Related papers: Windmills of the minds: an algorithm for Fermat's …
Recently Lieb and Seiringer showed that the Bessis-Moussa-Villani conjecture from quantum physics can be restated in the following purely algebraic way: The sum of all words in two positive semidefinite matrices where the number of each of…
We present an elementary proof of Fermat's Last Theorem. No ancillary results are used, not even the most basic ones. The proof directly leads to a contradiction of the Fermat equation in the set of integers.
The matrix model formulation of two dimensional string theory has been shown to admit time dependent classical solutions whose closed string duals are geodesically incomplete space-times with space-like boundaries. We investigate some…
We give an informal summary of ongoing work which uses tools distilled from the theory of fibre bundles to classify and connect invariant fields associated with spin motion in storage rings. We mention four major theorems. One ties…
We present a streamlined, slightly modified version, in the two-variable situation, of a beautiful, but not so well known, theory by B\"{o}gel, already from the 1930s, on an alternative higher dimensional calculus of real functions, a…
We provide a geometric interpretation of Brillhart's celebrated algorithm for expressing a prime $p\equiv 1\pmod 4$ as the sum of two squares.
The algebraic formulation of Wick's theorem that allows one to present the vacuum or thermal averages of the chronological product of an arbitrary number of field operators as a determinant (permanent) of the matrix is proposed. Each…
We present an elementary inductive proof which Euler could have obtained, for the corresponding result as the title indicates, had he refined a bit his proof for Fermat's assertion on representing primes as two squares.
Two-points nonlocal problem for the first order differential evolution equation with an operator coefficient in a Banach space $X$ is considered. An exponentially convergent algorithm is proposed and justified in assumption that the…
An optimal algebraic model of particle physics has a number of checkpoints to pass. As a minimum, models should $\langle 1 \rangle$ conform to the Coleman-Mandula theorem (or establish a loophole), $\langle 2 \rangle$ evade familiar fermion…
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.
Despite the astonishing successes of quantum mechanics, due to some fundamental problems such as the measurement problem and quantum arrival time problem, the predictions of the theory are in some cases not quite clear and unique.…
Our paper is the first study of what one might call "reverse mathematics of explicit fixpoints". We study two methods of constructing such fixpoints for formulas whose principal connective is the intuitionistic Lewis arrow. Our main…
The theorem of factorisation forests shows the existence of nested factorisations -- a la Ramsey -- for finite words. This theorem has important applications in semigroup theory, and beyond. The purpose of this paper is to illustrate the…
We present a proof of Arrow's theorem from social choice theory that uses a fixpoint argument. Specifically, we use Banach's result on the existence of a fixpoint of a contractive map defined on a complete metric space. Conceptually, our…
This paper addresses the problem of checking invariant properties for a large class of symbolic transition systems, defined by a combination of SMT theories and quantifiers. State variables can be functions from an uninterpreted sort…
We consider two orthogonal points of view on finite permutations, seen as pairs of linear orders (corresponding to the usual one line representation of permutations as words) or seen as bijections (corresponding to the algebraic point of…
We study infinite words fixed by a morphism and their derived words. A derived word is a coding of return words to a factor. We exhibit two examples of sets of morphisms which are closed under derivation --- any derived word with respect to…
The interface between classical physics and quantum physics is explained from the point of view of quantum information theory (Feynman Processes). The interpretation depends on a hefty sacrifice: the classical determinism or the arrow of…
Comments about the paper by Elsholz, Fermat's last theorem implies Euclid's infinitude of primes, (2021), and simplification.