https://arxiv.org/abs/2410.20392

cross-posted from: https://sopuli.xyz/post/22688165

Random thought on magic squares:

If I view the smallest possible non-trivial magic square

 undefined

    
2 7 6
9 5 1
4 3 8


  

since its rows and diagnoals sum up to 2+5+8 = 2+7+6 = 4+5+6 = 2+9+4 = … = 15

in the article as a 3x3 Matrix, its determinant is Δ = -360 . Its inverse:

 undefined

    
-37/360 19/180 23/360
17/90 1/45 -13/90
-7/360 -11/180 53/360

  

note how this is a magic square, rows and diagonals sum up to 1/15.

https://matrix.reshish.com/inverse.php

Now if you are really bored (I can not do this): proof that for any non trivial magic squares the inverse …

• exists (i.e. every non-trivial magic square has an inverse)
• is a magic square.

Extracting Fernando Gouvêa's article on Spivak's Calculus book. I, like many others, used this book as my first introduction to "real" math, and it still has an important place in my heart. But the rest of the memorial is definitely worth reading. I had no idea that Spivak was gay, and it is good to see that representation.

Michael Spivak’s Calculus

By Fernando Q. Gouvêa

Let me begin with some autobiography. I was introduced to calculus during my first year at the University of São Paulo, in Brazil. At that time, we didn’t use a textbook; instead, we used references and small booklets of notes, prepared by one of the teachers. The references were a variety of books that our professors felt could be consulted with profit. Among them was Spivak’s Calculus. I didn’t buy a copy at first, because I was fairly happy with the notes and with the books I already had. But the name stuck in my head.

A couple of months into the course, I was strolling through the aisles of my favorite bo

A link from @[email protected] to a 1972 talk by Grothendieck (including a recording; I don't think I'd ever actually heard his voice before!). It's interesting how complaints that seem very modern have existed for so long.

I’ve been taking every opportunity to meet scientists, whether in public discussions like this one or in private, and raise these questions. In particular: “Why do we do scientific research?” [...] The extraordinary thing is to see how incapable my colleagues are of answering this question. In fact, for most of them, the question is simply so strange, so extraordinary, that they refuse even to contemplate it. In any case, they are extremely reluctant to give any kind of answer.

I’ve come to realize that in fact this satisfaction that scientists are supposed to derive from exercising their cherished profession, is a pleasure… which is not a pleasure for everyone! [...] Once you’ve got your job, it’s an imper

Calegari's Notices essay mentioned in the article.