Theorem of the Day

List of pending theorems with web resources

At some time in the future I hope there will be a page for each of the following theorems and, as I come across them, record web resources to help me. Links to pageswhich I want to study in the hopes of improving existing theorems are also kept here, in which case the theorem names link to their entry in my main theorem list.

Please email me and with either theorems you would like to see added to the list or weblinks which you think will be valuable to me.


Main List of Theorems
Theorem of the Day Home Page

The Baire Category Theorem
"The Baire Category [theorem] is a profound triviality which condenses the folk wisdom of a generation of ingenious mathematicians into a single statement." Tom Körner See under Course Notes, Notes for the Part II course Linear Analysis (the quote is in Section 6

Bell's Theorem

Bezout's Theorem

The Billiards Circuit Theorem

Bloom's Egyptian Fraction Theorem

Busy Beaver Theorem


Cauchy's Integral Formula

Cauchy's Residue Theorem

Cauchy–Schwarz Inequality

Combinatorial Nullstellensatz

Cook's Theorem on NP-completeness

Decidability of Tiling

Dunn and Pretty's Triangle-Halving Deltoid

The Erdos conjecture on arithmetic progressions

Euclid Book 1 Proposition 1

Frobenius' theorem on real division algebras

The Fundamental Theorem of Arithmetic

The Fundamental Lemma of the Calculus of Variations

The Fundamental Theorem of Galois Theory

Gauss's Linking formula

Goldbach's Summation Identity

The Hahn–Banach Theorem

The Hall–Paige Conjecture

The Ham Sandwich Theorem
Breuer, F. Uneven Splitting of Ham Sandwiches. Discrete Comput Geom 43, 876–892 (2010).

Hensel's Lemma,Yuchen.pdf

The Hopf Umlaufsatz

L'Hospital's Rule

The Impossibilities

Legendre's Theorem on Factorial Factors

The Lonely Runner Conjecture

The Mandelbrot set is connected

The Mean-value theorem

Menelaus' and Ceva's theorems (and triple product rule)

Pappus's theorem
A comment on Twitter from @ArthurNewlands reminds me to upgrade this page! "I love this theorem for many reasons. Because it is a special case of Pascal's Hexagrammum Mysticum, which is, in turn, a special case of Cayley–Bacharach; because of its dual form; because it helps characterise a projective plane over a field; because implies Desargues' thm etc."

The Pentagonal Tiling Theorem

The PCP Theorem

The Road-colouring Theorem

The Shoelace formula

Sierpinski's inequality

Tarski's high school algebra problem's_high_school_algebra_problem

The Tarski–Seidenberg theoremm

The Toeplitz Square Peg Problem

Tunnell's Theorem

The Universal Coefficient Theorem in Homology

Van der Waerden’s Theorem on Arithmetic Progressions

Yenoda's Lemma

Zermelo's Theorem in Game Theory
Main List of Theorems
Theorem of the Day Home Page