Related papers: A double-inductive proof of Moessner's theorem
In this note I provide two extensions of a particular case of the classical Poncelet theorem.
A more detailed derivation of the Heisenberg uncertainty principle from the certainty principle is given.
In this paper we give an elementary proof of the local sum conjecture in two dimensions. In a remarkable paper [CMN, arXiv:1810.11340], this conjecture has been established in all dimensions using sophisticated, powerful techniques from a…
We present a simpler way than usual to deduce the completeness theorem for the second-oder classical logic from the first-order one. We also extend our method to the case of second-order intuitionistic logic.
We present a self-contained elementary and detailed exposition of Mertens' own proof of his theorem on the divergence of the series of the reciprocals of the primes and compare it with the modern proofs. His proof contains explicit…
In this note we give a detailed proof of a theorem of Aubin.
We present a sequent-based deductive system for automatically proving entailments in separation logic by using mathematical induction. Our technique, called mutual explicit induction proof, is an instance of Noetherian induction.…
This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.
We prove a generalization of classical Montel's theorem for the mixed differences case, for polynomials and exponential polynomial functions, in commutative setting.
We give an elementary proof to Hasse theorem.
We give a simple short proof of Brooks' theorem using only induction and greedy coloring, while avoiding issues of graph connectivity. The argument generalizes easily to some extensions of Brooks' theorem, including its variants for list…
We present a simple proof of the Riemann's Hypothesis (RH) where only undergraduate mathematics is needed.
We present an astonishingly simple and elegant proof of the celebrated Basel problem.
It is discussed that Zeeman's theorem can be directly obtained from Liouville's theorem if we assume sufficient differentiability.
Working from definitions and an elementarily obtained integral formula for the Euler-Mascheroni constant, we give an alternative proof of the classical Puiseux representation of the exponential integral.
To determine Euler numbers modulo powers of two seems to be a difficult task. In this paper we achieve this and apply the explicit congruence to give a new proof of a classical result due to M. A. Stern.
There are several proofs of the Fundamental Theorem of Algebra, mainly using algebra, analysis and topology. In this article, we have shown that the Fundamental Theorem of Algebra can be proved using Nevanlinna's first fundamental theorem…
Many proofs of the fundamental theorem of algebra rely on the fact that the minimum of the modulus of a complex polynomial over the complex plane is attained at some complex number. The proof then follows by arguing the minimum value is…
We expose here a short proof of Cramer's theorem in R based on convex duality.
We give a proof of the Bourgain-Milman theorem using complex methods. The proof is inspired by Kuperberg's, but considerably shorter.