Related papers: Fermat's Last Theorem and its another Proof

This paper presents a short and simple proof of the Four-Color Theorem that can be utterly checkable by human mathematicians, without computer assistance. The new key idea that has allowed it and the global structure of the proof are…

Our goal in the present paper is to give a new ergodic proof of a well-known Veech's result, build upon our previous works.

A simple proof of Egorov's theorem for infinite measure is given

We present a simple proof of the fundamental theorem of Galois theory, which establishes a correspondence between the intermediate fields of a finite Galois extension and the subgroups of its Galois group. The proof is based on the…

This paper contains a new elementary proof of the Fundamental Theorem of Calculus for the Lebesgue integral. The hardest part of our proof simply concerns the convergence in ${\rm L}^1$ of a certain sequence of step functions, and we prove…

In this paper the circulant Hadamard conjecture is proved.

The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…

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

A new description is given of all solutions to the relaxed commutant lifting problem. The method of proof is also different from earlier ones, and uses only an operator-valued version of a classical lemma on harmonic majorants.

In [J. Combin. Theory Ser. B 70 (1997), 2-44] we gave a simplified proof of the Four-Color Theorem. The proof is computer-assisted in the sense that for two lemmas in the article we did not give proofs, and instead asserted that we have…

I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.

We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.

The classical Technical Lemma for congruences is not difficult to prove but it is very efficient in its applications. We present here a Technical Lemma for congruences on \emph{finite lattices}. This is not difficult to prove either but it…

In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.

In this note we exhibit a very simple proof of McNaughton Theorem, almost right out of the definitions, and at the same time we observe that this theorem does not depend of Chang's completeness theorem.

In this paper, we give a new and short proof of a Theorem on k-hypertournament losing scores due to Zhou et al.[7].

Standard proofs of Lusin's theorem, using simple functions, are sometimes quite elaborate. Here, we give a one-sentence proof of Lusin's theorem. We do not believe our approach, by way of inverse images, is new. However, this particular…

We show that the subgroup lattice of any finite group satisfies Frankl's Union-Closed Conjecture. We show the same for all lattices with a modular coatom, a family which includes all supersolvable and dually semimodular lattices. A common…

We prove a generalization of Istvan F\'ary's celebrated theorem to higher dimension.

Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…