Related papers: Georg Mohr's "Euclides Danicus" -- Preliminary Ver…

The Euler-Mascheroni constant is calculated by three novel representations over these sets respectively: 1) Tur\'an moments, 2) coefficients of Jensen polynomials for the Taylor series of the Riemann Xi function at s=1/2+i.t and 3) even…

I attempted to write the full translation of this article to make the remarkable proof of Pierre Deligne available to a greater number of people. Overviews of the proofs can be found elsewhere. I especially recommend the notes of James…

As a first application of a very old theorem, known as Herschel's theorem, we provide direct elementary proofs of several explicit expressions for some numbers and polynomials that are known in combinatorics. The second application deals…

This paper contains the proof of Macdonald's duality and evaluation conjectures, the definition of the difference Fourier transform, the recurrence theorem generalizing Pieri rules, and the action of GL(2,Z) on the Macdonald polynomials at…

In the paper we formulate and verify a difference counterpart of the Macdonald-Mehta conjecture and its generalization for the Macdonald polynomials. Namely, we determine the Fourier transforms of the polynomials multiplied by the Gaussian,…

We sketch several proofs of F\'ary--Milnor theorem.

In 1962 Charles Hartshorne published a modal logic proof formalizing Anselm of Canterbury's ontological argument for the necessary existence of God. This article presents Kurt G\"odel's notes on this proof which have now been discovered in…

This expository and review paper deals with the Diamond Lemma for ring theory, which is proved in the first section of G. M. Bergman, The Diamond Lemma for Ring Theory, Advances in Mathematics, 29 (1978), pp. 178-218. No originality of the…

We present a short new proof of the canonical polynomial van der Waerden theorem, recently established by Girao [arXiv:2004.07766].

We give a new proof of Lucas' Theorem in elementary number theory.

This paper presents a simple proof of Dekel (1986)'s representation theorem for betweenness preferences. The proof is based on the separation theorem.

We propose two different derivations of Pythagoras Theorem and apply the same to study discrete and continuum states.

We present logarithmic series for u, ln u and the Euler-Mascheroni constant gamma. It was indicated by J. Sondow that Theorem 4 and all proofs are new. All proofs are elementary. We present some conjectures.

We re-derive Thales, Pythagoras, Apollonius, Stewart, Heron, al Kashi, de Gua, Terquem, Ptolemy, Brahmagupta and Euler's theorems as well as the inscribed angle theorem, the law of sines, the circumradius, inradius and some angle bisector…

Annotated parallel text in Latin and English of the paper of Adam Adamandy Kocha\'nski "Solutio Theorematum Ab illustri Viro in Actis hujus Anni Mense Januario, pag. 28. propositorum", Acta Eruditorum, Lipsiae 1682, pp. 230-236, in which he…

The result of this paper is proved in arXiv:1112.1163

Douglass B. Morris announced in 1970 that it is consistent with ZF that "For every $\alpha$, there exists a set $A_\alpha$ which is the countable union of countable sets, and $\mathcal P(A_\alpha)$ can be partitioned into $\aleph_\alpha$…

In this note, while giving an overview of the state of art of the well known Hadamard conjecture, which is more than a century old and now it has been established by using the methods given in the two papers by Mohan et al [6,7].

We prove several extensions of the Erdos-Fuchs theorem.

Between 1941 and 1962, scalar-tensor theories of gravitation were suggested four times by different scientists in four different countries. The earliest originator, the Swiss mathematician W. Scherrer, was virtually unknown until now…