  Wow so he was 74 when he wrote that answer, and this comment that he followed up with: > I try to write what seems real. By now, I have no cause to fear how I will be judged, which makes it much easier for me.
  - deleted 3y ago
    [deleted]
  - susam 3y ago
    I especially liked this comment that proposed that this answer be called Thurston's Paean: > This seems like an ideal counterpoint to Hardy's Lament. I'm calling it Thurston's Paean :). Seems poignant now that he has passed. -- Suresh Venkat (Aug 22, 2012) I agree. I have now dedicated a page to Thurston's answer at https://susam.net/maze/thurstons-paean.html https://susam.net/maze/thurstons-paean.html hoping that it'll make the term Thurston's Paean slightly more popular.
    - jdsalaro 3y ago
      We're doing this, aren't we? :) Let's hope the BART and ChatGPT folks crawl it soon enough haha https://jdsalaro.com/bookmark/quote/thurstons-paean/ https://jdsalaro.com/bookmark/quote/thurstons-paean/
    - two_handfuls 3y ago
      Forgive the naïve question, but what is Hardy's lament?
      - ducttapecrown 3y ago
        Hardy's lament is a short popular essay about how the famous professional mathematician Hardy experiences math as art with the curiosity of a child, and yet the average school math education evokes a prison of rote exercise. It was written in 1940 and I think at some point he says something about number theory being pure math with no applications. Ironically I'm submitting this comment over https so he was wrong about that. https://en.wikipedia.org/wiki/A_Mathematician%27s_Apology https://en.wikipedia.org/wiki/A_Mathematician%27s_Apology
  - MYEUHD 3y ago
    > Wow so he was 74 when he wrote that answer Actually, he was 64
    - arcanemachiner 3y ago
      That was just GP honoring the title of the post.
      - susam 3y ago
        What do you mean? http://web.archive.org/web/20230718104503/https://news.ycombinator.com/item?id=36744690 http://web.archive.org/web/20230718104503/https://news.ycomb... shows "(2010)" and 2010 - 1946 = 64.
        bobthepanda 3y ago
        It’s a joke about the parent comment being bad at math, so maybe they don’t need to contribute
    - KnobbleMcKnees 3y ago
      Yeah, fatigue got the better of me there
- perihelions 3y ago
  So, where he writes on StackOverflow - "Is there, for example any real reason that even such famous results as... the Poincaré conjecture, really matter?" He is writing from the perspective of someone who played a key role in solving the Poincaré conjecture. Remarkable context! (Though the word "Poincaré" doesn't technically appear in his Wikipedia biography; it's disguised as "geometrization conjecture").
  - fsckboy 3y ago
    and where he writes "I think of mathematics as having a large component of psychology, because of its strong dependence on human minds. Dehumanized mathematics would be more like computer code, which is very different" he's just blowing smoke. smh so dumb.
- bjornlouser 3y ago
  Mentioned in a comment of that MO question is Thurston's "On proof and progress in mathematics" https://arxiv.org/abs/math/9404236 https://arxiv.org/abs/math/9404236
Rygian 3y ago
I scrolled up the page and saw the following banner, which (in hindsight) couldn't be more wrong. > This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.
- enriquto 3y ago
  It's a longtime trope of these "stack" sites: the best questions with the best answers are those that are marked as offtopic, closed, deleted, downvoted or otherwise rejected. It's a marker of good quality at this point.
  - tux3 3y ago
    Marker of good quality would be too far (and biased), as the every growing mass of genuinely hard to salvage closed question certainly outnumbers the interesting ones But it sure looks to be bimodal. Marker of the really bad, and the so-good-it's-closed
    - mannykannot 3y ago
      I would guess that this bimodality correlates with one in the personalities of those who become moderators - on the one hand, those who are willing to put a lot of effort into keeping the community relevant, and on the other, those who abhor any perceived irregularity. On occasion, when I get invitations to participate in moderator elections, I look to see if I recognize any of the candidates. Once or twice, I have looked through the candidates' resumes, and one thing that struck me was that some of them did a lot more down-voting than up-voting. Make of that what you will.
  - jimhefferon 3y ago
    I also have found that often the answers that make me reflect the most on SO are treated this way by the mods. Does this effect have a name?
jonsen 3y ago
From a comment there: > Thematically this is similar to a (much longer) essay Dr. Thurston wrote several years ago, which I highly recommend: https://arxiv.org/abs/math/9404236 https://arxiv.org/abs/math/9404236
w4termelon 3y ago
So, what's so special about this answer? Seems like a pasta, replace "mathematics" by {SUBJECTNAME} and you get yet another popular idea of the day. Startup founders, for one, having been claiming they are "contributing to humanity" for ages now.
- pxc 3y ago
  People often think of mathematics as uniquely objective, and as standing apart from the social processes of collaboration and invention. And mathematics kind of is special in some of those ways. But mathematicians know, while laypeople might not, that at its core, mathematics remains a social endeavor just like the rest of the sciences. That's the piece which is a really valuable reminder imo.
