Greg Stanton

@radokirov @michael_nielsen Sure thing! timothychow.net/forcing.pdf michaelnotebook.com/df/index.html

@HigherMathNotes @michael_nielsen I am not aware of either of those, so need to read up on them first, but thanks for putting them on my radar.

Yes! I've been wondering if discovery fiction (in the sense of @michael_nielsen) and open-exposition problems (as introduced by Timothy Chow) might start to receive greater attention. It's also interesting to consider how AI might assist in these more subjective areas.

📢Stunning math & AI update "I still did not see how to prove this inequality, but I decided to try my luck giving it to ChatGPT Pro, which... gave me a duality-based proof..."—Terence Tao (3/23/26) How Fields medalist Tao used AI in his latest work: terrytao.wordpress.com/2026/03/23/loc…

@CoryMSimon There's a precise connection between the discrete generating functions from de Moivre (they solve recurrence relations, i.e. difference equations) and the continuous Laplace transform (it solves differential equations). Very cool story, but that's for another day!

@CoryMSimon So there you have it. You now have the short version (in a single tweet), and a longer version haha. I hope you don't mind the extra detail. That's not the full story, of course. What about other uses of the Laplace transform, like solving differential equations?

finally got around to learning about moment-generating functions (MGFs) for dealing with probability distributions. the MGF for a random variable is just a flipped, two-sided Laplace transform of its probability density. take a derivative of the MGF and evaluate at zero, voilà, we get a moment of the distribution, explaining the name. web.ma.utexas.edu/users/gordanz/…