6 ms·

A 1940 Letter of André Weil on Analogy in Mathematics (2003) [pdf]

88 points by gone35 2y ago

bmitc 2y ago
Is an interesting read, but it's striking how condescending he is at the outset. How about let the reader decide what they understand or not? There's no use in saying anything regarding that.
- EdwardCoffin 2y ago
  Did you read the introduction? It says: Weil wrote this fourteen-page letter to Simone Weil, his sister ... (Keep in mind that the letter was not written for a mathematician, even though Simone could not understand most of it.)
  - bmitc 2y ago
    Yes I did. And?
    - monktastic1 2y ago
      And without that context, his sister may have been perplexed as to why he would dive into complicated math that he should have known she wouldn't understand. Consider that sometimes when you read ego or aggression into writing, it's not coming from the author's mind but is a projection of your own.
- ThrowawayR2 2y ago
  One would think that he would know whether his own sister, the recipient, would have sufficient mathematical background to understand his work.
  - bmitc 2y ago
    Exactly, so why take the time to remind her of that? Ego is why.
    - ThrowawayR2 2y ago
      A more positive interpretation could be something like "I can't express what I want to say without going into topics that I know you have no familiarity with. But I'm aware of that and am not just insensitively bombarding you with jargon."
      - 082349872349872 2y ago
        Indeed. This is a six (printed) page letter, and already at a page or two in I wouldn't be surprised if it would take that many textbooks (how many printed pages?) to get SAW from where ever she left off (I don't recall maths being very prominent in classics/philosophy departments; note AW's description of a field) to where she could have a hope of seeing the moon itself, beyond the finger pointing at it.
- HarHarVeryFunny 2y ago
  The intended reader was his sister, who he sent the letter to. This was a private letter, not a publication. His sister had evidentially asked him about his work (maybe to give him something positive to talk about given that he was in prison). "Some thoughts I have had of late, concerning my arithmetic-algebraic work, might pass for a re- sponse to one of your letters, where you asked me what is of interest to me in my work. So, I decided to write them down, even if for the most part they are incomprehensible to you." It might seem condescending to speak to his sister like this, but perhaps he understood her intent well enough, and was essentially acknowledging it.
  - samstave 2y ago
    Likely even less so... That was likely just how colloquially he is saying to his kin "Tahnks for prodding me about what I thought of my work... so Ill put some write it out here, for good measure, so dont worry if you dont get it..." Basically he is saying, let me document this for myself, at the appreciated behest of sis.
    - drdec 2y ago
      > let me document this for myself, at the appreciated behest of sis. Tell me you live in the information age without telling me you live in the information age
    - kergonath 2y ago
      Do not get upset on behalf of his sister. You do not know either her or him. Besides, she was perfectly able to get upset and make it known on her own.
  - vixen99 2y ago
    Maybe not everyone knows that the sister was Simone - much better known than her brother in the world outside mathematics.
- larve 2y ago
  (native french) It is also a letter originally written in french in 1940: http://denise.vella.chemla.free.fr/transc-AWSW.pdf http://denise.vella.chemla.free.fr/transc-AWSW.pdf . It uses "tu" which is the affectionate/intimate version of you, the language used is as is quite common in educated households (and the weil's certainly was) is "language soutenu", which is quite formal sound and elaborate (french people love their language), and while I can see how it could strike one as cold, especially in english-speaking countries, it doesn't seem condescending to me in the least, on the contrary.
  - 082349872349872 2y ago
    > french people love their language as well as their anglicisms, mdr: > ... il avait aussi un theorema egregium, et je ne sais plus which is which.
    - defrost 2y ago
      Lost in Translation: it is gliding for me https://www.dailymotion.com/video/x2rdc71 https://www.dailymotion.com/video/x2rdc71
      - 082349872349872 2y ago
        unfortunately subtitles are never going to do LNA HO justice: https://www.dailymotion.com/video/xefrls https://www.dailymotion.com/video/xefrls (wait, did M Polnareff invent the lyric video here?)
        defrost 2y ago
        I expected a No True Belgian response and was instead pleasantly surprised. I'd have guessed he invented Boggle, the intertubes have that at 1972, 18 years earlier. I have no words for the French here in '67: https://www.youtube.com/watch?v=3LZbw6YCcm4 https://www.youtube.com/watch?v=3LZbw6YCcm4
        2y ago
diedragidcu 2y ago
[dead]
lupire 2y ago
"however it is beautiful and surprising that the prime numbers p for which m is a residue are precisely those which belong to certain arithmetic progressions of increment 4m; for the others m is a non-residue" Fascinating. At first I was confused because I thought he was referring to the law of reciprocity. But it's actually a different law: m = 3 = not a square mod 5. (reciprocal) = not a square mod 7. (not reciprocal) = 5² mod 11. (not reciprocal) = 4² mod 13. (reciprocal) Add 4*3 = 12: = not a square mod 17 (reciprocal) = not a square mod 19 (not reciprocal) = 7² mod 23. (not reciprocal) Add 4*3 = 12: = not a square mod 29 (reciprocal) = not a square mod 31 (not reciprocal)
- eapriv 2y ago
  This easily follows from the law of reciprocity.
vedangvatsa 2y ago
[flagged]
- ThrowawayR2 2y ago
  If you look at the above poster's comment history, all of the posts contain the link in the second paragraph. It's an ad prefixed with a paragraph of what is probably LLM generated slop.
082349872349872 2y ago
> The unwritten laws of modern mathematics forbid writing down such views if they cannot be stated precisely nor, all the more, proven. To tell the truth, if this were not the case, one would be overwhelmed by work that is even more stupid and if not more useless compared to work that is now published in the journals. But one would love it if Hilbert had written down all that he had in mind. Here we've had some (technical) progress since 1940: modern Hilberts may publish their proven results, arxiv their useless work, and blog their work that is even more stupid?
- vouaobrasil 2y ago
  I truly believe that there is an ideal point of efficiency for every human process. Make something too easy and too mechanical, and it loses its charm because it is lost in a sea of mediocrity. Publishing and producing work is like that these days. Yes, in absolute number, more work might be done, but is that worth the overall decline in the attraction of a discipline? Personally, I believe the world would be a better place if scientific research weren't a race for citations.
  - ykonstant 2y ago
    A few decades ago, pure mathematics was a genuine exception to the "race for citations". Hiring committees were more interested in the profundity of results than their number. For various understandable reasons, this last bastion fell and now PhD students and postdocs are expected to have many on top of ground-breaking results. It is important to emphasize to young researchers that the vision of getting tenure after a few ground-breaking results is a relic of the past (exceptions always exist). Sadly, I was enraptured by the romanticism of the old style research loop as a PhD student, and being not-very-savvy to say the least, I missed the bullet train by mistaking it for a horse carriage.
    - vouaobrasil 2y ago
      Yes, that is a very interesting point. You are very right though, that the trend has changed and there's a pressure now. I don't think your own experience is necessarily a bad thing. It's best to stick with your own ideals rather than bend to the will of others.
aaplok 2y ago
> Keep in mind that the letter was not written for a mathematician, even though Simone could not understand most of it. I'd love to see a citation here. Simone Weil referenced mathematics a lot in her philosophical writing, and, growing up in the shadow of her brother, had been exposed to mathematics all her life.