tomrod 3y ago
This is beautiful. I unfortunately haven't seen Thurston's work before. Much respect for this man.
macleginn 3y ago
"The world does not suffer from an oversupply of clarity and understanding (to put it mildly)" – how this can be remedied by mathematical thinking, though, is rather unclear. Take the USSR with its strong tradition of math education in secondary schools and math research. Despite producing a lot of important results and some painfully beautiful math books, like Gelfand's Linear algebra, it has more or less zero effect on the wider society or even wider intellectual discourse.
- hyperparameter 3y ago
  > Despite producing a lot of important results and some painfully beautiful math books, like Gelfand's Linear algebra, it has more or less zero effect on the wider society or even wider intellectual discourse. In Computer Science we have Adelson-Velsky and Landis's self-balanced binary trees, and many other results, as well as other results in math and the sciences. In engineering and otherwise the USSR launched the first satellite, person in space, sent the first probes to the moon and other planets, and pushed the US into space. The civil rights moment in the US was often accused of being communist because - a lot of it was communist, and supported by the USSR, at least in the days of Paul Robeson and the Scottsboro Boys and Martin Luther King at the Highland Folk school (billboards through the South had a picture of King there "King at communist training school"). Actually if you watch the Nightline of Mandela coming to the US, half the speakers accused him of being a USSR-aligned communist. The USSR contributed to the anti-colonial struggles around the world - from China to Cuba to Vietnam, and contributed to it in other countries like India. Plus it did most of the fighting in WWII for the US and UK to defeat Germany (of course nowadays the US and UK flipped it to Germany against Russia). The USSR also helped push a blue collar working class proletariat into a kind of middle class. This began being rolled back even when the USSR still existed but was weak, and is still being rolled back.
  - mmmmmmtoes 3y ago
    [dead]
  - rcxdude 3y ago
    > Plus it did most of the fighting in WWII for the US and UK to defeat Germany (of course nowadays the US and UK flipped it to Germany against Russia). That's quite a spin on history. The USSR (already an imperialist power) and germany secretly divvied up eastern europe between themselves before Germany started the war, and it was only Germany's betrayal of that deal which led to the USSR actually joining the fight against Germany, with the US and UK finding it a convenient way to wear down a shared foe to provide them with some of their industrial capacity. You make it sound like this was some kind of puppet mastery by the US and UK (which to be clear, are not saints either, but decidedly on the right side in WWII) as opposed to two imperialist powers seeking to conquer others by force fighting amongst themselves.
FrustratedMonky 3y ago
Good point about understanding. Lets say there is a catastrophe, world goes to hell, understanding is lost. Then people go into a library and start opening books. The arcane symbols of Math would be indistinguishable from books of magic. Without the understanding, fresh minds would be hard pressed to distinguish math formula from magic runes. The understanding of the math comes from some community of people passing it along from generation to generation more than from the symbols.
- mejutoco 3y ago
  Principia Mathematica for sure. Other, like visual proofs would pass this test better I believe.
Errancer 3y ago
I feel like this comment hits at the general discussion of "Why should I learn something which I won't be the best at?" and it applies just as well to maths, science and arts: you should learn it since if you really enjoy it then you can contribute by maintaining a healthy community around it; and this can mean really working on the community or just being a person who can understand the value of discoveries of others. Having a good audience is the dream of every artist and I think this applies quite universally.
wwweston 3y ago
This is a comment I think about a lot lately when it comes to discussions of AI and art too — if there’s a hazard in “dehumanized mathematics” and value in mathematics as community and reflection of human understanding then surely there’s something similar in art as communal conversation and reflection of human experience.
effed3 3y ago
I'm my mind echoed something like... "don't ask yourself what you can do for mathematics, but what mathematics can do for you.." in my opinion the 1st/biggest contribution to math (and any science, discipline, art, and work) is to study/pratice it, is the best contribution to a living body of knowledge and wisdom, new ideas and discovery are side effect, welcomed, but not mandatory.. but is the discipline involved that change the single and later the world. The sea is made of drops.. the true goal is the/any-single way in praticing, not the end/highest point (if exist).
lo_zamoyski 3y ago
