MichaelMaths

The official X account for MichaelMaths — interesting math videos covering a range of different topics, mainly analysis focused (studying MDSAI @ UWaterloo)

[MichaelMaths @michaelmaths_]

@CharlieYYang @Almost_Sure Yeah exactly

[MichaelMaths @michaelmaths_]

@CharlieYYang @Almost_Sure I’ve seen a number of regularized results where the answer ends up being the same as the constant term in the series expansion. Same thing with harmonic series converging through Ramanujan summation or a limit of averaging with the Zeta function to the Euler Mascheroni constant.

[CM @Creative_Math_]

No sequence will ever top the “Attention is not Explanation” and “Attention is not not Explanation” papers

[Steven Strogatz @stevenstrogatz]

I really enjoyed Apoorva's essay. It's rare these days to hear what a *student* thinks about what's going on in AI and Math, and I highly recommend you take a look at her piece – it's thoughtful, curious, idealistic, and unmistakably human.

[Shubhendu Trivedi @_onionesque]

Looks promising https://t.co/PT5DOkE5Pq

[Almost Sure @Almost_Sure]

Projective plane: visualising solutions to

x/(y+z) + y/(x+z) + z/(x+y) = 4

A surface in 3d space.

Invariant under scaling: if (x,y,z) is a solution then so is (ax, ay,az).
Solutions are a set of lines through the origin. Or a cubic curve on the plane z=1, or on unit sphere.

[Sam Walters ☕️ @SamuelGWalters]

A simple proof that there is no measure on infinite dimensional Hilbert space similar to the standard Lebesgue measure on Euclidean space ℝⁿ. #math #calculus #MeasureTheory #geometry #HilbertSpace

[Wolfram @WolframResearch]

"This was a great shock to existing thinking about the foundations of mathematics. And indeed to this day Gödel's Theorem has continued to be widely regarded as a surprising and rather mysterious result..."
—@stephen_wolfram
https://t.co/023gpog2yE

[ricky @rickyflows]

Finally we’re free from Euler’s tyranny

[caruihnugte 🇵🇸🔶 @caruih]

Sies siete

[Daniel Litt @littmath]

Here at [famous scientist’s name].ai, we’re developing tools to accelerate science. Unlike academia, which has stifled the production of high quality scientific work by demanding it be correct, here at [fsn].ai, we know that you can just do (wrong) things.

[MichaelMaths @michaelmaths_]

Here's a neat proof of an Euler-type product representation of π. The way multiplicativity allows the Euler product to unfold into a Dirichlet series, which then coincides with the Leibniz series for π/4, is especially elegant and satisfying.

[MichaelMaths @michaelmaths_]

@chris_juravich I remember a while back I found another proof of the trivial zeros of ζ(s) being at s = -2n using Abel regularization for η(s). The resulting polynomials, I believe called Euler or Eulerian polynomials, had symmetric alternating coefficients, forcing them to vanish as t→1.

[Math Cafe @Riazi_Cafe_en]

Gelfand's proof for Cauchy-Schwarz Inequality for real inner product spaces

Source: I.M. Gelfand, "Lectures on Linear Algebra" (https://t.co/uOq1RO2bz6).

[Maaike Verbruggen @M__Verbruggen]

Yes PhDs around the world, please adopt this method

(If all my competitors just generate junk instead of doing research my job security is secured)

[kevin meissner @pwnkip]

for years, society was limited to only 16 syrup squares per waffle but with recent combinatorial optimization breakthroughs our research department has achieved previously unheard of densities of waffle syrup

[MichaelMaths @michaelmaths_]

@2oovy Congrats!! 🥳 🎉

[MichaelMaths @michaelmaths_]

@chainmonkey2 @KenOno691 That would be more like Willan’s formula, that essentially encodes a brute force sieve for primes using Wilson’s theorem in a sum

[Grant Sanderson @3blue1brown]

Well, math terminology being what it is, something like this was bound to happen eventually.

(If you're curious about why these balls are so puny, the full talk is up on YouTube)

[Francisco Roldán @fqroldan]

By far the most important comment I've gotten in referee reports (not joking). I think about it and re-implement it ~once per week.