As my wife ate her porridge this morning she asked "what exactly are oats?" and it turned out to be an interesting question because of Vavilonian mimicry.
When to automate a repetitive task:
NO-BRAINER: "This is obviously going to be faster to automate than to do it by hand _even once_. Let's automate it right now, and not do it by hand at all."
FORESIGHTED: "Doing it once by hand is faster than automating it, but I'm going to have to do it a lot of times, so it still saves time to automate it first."
NEED A RUN-UP: "I don't yet understand this task well enough to automate it, so I'll do it a few times by hand first to get the idea."
RAN OFF THE RUNWAY: "Great, now I've done this by hand a few times, I think I can automate it reliably! Oh, oops, turned out I only had one more case of it left to do."
TERRIFIED OF RUNNING OFF THE RUNWAY: "This is a one-off, so it would be a waste of time to automate it, I'll just do it manually."
[next day] "Oh, oops, I made a mistake and have to do it again. But it should be fine this time."
[a month later] "Even though I've had to redo it 25 times already, surely _this_ is the last time? So it would still be a waste of time to automate it."
Everybody knows from school how to solve a quadratic equation of the form $x^2-px+q=0$ graphically. But this method can become tedious if several equations ought to be solved, as for each pair $(p,q)$ a new parabola has to be drawn. Stunningly, there is one single curve that can be used to solve every quadratic equation via drawing tangent lines through a given point $(p,q)$ to this curve. In this article we derive this method in an elementary way and generalize it to equations of the form $x^n-px+q=0$ for arbitrary $n \ge 2$. Moreover, the number of solutions of a specific equation of this form can be seen immediately with this technique. Concluding the article we point out connections to the duality of points and lines in the plane and to the the concept of Legendre transformation.
Want to know how generating functions work?
How about proving the Ramanujan identities? How about doing all that, with *pictures*?
This course I've recently found and this excellent expository video of "The Art of Bijective Combinatorics" is an absolutely stunning way of doing all that!
For those who want to test their perception of colour, I made a little game called "What's My JND"
@hallasurvivor
I guess part of this experience is just letting the thing find a place in your web of mathematical concepts. You build up strands of “Oh, they’re an example of…” and “They’re useful for…” and so on, and it starts to feel a bit less alien
And as your web becomes broader and denser there are more points for the new idea to hook into. And then perhaps the new concept helps to scaffold together two ideas that seemed unrelated, and it feels like a natural part of the landscape
Half a year ago, I filled in some sorry's for the massive project [1] to formalize the Fields-medal winning proof that sphere packing in dimension 8 is optimized by the E8-lattice. Last week it was announced that all remaining sorry's were filled by Gauss, an autoformalization agent. Gauss was able to build on the blueprint and other scaffolding built by the community. A few days later, Gauss also formalized the proof in dimension 24, this time working directly from the published paper, without mayor community input [3].
Since Lean verifies the generated proofs, hallucinations are not a problem.
The community now processes the generated proofs to make sure it satisfies the community standards and remains usable in the future [2].
[1] https://thefundamentaltheor3m.github.io/Sphere-Packing-Lean/
@Scmbradley
Cocaine Bear is surprisingly better than it has any right to be
Also, seconding the recommendation of Kung Fu Hustle
Oh, and Kung Fury starts as a brilliantly over the top parody of 80s action films, and then becomes even more absurd, all crammed into 30 minutes (Contains cartoon-style violence and gore from the start)
https://www.youtube.com/watch?v=W6hKGVP8Dhc
Dan Piponi
Simon Tatham
Interesting Esoterica
ARBB
keithamus
Raphael APPENZELLER