We must distinguish between theoria, praxis, and poiesis. Praxis, or the practical, has as its end action, something other than itself. When I clean my house, I don't do this for its own sake, I do this for the sake of having a clean house to live in. Similarly, poiesis, or production, also has something other than itself as an end, some thing. When I cook dinner, I don't cook it for its own sake, I cook it to feed myself and others. On the other hand, theoria, or theory, has as its end truth. The truth has practical consequences, of course, but there are truths that are valuable knowing for their own sake. Ends, of course, need a terminus. While a practical or productive act terminates in something other than itself, you must now ask what the end itself is for. Is it for itself, or something else further still? When we follow practical and productive ends, they must ultimately terminate at something that is not for the sake of anything else, but is valuable in itself. Indeed, when I said the truth has practical consequences, it was an understatement; the entire regime of practical and productive activity presupposes an ultimate end for the sake of which it exists, that justifies it, that it is in service of. I will omit discussion of the ultimate here intentionally, because my purpose here is to frame the problem first and predispose the mind toward the answer; giving the answer straight away, or an answer, is more likely to trigger reflexive prejudices here, I think. Once framed this way, people are liberated to ask "whom or what do I ultimately serve? why do I live? why do I act?". The vista of ends and order is thrown open for examination. This clarity enables one to leave Plato's "cave" and makes it difficult to obfuscate and settle for cheap answers as it can corner the conscience into pestering us to reject dishonest rationalizations. Of course, people will often try to do so, but doing so is more likely to gnaw at the soul, something that can prompt people to keep searching instead of holing up in an intellectual ghetto and persist in mediocrity. Now you can approach the original question.
- haswell 3y ago
  > We must distinguish between theoria, praxis, and poiesis. Must we? > When I clean my house, I don't do this for its own sake, I do this for the sake of having a clean house to live in. Why not both? A clean house isn’t necessary for survival. Why do you enjoy a clean house? For its own sake perhaps? Many would argue that we do these things for the sake of them as much as we do these things out of necessity. Reframed slightly, we do many things for the sake of doing them, and we seem to enjoy bringing this mindset to the necessities of life. Mihaly Csikszentmihalyi explores this extensively in Flow, and it’s a recurrent theme in many contemplative traditions. > When I cook dinner, I don't cook it for its own sake, I cook it to feed myself and others. Again, why not both? If the only value gained from cooking is sustenance, why do we enjoy dessert? Why do we enjoy it more when other people are with us? I’m not saying we don’t do things for reasons or that it’s uninteresting to assign labels to those reasons and explore them, but such intellectual/philosophical framings are ultimately just reductions of unfolding experience into a low resolution explanation of reality relative to our immersion in it. Should we explore these ideas? Yes. Must they be the foundation from which we explore other ideas? I don’t think so. Sometimes, sure.
adamsmith143 3y ago
Just want to point out how cool it is that a Field Medal winner is on MO. Don't know if any Turing Award winners or someone like Jeff Dean is on StackOverflow.
ke88y 3y ago
> Mathematical ideas, even simple ideas, are often hard to transplant from mind to mind.... Our understanding frequently deteriorates as well... The experts in a subject retire and die, or simply move on to other subjects and forget.... In short, mathematics only exists in a living community of mathematicians that spreads understanding and breaths life into ideas both old and new. One of the great things about software is that you don't need a living community that holds every bit of every code base in their head. You can rely on abstraction boundaries, and then jump down rabbit holes only if and when necessary. I really wonder how the work of Mathematics will change once computer-encoded proofs become mainstream. I have to imagine that will happen within the next generation or two -- as soon as the automation becomes more helpful than the hindrance of formality.
- Ericson2314 3y ago
  https://github.com/leanprover-community/mathlib https://github.com/leanprover-community/mathlib https://1lab.dev/ https://1lab.dev/ You can watch the next generation, or participate, right now.
- robryk 3y ago
  I think you're missing his point. He does acknowledge that statements of facts and their proofs can be easily communicated, but claims that the understanding their discovery was a side effect of cannot be communicated easily. This is not affected by having a better way to express facts and their proofs.
  - ke88y 3y ago
