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We prove the Aharoni Berger Conjecture

The paper contains an alternative proof of M. Kontsevich Formality Theorem.

This article aims at clarifying the language and practice of scientific experiment, mainly by hooking observability on calculability.

We prove a variation of Gronwall's lemma.

A short and almost elementary proof of the Boros-F\"uredi-B\'ar\'any-Pach-Gromov theorem on the multiplicity of covering by simplices in $\mathbb R^d$ is given.

We present a very simple example of a theorem with constructive and non-constructive proofs: the equation c^2 x^2 - (c^2 + c)x + c = 0 has a solution.

We prove Burkholder inequality using Bregman divergence.

In this note we give a detailed proof of a theorem of Aubin.

We proved three theorems of $S$-version of the mulyiplicity one.

We give a categorical account of Arrow's theorem, a seminal result in social choice theory.

We present a solution of Exercise 1.2.1 of [2] which yields a short new proof of a key step in one of proofs of Brouwer's fixed point theorem, 1910. A few people asked the author about the details of the solution and they might be…

We present a short proof of the Church-Rosser property for the lambda-calculus enjoying two distinguishing features: Firstly, it employs the Z-property, resulting in a short and elegant proof; and secondly, it is formalized in the nominal…

The purpose of this article is to provide a version of Bloch-Wigner theorem over the class of rings with many units.

We give a short proof of the strong law of large numbers based on duality for random walk

In the paper it is demonstrated that Bells theorem is an unprovable theorem.

A very short and direct proof along the lines of the Kamae-Katznelson-Weiss approach.

The better title is "Yet another FALSE proof of the 4-colour theorem." Please consider all versions of this paper as historical material on the way to a non-computer proof of the 4-colour theorem. Interpreted as proofs, all versions are…

We intoduce a local version of the Jordan-Brouwer separation theorem and deduce some global statements, some of which may follow from known results, but the technique is new.

In this paper, we give a simple counter example to the famous Hodge conjecture.

We add another brick to the large building comprising proofs of Pick's theorem. Although our proof is not the most elementary, it is short and reveals a connection between Pick's theorem and the pointwise convergence of multiple Fourier…