88 points by gone35 2y ago

Is an interesting read, but it's striking how condescending he is at the outset. How about let the reader decide what they understand or not? There's no use in saying anything regarding that.

EdwardCoffin 2y ago
Did you read the introduction? It says: Weil wrote this fourteen-page letter to Simone Weil, his sister ... (Keep in mind that the letter was not written for a mathematician, even though Simone could not understand most of it.)
- bmitc 2y ago
  Yes I did. And?
  - monktastic1 2y ago
    And without that context, his sister may have been perplexed as to why he would dive into complicated math that he should have known she wouldn't understand. Consider that sometimes when you read ego or aggression into writing, it's not coming from the author's mind but is a projection of your own.
ThrowawayR2 2y ago
One would think that he would know whether his own sister, the recipient, would have sufficient mathematical background to understand his work.
- bmitc 2y ago
  Exactly, so why take the time to remind her of that? Ego is why.
  - ThrowawayR2 2y ago
    A more positive interpretation could be something like "I can't express what I want to say without going into topics that I know you have no familiarity with. But I'm aware of that and am not just insensitively bombarding you with jargon."
    - 082349872349872 2y ago
      Indeed. This is a six (printed) page letter, and already at a page or two in I wouldn't be surprised if it would take that many textbooks (how many printed pages?) to get SAW from where ever she left off (I don't recall maths being very prominent in classics/philosophy departments; note AW's description of a field) to where she could have a hope of seeing the moon itself, beyond the finger pointing at it.
HarHarVeryFunny 2y ago
The intended reader was his sister, who he sent the letter to. This was a private letter, not a publication. His sister had evidentially asked him about his work (maybe to give him something positive to talk about given that he was in prison). "Some thoughts I have had of late, concerning my arithmetic-algebraic work, might pass for a re- sponse to one of your letters, where you asked me what is of interest to me in my work. So, I decided to write them down, even if for the most part they are incomprehensible to you." It might seem condescending to speak to his sister like this, but perhaps he understood her intent well enough, and was essentially acknowledging it.
- samstave 2y ago
  Likely even less so... That was likely just how colloquially he is saying to his kin "Tahnks for prodding me about what I thought of my work... so Ill put some write it out here, for good measure, so dont worry if you dont get it..." Basically he is saying, let me document this for myself, at the appreciated behest of sis.
  - drdec 2y ago
    > let me document this for myself, at the appreciated behest of sis. Tell me you live in the information age without telling me you live in the information age
  - kergonath 2y ago
    Do not get upset on behalf of his sister. You do not know either her or him. Besides, she was perfectly able to get upset and make it known on her own.
- vixen99 2y ago
  Maybe not everyone knows that the sister was Simone - much better known than her brother in the world outside mathematics.
larve 2y ago
(native french) It is also a letter originally written in french in 1940: http://denise.vella.chemla.free.fr/transc-AWSW.pdf http://denise.vella.chemla.free.fr/transc-AWSW.pdf . It uses "tu" which is the affectionate/intimate version of you, the language used is as is quite common in educated households (and the weil's certainly was) is "language soutenu", which is quite formal sound and elaborate (french people love their language), and while I can see how it could strike one as cold, especially in english-speaking countries, it doesn't seem condescending to me in the least, on the contrary.
- 082349872349872 2y ago
  > french people love their language as well as their anglicisms, mdr: > ... il avait aussi un theorema egregium, et je ne sais plus which is which.
  - defrost 2y ago
    Lost in Translation: it is gliding for me https://www.dailymotion.com/video/x2rdc71 https://www.dailymotion.com/video/x2rdc71
    - 082349872349872 2y ago
      unfortunately subtitles are never going to do LNA HO justice: https://www.dailymotion.com/video/xefrls https://www.dailymotion.com/video/xefrls (wait, did M Polnareff invent the lyric video here?)
      - defrost 2y ago
        I expected a No True Belgian response and was instead pleasantly surprised. I'd have guessed he invented Boggle, the intertubes have that at 1972, 18 years earlier. I have no words for the French here in '67: https://www.youtube.com/watch?v=3LZbw6YCcm4 https://www.youtube.com/watch?v=3LZbw6YCcm4
        2y ago