    No, I get his point. I think the transmission of knowledge and insight and clarity works very differently for executable artifacts than for artifacts written in natural language. > This is not affected by having a better way to express facts and their proofs. But it is if those expressions are possible to interact with and use through not only conceptual abstraction but also procedural abstraction. With good proof automation? Maybe you can interact and play with ideas through many layers of automation-enabled abstraction. Maybe you have a tactic or ATP procedure that uses a lemma in clever ways without you even knowing it exists, and only after building on that edifice for years do you bother to dig in and understand what the proof automation is even using. Mind you: not what the lemma means or how it's proven or the underlying historical development of ideas, but that it even exists. Maybe you never dig in and realize it exists. Maybe you use these new theorems and proofs -- discovered only through extremely essential and clever use of a critical lemma you don't even know that you are using -- to do something useful in the world. That can't happen today; not really. It would take very powerful proof automation for this world to exist. Code and books are very different things.
ke88y 3y ago
I really like this view of academic research in general. The field does not exist as a means unto itself, but as a tool for helping and contributing to humanity. A service mindset. That's how I have always viewed both research and teaching. The most frustrating part of academia, and one of the main reasons I left, was the sense that everyone had completely lost their service mindset. The result is a set of sclerotic institutions -- protected from competition by rules and norms motivated by an ostensibly noble purpose -- wrecking havoc on society. In research, in particular, it's now rare to find researchers who really give a damn about anyone except themselves. Their PhD students are tools for increasing faculty influence. The motivation section of their grants are polite lies and everyone knows it. The whole thing is a big inside joke that people laugh about in elevator bays, backed by billions of taxpayer dollars. The selfishness and complete disinterest in stewardship of public funds is nauseating. But things are worst in undergraduate education. You occasionally meet someone worried about the educational mission, but no one was ever interested in the overall well-being of students. Financial well-being, in particular, is a verboten topic. The question of whether a particular degree program might be doing irreversible and crippling financial damage to nearly every student is considered rude. The question of whether requiring a certain course might be a waste of a customer's money is derided ("they aren't customers!", despite paying mid 5 figures per year for shockingly little face-to-face time.) Academia has completely lost its historically service-oriented pursuit. The faculty are motivated by a combination of laziness, entitlement, and ego. The administration is motivated by the same incentives as any other industry. But huge quantities of tax dollars are locked up in this broken and corrupt industry.
- everybodyknows 3y ago
  It would help if you could tell us about your specific positions in academia, those which informed these observations.
  - ke88y 3y ago
    PhD student and faculty (quite briefly). Serving on grant panels also informed this view, but looking back, I think I was already getting disgusted by the culture of academia around my second year of grad school. My immediate family spent/spends much more time in academia than I, including the person I live with who has built their career in academia. My own experience of academia was actually quite positive -- I enjoyed my PhD years, was well-supported, received many tenure-track offers from elite institutions immediately out of my PhD, and I left on better than good terms with coworkers and former colleagues. My assessment isn't a result of personal bitterness or a failure to "win the game", if that's what you're getting at. Quite the opposite, in fact -- doing extremely well in the early career game afforded me the personal confidence to leave the track to which I had previously committed. (FWIW, the fact that I'll retire many decades earlier than I would've otherwise was not immaterial to my decision making)
BSEdlMMldESB 3y ago
> Mathematical ideas, even simple ideas, are often hard to transplant from mind to mind. this is a problematic way to frame the issue which I agree is very difficult. by framing it like this, I think, it sets up this task to be impossible. I'm also considering a subtle distinction between 'teaching' and 'education' he's using a teaching framework. to put the idea in the head of the student. but education is more about guiding the student to find the answer on their own; if teaching is difficult, education may seem freaking impossible. with a 'teaching framework' simple ideas are more difficult (and complex ones turn impossible) but with the 'education framework' (which in my direct experience is not available publicly) simple ideas may be trickier, but the hope is that sophisticated ideas will become easier to communicate.... dunno
CliffStoll 3y ago
Bill Thurston! He did amazing topology - hyperbolic knot compliments, Foliations, eversion of the sphere, geometrization conjecture... A brilliant man. I had the honor of meeting him several times here in Berkeley; he encouraged me to make Klein bottles and other topological shapes.
- Munksgaard 3y ago
  Cliff! I've had a plan to buy a bottle from you for a long time. Do you still have any left?
joewferrara 3y ago
This essay by the same person who answered the mathoverflow post greatly expands on the ideas in the post. https://arxiv.org/pdf/math/9404236.pdf https://arxiv.org/pdf/math/9404236.pdf It’s a great read for young people interested in mathematics and influenced me while in undergrad deciding to persue a PhD in math. Thurston, the author, was one of the best mathematicians of his time.

