Related papers: A simple proof of the Lebesgue decomposition theor…

We describe two distinct simple, short and self contained proofs of the composition lemma.

This article provides a simple proof of the quadratic formula, which also produces an efficient and natural method for solving general quadratic equations. The derivation is computationally light and conceptually natural, and has the…

We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.

Several Lebesgue-type decomposition theorems in analysis have a strong relation to the operation called: parallel sum. The aim of this paper is to investigate this relation from a new point of view. Namely, using a natural generalization of…

These notes are a self-contained short proof of the stability of persistence diagrams.

We give a direct, purely arithmetical and elementary proof of the strong normalization of the cut-elimination procedure for full (i.e. in presence of all the usual connectives) classical natural deduction.

We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.

In this note we obtain a new convergence result for the Adomian decomposition method.

We give a short and self-contained proof of the Decomposition Theorem for the non-small resolution of a Special Schubert variety. We also provide an explicit description of the perverse cohomology sheaves. As a by-product of our approach,…

We give an elementary proof to Hasse theorem.

We present an astonishingly simple and elegant proof of the celebrated Basel problem.

A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.

We present an elementary proof of the fundamental theorem of algebra, following Cauchy's version but avoiding his use of circular functions. It is written in the same spirit as Littlewood's proof of 1941, but reduces it to more elementary…

The purpose of this article is to present my new proof of the the construction and the convergence theorem of spectral sequences of filtered complexes, which is much shorter and cleaner than the "standard" proof.

We provide a simple proof of Kamp's theorem.

We give a new proof of the fundamental theorem of algebra. It is entirely elementary, focused on using long division to its fullest extent. Further, the method quickly recovers a more general version of the theorem recently obtained by…

The aim of this short paper is to give a practical introduction to functional interpretation of proofs for computer scientists interested in synthesis.

We present simple and direct proof to an important case of Nash-Moser-Ekeland theorem.

We give a new simpler proof of a theorem of Jayne and Rogers.

We revisit a classic proof of the Blaschke-Lebesgue theorem. It is based on the support function of a convex curve and the approximation of constant width curves by Reuleaux polygons.