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
- 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.
- Upper triangular matrices product (Mathematics Exercise)Prove that the product of two upper triangular matrices is also upper triangular.
- Solving a Quadratic Equation (Mathematics Exercise)Practice solving a quadratic equation using the quadratic formula.
Deep Dives
Explore in-depth articles and essays on foundational topics, advanced concepts, and the philosophy of mathematics and physics.
Coming soon: Rigorous explorations of infinity, symmetry, quantum paradoxes, and more.
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.