187 points by susam 3y ago

Some background about the author of this MathOverflow answer: > William Paul Thurston (October 30, 1946 – August 21, 2012) was an American mathematician. He was a pioneer in the field of low-dimensional topology and was awarded the Fields Medal in 1982 for his contributions to the study of 3-manifolds. Source: https://en.wikipedia.org/wiki/William_Thurston https://en.wikipedia.org/wiki/William_Thurston

KnobbleMcKnees 3y ago
Wow so he was 74 when he wrote that answer, and this comment that he followed up with: > I try to write what seems real. By now, I have no cause to fear how I will be judged, which makes it much easier for me.
- deleted 3y ago
  [deleted]
- susam 3y ago
  I especially liked this comment that proposed that this answer be called Thurston's Paean: > This seems like an ideal counterpoint to Hardy's Lament. I'm calling it Thurston's Paean :). Seems poignant now that he has passed. -- Suresh Venkat (Aug 22, 2012) I agree. I have now dedicated a page to Thurston's answer at https://susam.net/maze/thurstons-paean.html https://susam.net/maze/thurstons-paean.html hoping that it'll make the term Thurston's Paean slightly more popular.
  - jdsalaro 3y ago
    We're doing this, aren't we? :) Let's hope the BART and ChatGPT folks crawl it soon enough haha https://jdsalaro.com/bookmark/quote/thurstons-paean/ https://jdsalaro.com/bookmark/quote/thurstons-paean/
  - two_handfuls 3y ago
    Forgive the naïve question, but what is Hardy's lament?
    - ducttapecrown 3y ago
      Hardy's lament is a short popular essay about how the famous professional mathematician Hardy experiences math as art with the curiosity of a child, and yet the average school math education evokes a prison of rote exercise. It was written in 1940 and I think at some point he says something about number theory being pure math with no applications. Ironically I'm submitting this comment over https so he was wrong about that. https://en.wikipedia.org/wiki/A_Mathematician%27s_Apology https://en.wikipedia.org/wiki/A_Mathematician%27s_Apology
- MYEUHD 3y ago
  > Wow so he was 74 when he wrote that answer Actually, he was 64
  - arcanemachiner 3y ago
    That was just GP honoring the title of the post.
    - susam 3y ago
      What do you mean? http://web.archive.org/web/20230718104503/https://news.ycombinator.com/item?id=36744690 http://web.archive.org/web/20230718104503/https://news.ycomb... shows "(2010)" and 2010 - 1946 = 64.
      - bobthepanda 3y ago
        It’s a joke about the parent comment being bad at math, so maybe they don’t need to contribute
  - KnobbleMcKnees 3y ago
    Yeah, fatigue got the better of me there
perihelions 3y ago
So, where he writes on StackOverflow - "Is there, for example any real reason that even such famous results as... the Poincaré conjecture, really matter?" He is writing from the perspective of someone who played a key role in solving the Poincaré conjecture. Remarkable context! (Though the word "Poincaré" doesn't technically appear in his Wikipedia biography; it's disguised as "geometrization conjecture").
- fsckboy 3y ago
  and where he writes "I think of mathematics as having a large component of psychology, because of its strong dependence on human minds. Dehumanized mathematics would be more like computer code, which is very different" he's just blowing smoke. smh so dumb.
bjornlouser 3y ago
Mentioned in a comment of that MO question is Thurston's "On proof and progress in mathematics" https://arxiv.org/abs/math/9404236 https://arxiv.org/abs/math/9404236

Rygian 3y ago

I scrolled up the page and saw the following banner, which (in hindsight) couldn't be more wrong. > This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.

enriquto 3y ago
It's a longtime trope of these "stack" sites: the best questions with the best answers are those that are marked as offtopic, closed, deleted, downvoted or otherwise rejected. It's a marker of good quality at this point.
- tux3 3y ago
  Marker of good quality would be too far (and biased), as the every growing mass of genuinely hard to salvage closed question certainly outnumbers the interesting ones But it sure looks to be bimodal. Marker of the really bad, and the so-good-it's-closed
  - mannykannot 3y ago
    I would guess that this bimodality correlates with one in the personalities of those who become moderators - on the one hand, those who are willing to put a lot of effort into keeping the community relevant, and on the other, those who abhor any perceived irregularity. On occasion, when I get invitations to participate in moderator elections, I look to see if I recognize any of the candidates. Once or twice, I have looked through the candidates' resumes, and one thing that struck me was that some of them did a lot more down-voting than up-voting. Make of that what you will.
- jimhefferon 3y ago
  I also have found that often the answers that make me reflect the most on SO are treated this way by the mods. Does this effect have a name?

