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.
Bell's Theorem
www.quantamagazine.org/a-new-theorem-maps-out-the-limits-of-quantum-physics-20201203/
The Billiards Circuit Theorem
www.tandfonline.com/doi/full/10.1080/00029890.2023.2230860
Bloom's Egyptian Fraction Theorem
arxiv.org/abs/2305.02689
Cantor–Bernstein–Schröder
https://arxiv.org/abs/math/0605779
Cauchy's Integral Formula
robjlow.blogspot.com/2019/04/cauchy-and-other-mean-value-theorem.html
Cauchy's Residue Theorem
en.wikipedia.org/wiki/Residue_theorem
Combinatorial Nullstellensatz
en.wikipedia.org/wiki/Restricted_sumset
Cook's Theorem on NP-completeness
https://quorasessionwithscottaaronson.quora.com/Do-you-expect-that-P-NP-is-decidable-in-ZFC-and-what-about-BQP-or-RP-1111
Decidability of Tiling
https://arxiv.org/abs/1602.05738
https://terrytao.wordpress.com/2022/11/29/a-counterexample-to-the-periodic-tiling-conjecture-2/
https://www.quantamagazine.org/mit-math-students-continue-aristotles-tetrahedra-tiling-20210209/
https://www.quantamagazine.org/computer-search-settles-90-year-old-math-problem-20200819/
Dunn and Pretty's Triangle-Halving Deltoid
https://ems.press/content/serial-article-files/4415
https://link.springer.com/article/10.1007/s00022-005-0006-0
https://dl.acm.org/doi/abs/10.1016/j.aam.2022.102342
https://msp.org/involve/2015/8-2/involve-v8-n2-p11-p.pdf
The Erdos conjecture on arithmetic progressions
https://www.quantamagazine.org/landmark-math-proof-clears-hurdle-in-top-erdos-conjecture-20200803/
Euclid Book 1 Proposition 1
http://cgm.cs.mcgill.ca/~godfried/teaching/dm-reading-assignments/Euclid-Second-Proposition-Math-Intell.pdf
Frobenius' theorem on real division algebras
https://danshved.wordpress.com/2013/05/09/frobenius-theorem-on-real-division-algebras /
The Fundamental Theorem of Arithmetic
https://www.sciencedirect.com/science/article/pii/031508609290075M
The Fundamental Theorem of Galois Theory
https://www.quantamagazine.org/how-galois-groups-used-polynomial-symmetries-to-reshape-math-20210803/
Goldbach's Summation Identity
https://www.researchgate.net/publication/262857022_Series_Involving_the_Zeta_Functions_and_a_Family_of_Generalized_Goldbach-Euler_Series
https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/bibiloni206.pdf
The Hahn–Banach Theorem
abstrusegoose.com/124
The Hall–Paige Conjecture
https://cameroncounts.wordpress.com/2018/12/18/the-hall-paige-conjecture/
https://download.arxiv.org/pdf/2003.01798v2.pdf
Hensel's Lemma
https://math.uchicago.edu/~may/REU2018/REUPapers/Chen,Yuchen.pdf
https://www.quantamagazine.org/how-the-towering-p-adic-numbers-work-20201019/
The Hopf Umlaufsatz
https://people.math.harvard.edu/~knill/teaching/math22a2018/handouts/lecture15.pdf
https://www2.math.upenn.edu/~pjmcgrat/research/umlaufsatz.pdf
https://mathematik.com/Hopf/
L'Hospital's Rule
https://web.math.ucsb.edu/~agboola/teaching/2021/winter/122A/rudin.pdf
The Impossibilities
https://www.maa.org/sites/default/files/pdf/upload_library/22/Allendoerfer/Suzuki.pdf
https://www.jstor.org/stable/30037438
https://www.britannica.com/topic/Trisecting-the-Angle-Archimedes-Method-724632#ref1074301
Legendre's Theorem on Factorial Factors
https://www.cut-the-knot.org/blue/LegendresTheorem.shtm l
The Lonely Runner Conjecture
https://terrytao.wordpress.com/2017/01/10/some-remarks-on-the-lonely-runner-conjecture/
The Mean-value theorem
https://abesenyei.web.elte.hu/publications/meanvalue.pdf
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 Road-colouring Theorem
en.wikipedia.org/wiki/Road_coloring_theorem
The Shoelace formula
https://gdz.sub.uni-goettingen.de/id/PPN352846038_0001
Tarski's high school algebra problem
https://en.wikipedia.org/wiki/Tarski's_high_school_algebra_problem
The Toeplitz Square Peg Problem
https://terrytao.wordpress.com/2016/11/22/an-integration-approach-to-the-toeplitz-square-peg-problem/
Tunnell's Theorem
https://www.math.rug.nl/~top/Chandrasekar.pdf
The Universal Coefficient Theorem in Homology
https://digitalcommons.colby.edu/cgi/viewcontent.cgi?article=1883&context=honorstheses
Van der Waerden’s Theorem on Arithmetic Progressions
https://pointatinfinityblog.wordpress.com/tag/van-der-waerden/
http://www.cs.umd.edu/~gasarch/TOPICS/vdw/GKPbook.pdf
https://www.sciencedirect.com/science/article/pii/S0097316508000137
https://arxiv.org/pdf/2102.01543.pdf
Yenoda's Lemma
https://terrytao.wordpress.com/2023/08/25/yonedas-lemma-as-an-identification-of-form-and-function-the-case-study-of-polynomials/
Zermelo's Theorem in Game Theory
https://en.wikipedia.org/wiki/Zermelo%27s_theorem_(game_theory)