black-hole-entropy

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"The problem with the singularity is that once we are in the upper quadrant, i.e., once we have gone through the horizon and are 'inside the black hole,' we can't avoid eventually hitting it. Indeed, it is not really a place. As already discussed last lecture, it is really, in a sense, a time. We can avoid an obstacle in space--we go around it--but we cannot avoid 'hitting the future.' We can escape from things, even from freedom, but not from the future."

-Leonard Susskind, General Relativity (2023)

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“You can use this at a party if the person you’re talking to is someone you’re trying to impress, or if you’re trying to get them to go away. It works in both cases.”

— Analysis Professor on proving the real numbers are not countable

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“If you have lived a good life, you will have a differential equation of this form.”

— Classical Mechanics professor on linear homogeneous equations

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“Irrelevant operators are more relevant than relevant operators, sometimes.”

— Particle Physics Professor

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You know, people think mathematics is complicated. Mathematics is the simple bit. Its the stuff we can understand. Its cats that are complicated. I mean, what is it in those little molecules and stuff that make one cat behave differently than another, or that make a cat? And how do you define a cat? I have no idea.

— John Horton Conway

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“Now, lets see if I can pass my own course…”

— Quantum physics lecturer who left the solutions to that week’s problems at home

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Jonathan Gleason was my friend who committed suicide just over a month ago… and I just found out that he wrote this 800+ page analysis textbook. By himself. Because he was teaching analysis and he was dissatisfied with the textbook he was assigned so he just…. wrote his own.

Even if you haven’t done any math… please just take a look at this. Scroll through it as fast as you like. It’s incredible that he put so much work and so much free time into this… I’m still in awe and I really want everyone to see it. In particular, if you want a good laugh, look at chapter 5 of the analysis textbook. The opening paragraph is SO Johnny.

He also wrote a linear algebra textbook, here. 

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catch, and release

[black-hole-entropy]

Jonathan Gleason was my friend who committed suicide just over a month ago… and I just found out that he wrote this 800+ page analysis textbook. By himself. Because he was teaching analysis and he was dissatisfied with the textbook he was assigned so he just…. wrote his own.

Even if you haven’t done any math… please just take a look at this. Scroll through it as fast as you like. It’s incredible that he put so much work and so much free time into this… I’m still in awe and I really want everyone to see it. In particular, if you want a good laugh, look at chapter 5 of the analysis textbook. The opening paragraph is SO Johnny.

He also wrote a linear algebra textbook, here. 

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“If you do enough math, you basically have to learn the entire Greek alphabet. On rare occasions, the Hebrew alphabet.”

— Linear algebra professor

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one of my favorite moments in math was at the Topos à l’IHÉS conference in 2015, where at the end of the week André Joyal, Olivia Caramello, Laurent Lafforgue, and Alain Connes held a panel on “The future of topos theory”

and at the end of the hour Maxim Kontsevich stood up and said

“there isn’t any”

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Yesterday I gave a knot theory talk that heavily featured checkerboard colorings/spanning surfaces. When my ‘snuggle the cat’ alarm (which goes off ten minutes before the actual ‘wake-up’ alarm because the little dude has been real polite about not waking me up before the alarm goes off, and I think that merits some consideration) woke me this morning, in my delirious end-of-the-week haze I started wondering if Shark was checkerboard colored, then thinking about the homology of his tabby fur parts.

I realized that neither his tabby nor white regions were path connected, because of an isolated tabby spot on his leg and an isolated white tuft on his back (video for reference). 

So I says to him, I says, “You ain’t got no trivial reduced zero^th homology groups, you know that about yourself?”

…Math makes you weird if you do enough of it. 

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So this is good, this is what you need. *touches white board* No, not because you want to write on it, because you will want to beat your head against it.

Physics prof (via scienceprofessorquotes)

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Generalisation is not the point of mathematics. To be honest, it’s usually rather dry. The challenge is to generalise in a rich and revealing direction.

Terry Gannon, Moonshine Beyond the Monster §3.3 (generalisations of the affine algebras: Kac-Moody algebras, Borcherds’ algebras, toroidal algebras)

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“Lander and Parkin’s paper about a conjecture by Euler (related to Fermat’s last Theorem), is probably the dream of everyone ever written a paper: It answers an interesting and important question, it’s correct beyond any doubt,  it’s easy to understand and only two sentences long.”

https://paperpile.com/blog/shortest-papers/

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Let’s be honest, most of physics history is just us being super dramatic. “Oh, our math isn’t adding up. Why its an ultraviolet catastrophe!”

out-of-context physics quotes (via oocphysicsquotes)