Updates April 2020-January 2021

After this, I stopped updating the website. Instead, I wrote book “Landscape of 21st Century Mathematics” that collects all these theorems by topics and, for many Theorems, provides more details and context. The book is published by Springer in 2021, see here .

18.01.2021 I have added Theorem The number of n-faces genus-g triangulations if g/n converges to a constant, selected from the most recent issue of Inventiones Mathematicae.

16.01.2021 I have added Theorem Amir’s conjecture for random walks on groups is true selected from the most recent issue of the Annals of mathematics, and also Theorem Approximation ratio 3/2 for the metric TSP is not optimal, which is one of the greatest 2020 results in the theory of algorithms.

06.01.2021 I have added Theorem Size of A\subset [N] without distincts degree polynomial progressions is \leq\frac{N}{(\log\log N)^c}, selected from the most recent issue of Forum of Mathematics, Pi.

21.12.2020 I have added Theorems Explicit examples of degree N polynomials with condition numbers O(\sqrt{N}), Chromatic number of G(n,\frac{1}{2}) is not concentrated on n^{\frac{1}{4}-\epsilon} consecutive values, and The hot spots conjecture is true for Lip domains, selected from the Journal of the AMS.

23.11.2020 I have added Theorem Kesten’s theorem holds for random Kronecker sequences on the torus T^d, selected from the most recent issue of Publications mathématiques de l’IHÉS.

14.11.2020 I have added Theorems Mason’s ultra-log-concavity conjecture for matroids independent sets is true, There exist full-sized groups that are profinitely rigid in the absolute sense, and Flat Littlewood polynomials exist, selected from the most recent issue of the Annals of Mathematics.

09.11.2020 I have added Theorem There exist coarsely non-amenable group that is coarsely embeddable into l^2, selected from the most recent issue of Acta Mathematica.

02.11.2020 I have added Theorem The set of non-weakly mixing IETs has Hausdorff codimension at most 1/2, selected from the most recent issue of Inventiones Mathematicae.

12.10.2020 I have added Theorem The Szemerédi–Trotter estimate holds for hypersurfaces in {\mathbb R}^d, selected from the most recent issue of Inventiones Mathematicae.

04.10.2020 I have added Theorem The Benjamini-Schramm conjecture is true for nonunimodular graphs, selected from the most recent issue of the Journal of the AMS.

21.09.2020 I have added Theorems The Weyl-type bound holds for Dirichlet L-functions of cube-free conductor, There are at most B_n X^{C\log^3 n} degree n number fields with discriminant \leq X, Hyperbolic motions of any shape exist in the Newtonian N-body problem and For every Banach space, its Rademacher type and Enflo type coincide, selected from the most recent issue of the Annals of Mathematics.

13.07.2020 I have added a very recent Theorem The size of A\subset \{1,...,N\} without 3-term progressions is O\left(\frac{N}{\log^{1+c} N}\right), \, c>0, which I learned from Gil Kakai’s  blog.

11.07.2020 I have added Theorem K_{d,d} maximises the normalised number of q-colorings over d-regular graphs, selected from the most recent issue of Inventiones Mathematicae.

29.06.2020 I have added Theorem Non-collision singularities exist in a planar Newtonian 4-body problem, selected from the most recent issue of Acta Mathematica.

01.06.2020 I have added Theorems Characterisation of polyhedral types inscribed in the hyperboloid or cylinder and The Julia set of the Feigenbaum polynomial has zero Lebesgue measure, selected from the most recent issue of Inventiones Mathematicae.

18.05.2020 I have added recent great Theorem The Schinzel-Zassenhaus conjecture on integer polynomials is true which I learned from this week Quanta magazine article.

01.11.2019 – 30.04.2020 An initial list of 414 Theorems has been added to the website. All the Theorems added after 30.04.2020 are explicitly listed on this page.

Go to the list of all theorems sorted by the submission date.