4 ms·

The Geometry of Schemes [pdf]

gsf_emergency_4 1y ago
Teach biologists that? https://web.archive.org/web/20250115224532/http://www.dam.brown.edu/people/mumford/blog/2014/Grothendieck.html https://web.archive.org/web/20250115224532/http://www.dam.br... https://golem.ph.utexas.edu/category/2014/12/can_one_explain_schemes_to_a_b.html https://golem.ph.utexas.edu/category/2014/12/can_one_explain... https://liorpachter.wordpress.com/2014/12/30/the-two-cultures-of-mathematics-and-biology/ https://liorpachter.wordpress.com/2014/12/30/the-two-culture... (2014) With someone actually trying in 2002, using TFB for inspiration & M2 as a very early Jupyter/sage https://web.archive.org/web/20250000000000*/https://mast.queensu.ca/~ggsmith/Papers/m2schemes_book.pdf https://web.archive.org/web/20250000000000*/https://mast.que... (These bloggers as well as creator of M1 may want to chip in a dozen cts)
pixelpoet 1y ago
What's up with the raccoon on page 67?
- sam1r 1y ago
  oh yeah! that is insane.
  - ALLTaken 1y ago
    I think it's cute! What if it's steganography or symbolic or a puzzle. If it's none of that, to complain about it is a bit too harsh.. for something on page 67.
- binarycrusader 1y ago
  Pretty sure that's a ferret.
- Syzygies 1y ago
  I know both authors, so I wrote them to ask. This is a rogue image that appears in various PDFs posted online, but not on Springer's official PDF or any print copy we've seen.
SherryMarcini 1y ago
The raccoon has ruined this for me…
bubblyworld 1y ago
Why is this on the front page of hacker news? Hopefully that comes across as a genuine question and not snark. I mean as an ex-mathematician I'm thrilled, but schemes are an incredibly abstract object used in an incredibly abstract branch of mathematics (algebraic geometry).
- nhatcher 1y ago
  I have the same question in my mind. Also thrilled though. I think there is a genuine fascination in HN and in general with Grothendieck [1], [2]. [1]: https://en.wikipedia.org/wiki/Alexander_Grothendieck https://en.wikipedia.org/wiki/Alexander_Grothendieck [2]: https://hn.algolia.com/?q=Grothendieck https://hn.algolia.com/?q=Grothendieck
  - bubblyworld 1y ago
    Interesting, yeah. I guess he was the mathematical equivalent of the "rogue" archetype. Brilliant, did things in his own way, total lack of respect for authority, shrouded in mystery. I can definitely see the appeal =)
- ssivark 1y ago
  Sometimes, the best way to learn about abstruse topics one has a passing curiosity in is to upvote what pops up on HN and hope that some nerd might drop by and comment with a simplified intuitive picture for plebs :-)
  - gsf_emergency_4 1y ago
    (Edited to be more helpful) These days, some nerds prefer to ask AI to confirm their "precious" intuitions of why schemes might be needed in the first place. To fix the problems with certain basic geometric notions of old timers? They are then so spooked that the AI instantly validates those intuitions without any relevant citations whatsoever that they decide not to comment But still leave warnings to gung-ho nerds in the form of low-code exercises
fermigier 1y ago
Published in 2000. (I studied schemes 10 years before, but I quit maths in 2000 so this book wouldn't have helped me. It seems like a good introduction, looking at the TOC. Grounded on actual geometry, not just category theory like other textbooks). Also, the racoon ?!
tug2024 1y ago
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Teach biologists that? https://web.archive.org/web/20250115224532/http://www.dam.brown.edu/people/mumford/blog/2014/Grothendieck.html https://web.archive.org/web/20250115224532/http://www.dam.br... https://golem.ph.utexas.edu/category/2014/12/can_one_explain_schemes_to_a_b.html https://golem.ph.utexas.edu/category/2014/12/can_one_explain... https://liorpachter.wordpress.com/2014/12/30/the-two-cultures-of-mathematics-and-biology/ https://liorpachter.wordpress.com/2014/12/30/the-two-culture... (2014) With someone actually trying in 2002, using TFB for inspiration & M2 as a very early Jupyter/sage https://web.archive.org/web/20250000000000*/https://mast.queensu.ca/~ggsmith/Papers/m2schemes_book.pdf https://web.archive.org/web/20250000000000*/https://mast.que... (These bloggers as well as creator of M1 may want to chip in a dozen cts)

pixelpoet 1y ago

What's up with the raccoon on page 67?

sam1r 1y ago
oh yeah! that is insane.
- ALLTaken 1y ago
  I think it's cute! What if it's steganography or symbolic or a puzzle. If it's none of that, to complain about it is a bit too harsh.. for something on page 67.
binarycrusader 1y ago
Pretty sure that's a ferret.
Syzygies 1y ago
I know both authors, so I wrote them to ask. This is a rogue image that appears in various PDFs posted online, but not on Springer's official PDF or any print copy we've seen.

SherryMarcini 1y ago

The raccoon has ruined this for me…

bubblyworld 1y ago

Why is this on the front page of hacker news? Hopefully that comes across as a genuine question and not snark. I mean as an ex-mathematician I'm thrilled, but schemes are an incredibly abstract object used in an incredibly abstract branch of mathematics (algebraic geometry).

nhatcher 1y ago
I have the same question in my mind. Also thrilled though. I think there is a genuine fascination in HN and in general with Grothendieck [1], [2]. [1]: https://en.wikipedia.org/wiki/Alexander_Grothendieck https://en.wikipedia.org/wiki/Alexander_Grothendieck [2]: https://hn.algolia.com/?q=Grothendieck https://hn.algolia.com/?q=Grothendieck
- bubblyworld 1y ago
  Interesting, yeah. I guess he was the mathematical equivalent of the "rogue" archetype. Brilliant, did things in his own way, total lack of respect for authority, shrouded in mystery. I can definitely see the appeal =)
ssivark 1y ago
Sometimes, the best way to learn about abstruse topics one has a passing curiosity in is to upvote what pops up on HN and hope that some nerd might drop by and comment with a simplified intuitive picture for plebs :-)
- gsf_emergency_4 1y ago
  (Edited to be more helpful) These days, some nerds prefer to ask AI to confirm their "precious" intuitions of why schemes might be needed in the first place. To fix the problems with certain basic geometric notions of old timers? They are then so spooked that the AI instantly validates those intuitions without any relevant citations whatsoever that they decide not to comment But still leave warnings to gung-ho nerds in the form of low-code exercises

fermigier 1y ago

Published in 2000. (I studied schemes 10 years before, but I quit maths in 2000 so this book wouldn't have helped me. It seems like a good introduction, looking at the TOC. Grounded on actual geometry, not just category theory like other textbooks). Also, the racoon ?!

tug2024 1y ago

[dead]