jonsen 3y ago

From a comment there: > Thematically this is similar to a (much longer) essay Dr. Thurston wrote several years ago, which I highly recommend: https://arxiv.org/abs/math/9404236 https://arxiv.org/abs/math/9404236

w4termelon 3y ago

So, what's so special about this answer? Seems like a pasta, replace "mathematics" by {SUBJECTNAME} and you get yet another popular idea of the day. Startup founders, for one, having been claiming they are "contributing to humanity" for ages now.

pxc 3y ago
People often think of mathematics as uniquely objective, and as standing apart from the social processes of collaboration and invention. And mathematics kind of is special in some of those ways. But mathematicians know, while laypeople might not, that at its core, mathematics remains a social endeavor just like the rest of the sciences. That's the piece which is a really valuable reminder imo.

tomrod 3y ago

This is beautiful. I unfortunately haven't seen Thurston's work before. Much respect for this man.

macleginn 3y ago

"The world does not suffer from an oversupply of clarity and understanding (to put it mildly)" – how this can be remedied by mathematical thinking, though, is rather unclear. Take the USSR with its strong tradition of math education in secondary schools and math research. Despite producing a lot of important results and some painfully beautiful math books, like Gelfand's Linear algebra, it has more or less zero effect on the wider society or even wider intellectual discourse.

hyperparameter 3y ago
> Despite producing a lot of important results and some painfully beautiful math books, like Gelfand's Linear algebra, it has more or less zero effect on the wider society or even wider intellectual discourse. In Computer Science we have Adelson-Velsky and Landis's self-balanced binary trees, and many other results, as well as other results in math and the sciences. In engineering and otherwise the USSR launched the first satellite, person in space, sent the first probes to the moon and other planets, and pushed the US into space. The civil rights moment in the US was often accused of being communist because - a lot of it was communist, and supported by the USSR, at least in the days of Paul Robeson and the Scottsboro Boys and Martin Luther King at the Highland Folk school (billboards through the South had a picture of King there "King at communist training school"). Actually if you watch the Nightline of Mandela coming to the US, half the speakers accused him of being a USSR-aligned communist. The USSR contributed to the anti-colonial struggles around the world - from China to Cuba to Vietnam, and contributed to it in other countries like India. Plus it did most of the fighting in WWII for the US and UK to defeat Germany (of course nowadays the US and UK flipped it to Germany against Russia). The USSR also helped push a blue collar working class proletariat into a kind of middle class. This began being rolled back even when the USSR still existed but was weak, and is still being rolled back.
- mmmmmmtoes 3y ago
  [dead]
- rcxdude 3y ago
  > Plus it did most of the fighting in WWII for the US and UK to defeat Germany (of course nowadays the US and UK flipped it to Germany against Russia). That's quite a spin on history. The USSR (already an imperialist power) and germany secretly divvied up eastern europe between themselves before Germany started the war, and it was only Germany's betrayal of that deal which led to the USSR actually joining the fight against Germany, with the US and UK finding it a convenient way to wear down a shared foe to provide them with some of their industrial capacity. You make it sound like this was some kind of puppet mastery by the US and UK (which to be clear, are not saints either, but decidedly on the right side in WWII) as opposed to two imperialist powers seeking to conquer others by force fighting amongst themselves.

FrustratedMonky 3y ago

Good point about understanding. Lets say there is a catastrophe, world goes to hell, understanding is lost. Then people go into a library and start opening books. The arcane symbols of Math would be indistinguishable from books of magic. Without the understanding, fresh minds would be hard pressed to distinguish math formula from magic runes. The understanding of the math comes from some community of people passing it along from generation to generation more than from the symbols.

mejutoco 3y ago
Principia Mathematica for sure. Other, like visual proofs would pass this test better I believe.

Errancer 3y ago

I feel like this comment hits at the general discussion of "Why should I learn something which I won't be the best at?" and it applies just as well to maths, science and arts: you should learn it since if you really enjoy it then you can contribute by maintaining a healthy community around it; and this can mean really working on the community or just being a person who can understand the value of discoveries of others. Having a good audience is the dream of every artist and I think this applies quite universally.

wwweston 3y ago

This is a comment I think about a lot lately when it comes to discussions of AI and art too — if there’s a hazard in “dehumanized mathematics” and value in mathematics as community and reflection of human understanding then surely there’s something similar in art as communal conversation and reflection of human experience.

effed3 3y ago

I'm my mind echoed something like... "don't ask yourself what you can do for mathematics, but what mathematics can do for you.." in my opinion the 1st/biggest contribution to math (and any science, discipline, art, and work) is to study/pratice it, is the best contribution to a living body of knowledge and wisdom, new ideas and discovery are side effect, welcomed, but not mandatory.. but is the discipline involved that change the single and later the world. The sea is made of drops.. the true goal is the/any-single way in praticing, not the end/highest point (if exist).