diedragidcu 2y ago

[dead]

lupire 2y ago

"however it is beautiful and surprising that the prime numbers p for which m is a residue are precisely those which belong to certain arithmetic progressions of increment 4m; for the others m is a non-residue" Fascinating. At first I was confused because I thought he was referring to the law of reciprocity. But it's actually a different law: m = 3 = not a square mod 5. (reciprocal) = not a square mod 7. (not reciprocal) = 5² mod 11. (not reciprocal) = 4² mod 13. (reciprocal) Add 4*3 = 12: = not a square mod 17 (reciprocal) = not a square mod 19 (not reciprocal) = 7² mod 23. (not reciprocal) Add 4*3 = 12: = not a square mod 29 (reciprocal) = not a square mod 31 (not reciprocal)

eapriv 2y ago
This easily follows from the law of reciprocity.

vedangvatsa 2y ago

[flagged]

ThrowawayR2 2y ago
If you look at the above poster's comment history, all of the posts contain the link in the second paragraph. It's an ad prefixed with a paragraph of what is probably LLM generated slop.

082349872349872 2y ago

> The unwritten laws of modern mathematics forbid writing down such views if they cannot be stated precisely nor, all the more, proven. To tell the truth, if this were not the case, one would be overwhelmed by work that is even more stupid and if not more useless compared to work that is now published in the journals. But one would love it if Hilbert had written down all that he had in mind. Here we've had some (technical) progress since 1940: modern Hilberts may publish their proven results, arxiv their useless work, and blog their work that is even more stupid?

vouaobrasil 2y ago
I truly believe that there is an ideal point of efficiency for every human process. Make something too easy and too mechanical, and it loses its charm because it is lost in a sea of mediocrity. Publishing and producing work is like that these days. Yes, in absolute number, more work might be done, but is that worth the overall decline in the attraction of a discipline? Personally, I believe the world would be a better place if scientific research weren't a race for citations.
- ykonstant 2y ago
  A few decades ago, pure mathematics was a genuine exception to the "race for citations". Hiring committees were more interested in the profundity of results than their number. For various understandable reasons, this last bastion fell and now PhD students and postdocs are expected to have many on top of ground-breaking results. It is important to emphasize to young researchers that the vision of getting tenure after a few ground-breaking results is a relic of the past (exceptions always exist). Sadly, I was enraptured by the romanticism of the old style research loop as a PhD student, and being not-very-savvy to say the least, I missed the bullet train by mistaking it for a horse carriage.
  - vouaobrasil 2y ago
    Yes, that is a very interesting point. You are very right though, that the trend has changed and there's a pressure now. I don't think your own experience is necessarily a bad thing. It's best to stick with your own ideals rather than bend to the will of others.

aaplok 2y ago

> Keep in mind that the letter was not written for a mathematician, even though Simone could not understand most of it. I'd love to see a citation here. Simone Weil referenced mathematics a lot in her philosophical writing, and, growing up in the shadow of her brother, had been exposed to mathematics all her life.