I was playing around, and stumbled upon something quite beautiful.. 👉If you sum over the volumes of all 2k-dimensional unit spheres, that sum converges to e^π. I have no idea why this should be true..

41 triple pendulums with 𝑠𝑙𝑖𝑔𝘩𝑡𝑙𝑦 different initial conditions (source:external-preview.redd.it/Cp2AZd3V52nIuM…)

Vertically oscillating points whose frequencies are their positions on the x-axis [ i.e. yᵢ = sin(xᵢ t) ]

An easy & inexpensive way to mimic an object blowing in the wind

crazy how much group theory i used to know. in hindsight, a bit too much

Fundamental physics is in a strange liminal space where the problems are so incredibly difficult one essentially has to gamble their entire career away to make progress.

BREAKING: Biden calls for a ban on congressional stock trading by politicians.

'A good proof is one that makes us wiser.' -- Yuri Manin

The Riemann zeta function has a singularity at 1, but its Cauchy principle value at 1 equals the Euler–Mascheroni constant.

ᴴᵃᵐˢᵗᵉʳ ᴮᵃˡˡ 🏐🏃‍♂️🪟🐹

Common misconception. Newtonian gravity (no spacetime) *also* allows a massless particle to be affected by gravity: in 1801, von Soldner calculated the trajectories of such particles by taking limits as M->0. Interestingly, the deflection is exactly half that predicted by GR.

complex Fourier Series

Noether's theorem: If a system has continuous symmetries, there are corresponding quantities conserved over time.

At the LHC, collisions occur every 25 nanoseconds, meaning that by the time the next collision happens, the data from the previous one has only traveled a few meters through the fiber-optic cables Yes, the speed of light is a limiting factor!

Jackson E&M

This is literally one postdoc catching a stray

This is wonderful: Roy Kerr who discovered an exact solution to Einstein's field equations for spinning black holes - a solution that Subrahmanyan Chandrasekhar called "shuddering before the beautiful" - attributes his success (where others had failed) to his maverick approach.

Plots in "circular coordinates" (not polar coordinates). First, x^5 . 🧵 1/5