lo_zamoyski 3y ago

We must distinguish between theoria, praxis, and poiesis. Praxis, or the practical, has as its end action, something other than itself. When I clean my house, I don't do this for its own sake, I do this for the sake of having a clean house to live in. Similarly, poiesis, or production, also has something other than itself as an end, some thing. When I cook dinner, I don't cook it for its own sake, I cook it to feed myself and others. On the other hand, theoria, or theory, has as its end truth. The truth has practical consequences, of course, but there are truths that are valuable knowing for their own sake. Ends, of course, need a terminus. While a practical or productive act terminates in something other than itself, you must now ask what the end itself is for. Is it for itself, or something else further still? When we follow practical and productive ends, they must ultimately terminate at something that is not for the sake of anything else, but is valuable in itself. Indeed, when I said the truth has practical consequences, it was an understatement; the entire regime of practical and productive activity presupposes an ultimate end for the sake of which it exists, that justifies it, that it is in service of. I will omit discussion of the ultimate here intentionally, because my purpose here is to frame the problem first and predispose the mind toward the answer; giving the answer straight away, or an answer, is more likely to trigger reflexive prejudices here, I think. Once framed this way, people are liberated to ask "whom or what do I ultimately serve? why do I live? why do I act?". The vista of ends and order is thrown open for examination. This clarity enables one to leave Plato's "cave" and makes it difficult to obfuscate and settle for cheap answers as it can corner the conscience into pestering us to reject dishonest rationalizations. Of course, people will often try to do so, but doing so is more likely to gnaw at the soul, something that can prompt people to keep searching instead of holing up in an intellectual ghetto and persist in mediocrity. Now you can approach the original question.

haswell 3y ago
> We must distinguish between theoria, praxis, and poiesis. Must we? > When I clean my house, I don't do this for its own sake, I do this for the sake of having a clean house to live in. Why not both? A clean house isn’t necessary for survival. Why do you enjoy a clean house? For its own sake perhaps? Many would argue that we do these things for the sake of them as much as we do these things out of necessity. Reframed slightly, we do many things for the sake of doing them, and we seem to enjoy bringing this mindset to the necessities of life. Mihaly Csikszentmihalyi explores this extensively in Flow, and it’s a recurrent theme in many contemplative traditions. > When I cook dinner, I don't cook it for its own sake, I cook it to feed myself and others. Again, why not both? If the only value gained from cooking is sustenance, why do we enjoy dessert? Why do we enjoy it more when other people are with us? I’m not saying we don’t do things for reasons or that it’s uninteresting to assign labels to those reasons and explore them, but such intellectual/philosophical framings are ultimately just reductions of unfolding experience into a low resolution explanation of reality relative to our immersion in it. Should we explore these ideas? Yes. Must they be the foundation from which we explore other ideas? I don’t think so. Sometimes, sure.

adamsmith143 3y ago

Just want to point out how cool it is that a Field Medal winner is on MO. Don't know if any Turing Award winners or someone like Jeff Dean is on StackOverflow.

ke88y 3y ago

> Mathematical ideas, even simple ideas, are often hard to transplant from mind to mind.... Our understanding frequently deteriorates as well... The experts in a subject retire and die, or simply move on to other subjects and forget.... In short, mathematics only exists in a living community of mathematicians that spreads understanding and breaths life into ideas both old and new. One of the great things about software is that you don't need a living community that holds every bit of every code base in their head. You can rely on abstraction boundaries, and then jump down rabbit holes only if and when necessary. I really wonder how the work of Mathematics will change once computer-encoded proofs become mainstream. I have to imagine that will happen within the next generation or two -- as soon as the automation becomes more helpful than the hindrance of formality.

