I don’t know who needs to hear this, but Physics ≠ Mathematics.
Not gonna lie, the intensity of reactions/emotions this simple statement evoked surprises me.
I mainly meant it as a joke on the "I don't know who needs to hear this" type of tweets.
The statement itself is (or should be) obvious to anyone with the smallest level perspective on these subjects.
In my experience, it's only smug math/physics undergrads and delusional people would think that one is better than the other or that one is contained in the other.
Of course, the overlap and interaction between Mathematics and Physics are immense, but both are so much bigger than the intersection.
The more you see that the more you appreciate their difficult, yet fruitful "marriage".
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Earlier this year a friend* and I've solved a long-standing problem which, in part, meant finding the eigenvectors of this matrix. In this thread, I'll review our result and bits of 170 years of history
*J.F. van Diejen, Talca
1/n
The title of our paper is "Elliptic Kac–Sylvester Matrix from Difference Lamé Equation" and it was recently published in the mathematical physics journal Annales Henri Poincaré.
Just to "name-drop" some of the characters that will appear in the story: Sylvester (duh), Jacobi, Boltzmann, two Ehrenfests, Schrödinger and Kac (obvs).
(I'll expand the thread over several days so please be patient.)
3/n
"Here's a photo of my boy, Peter. He doesn't yet know what the continuum is, but he doesn't know what fascism is either." - George Szekeres' message to Paul Erdős.
Peter Szekeres was born in Shanghai, where his parents George Szekeres and Esther Klein escaped from Nazi persecution in 1938.
Happy Ending Theorem: any set of five points in the plane in general position has a subset of four points that form the vertices of a convex quadrilateral.
Erdős gave this name to the theorem, because it led to the marriage of Szekeres and Klein
As a run-up to the "Introduction to Integrability" series (see my pinned tweet), I decided to share some interesting bits from the history of integrable systems.
Let's start at the beginning, shall we? So Newton...
#1 It all started with Newton solving the gravitational 2-body problem and deriving Kepler's laws of planetary motion as a result. I would argue that this was possible, because the Kepler problem is (super)integrable. [1/2]
This roughly means that there are many conversed physical quantities like energy, angular momentum, and the Laplace-Runge-Lenz vector. These conservation laws restrict the motion and allow for explicit analytic solutions of otherwise difficult equations. [2/2]