[HN Gopher] A 1940 Letter of Andre Weil on Analogy in Mathematic...
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A 1940 Letter of Andre Weil on Analogy in Mathematics (2003) [pdf]
Author : gone35
Score : 62 points
Date : 2024-08-07 07:31 UTC (3 days ago)
(HTM) web link (www.ams.org)
(TXT) w3m dump (www.ams.org)
| bmitc wrote:
| 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 wrote:
| 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 wrote:
| Yes I did. And?
| monktastic1 wrote:
| 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 wrote:
| One would think that he would know whether his own sister, the
| recipient, would have sufficient mathematical background to
| understand his work.
| bmitc wrote:
| Exactly, so why take the time to remind her of that? Ego is
| why.
| ThrowawayR2 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| > 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
| lupire wrote:
| "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 wrote:
| This easily follows from the law of reciprocity.
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