Ericson2314 3y ago
https://github.com/leanprover-community/mathlib https://github.com/leanprover-community/mathlib https://1lab.dev/ https://1lab.dev/ You can watch the next generation, or participate, right now.
robryk 3y ago
I think you're missing his point. He does acknowledge that statements of facts and their proofs can be easily communicated, but claims that the understanding their discovery was a side effect of cannot be communicated easily. This is not affected by having a better way to express facts and their proofs.
- ke88y 3y ago
  No, I get his point. I think the transmission of knowledge and insight and clarity works very differently for executable artifacts than for artifacts written in natural language. > This is not affected by having a better way to express facts and their proofs. But it is if those expressions are possible to interact with and use through not only conceptual abstraction but also procedural abstraction. With good proof automation? Maybe you can interact and play with ideas through many layers of automation-enabled abstraction. Maybe you have a tactic or ATP procedure that uses a lemma in clever ways without you even knowing it exists, and only after building on that edifice for years do you bother to dig in and understand what the proof automation is even using. Mind you: not what the lemma means or how it's proven or the underlying historical development of ideas, but that it even exists. Maybe you never dig in and realize it exists. Maybe you use these new theorems and proofs -- discovered only through extremely essential and clever use of a critical lemma you don't even know that you are using -- to do something useful in the world. That can't happen today; not really. It would take very powerful proof automation for this world to exist. Code and books are very different things.

ke88y 3y ago

I really like this view of academic research in general. The field does not exist as a means unto itself, but as a tool for helping and contributing to humanity. A service mindset. That's how I have always viewed both research and teaching. The most frustrating part of academia, and one of the main reasons I left, was the sense that everyone had completely lost their service mindset. The result is a set of sclerotic institutions -- protected from competition by rules and norms motivated by an ostensibly noble purpose -- wrecking havoc on society. In research, in particular, it's now rare to find researchers who really give a damn about anyone except themselves. Their PhD students are tools for increasing faculty influence. The motivation section of their grants are polite lies and everyone knows it. The whole thing is a big inside joke that people laugh about in elevator bays, backed by billions of taxpayer dollars. The selfishness and complete disinterest in stewardship of public funds is nauseating. But things are worst in undergraduate education. You occasionally meet someone worried about the educational mission, but no one was ever interested in the overall well-being of students. Financial well-being, in particular, is a verboten topic. The question of whether a particular degree program might be doing irreversible and crippling financial damage to nearly every student is considered rude. The question of whether requiring a certain course might be a waste of a customer's money is derided ("they aren't customers!", despite paying mid 5 figures per year for shockingly little face-to-face time.) Academia has completely lost its historically service-oriented pursuit. The faculty are motivated by a combination of laziness, entitlement, and ego. The administration is motivated by the same incentives as any other industry. But huge quantities of tax dollars are locked up in this broken and corrupt industry.

everybodyknows 3y ago
It would help if you could tell us about your specific positions in academia, those which informed these observations.
- ke88y 3y ago
  PhD student and faculty (quite briefly). Serving on grant panels also informed this view, but looking back, I think I was already getting disgusted by the culture of academia around my second year of grad school. My immediate family spent/spends much more time in academia than I, including the person I live with who has built their career in academia. My own experience of academia was actually quite positive -- I enjoyed my PhD years, was well-supported, received many tenure-track offers from elite institutions immediately out of my PhD, and I left on better than good terms with coworkers and former colleagues. My assessment isn't a result of personal bitterness or a failure to "win the game", if that's what you're getting at. Quite the opposite, in fact -- doing extremely well in the early career game afforded me the personal confidence to leave the track to which I had previously committed. (FWIW, the fact that I'll retire many decades earlier than I would've otherwise was not immaterial to my decision making)

BSEdlMMldESB 3y ago

> Mathematical ideas, even simple ideas, are often hard to transplant from mind to mind. this is a problematic way to frame the issue which I agree is very difficult. by framing it like this, I think, it sets up this task to be impossible. I'm also considering a subtle distinction between 'teaching' and 'education' he's using a teaching framework. to put the idea in the head of the student. but education is more about guiding the student to find the answer on their own; if teaching is difficult, education may seem freaking impossible. with a 'teaching framework' simple ideas are more difficult (and complex ones turn impossible) but with the 'education framework' (which in my direct experience is not available publicly) simple ideas may be trickier, but the hope is that sophisticated ideas will become easier to communicate.... dunno

CliffStoll 3y ago

Bill Thurston! He did amazing topology - hyperbolic knot compliments, Foliations, eversion of the sphere, geometrization conjecture... A brilliant man. I had the honor of meeting him several times here in Berkeley; he encouraged me to make Klein bottles and other topological shapes.

Munksgaard 3y ago
Cliff! I've had a plan to buy a bottle from you for a long time. Do you still have any left?

joewferrara 3y ago

This essay by the same person who answered the mathoverflow post greatly expands on the ideas in the post. https://arxiv.org/pdf/math/9404236.pdf https://arxiv.org/pdf/math/9404236.pdf It’s a great read for young people interested in mathematics and influenced me while in undergrad deciding to persue a PhD in math. Thurston, the author, was one of the best mathematicians of his time.