TheoremVault
Exploring the Foundations of Mathematics and Physics
"A repository of elegant proofs, deep theory, and challenging exercises."
Inspirational Quotes
"The essence of mathematics is not to make simple things complicated, but to make complicated things simple." — S. Gudder
"The most incomprehensible thing about the world is that it is comprehensible." — Albert Einstein
"Pure mathematics is, in its way, the poetry of logical ideas." — Albert Einstein
"Physics is like sex: sure, it may give some practical results, but that's not why we do it." — Richard Feynman
Mathematics
Uncover the beauty of mathematical proofs and explore abstract structures.
Explore Mathematics →Physics
Investigate fundamental laws and theories that govern the physical universe.
Discover Physics →Recent Additions
- Gojo's Infinity as a Conformal Metric: Placing a Point at Infinite Geodesic Distance (Mathematics Theory)Modeling Gojo's Infinity from Jujutsu Kaisen with differential geometry: a critique of a kernel-based metric where Gojo's position never appears, and an alternative conformal metric that places him at infinite geodesic distance from every other point in space.
- Can a Laser Spot Sweep Across the Moon Faster Than Light? (Physics Theory)If you point a laser at the Moon and flick your wrist, the spot can sweep across the lunar surface faster than the speed of light. We compute how fast it actually moves and explain why this does not contradict special relativity.
- Antisymmetric Matrix Diagonal (Mathematics Exercise)Prove that the diagonal elements of an antisymmetric matrix are zero.
- Commuting Matrices Product (Mathematics Exercise)Prove that if A commutes with B and A commutes with C, then A commutes with the product of B and C.
- Hermitian Matrix Diagonal (Mathematics Exercise)Prove that the diagonal elements of a Hermitian matrix are real.
Deep Dives
In-depth articles born from real debates, where popular culture meets rigorous mathematics and physics.
- Can a Laser Spot Sweep Across the Moon Faster Than Light? (Physics)Flick your wrist and the spot moves at 20c — yet special relativity survives. Here is why.
- Gojo's Infinity as a Conformal Metric (Mathematics)A Riemannian metric that places Gojo at infinite geodesic distance: each halving of the gap doubles its felt length.
Classic Proofs
A curated collection of the most elegant and influential proofs in mathematics and physics, explained with clarity and rigor.
Coming soon: Euclid's Elements, Galois theory, Noether's theorem, and more.
Challenging Problems
Test your skills with a selection of rigorous problems and exercises, from undergraduate classics to unsolved mysteries.
Coming soon: Problem sets, solution write-ups, and open questions.