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 lThe 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)
