Related papers: A really simple elementary proof of the uniform bo…
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.
We provide a short proof, not utilizing complex numbers, for the solution set of homogeneous second order linear differential equations with constant coefficients.
Every definably complete expansion of an ordered field satisfies an analogue of the Baire Category Theorem.
The non-transitivity without extra constraints in the Euler equation in any dimension is almost evident and can be derived, e.g., from Morse theory.
We give a short, explicit proof of Hindman's Theorem that in every finite coloring of the integers, there is an infinite set all of whose finite sums have the same color. We give several exampls of colorings of the integers which do not…
We present a powerful theorem for proving the irreducibility of tempered unitary representations of the free group.
This is a companion note to our paper 'A relative Szemer\'edi theorem', elaborating on a concluding remark. In that paper, we showed how to prove a relative Szemer\'edi theorem for $(r+1)$-term arithmetic progressions assuming a linear…
We present a conjecture about partitions, with a very elementary formulation.
We prove two versions of a boundary Harnack principle in which the constants do not depend on the domain.
We prove a version of the classical 'generic smoothness' theorem with smooth varieties replaced by non-commutative resolutions of singular varieties. This in particular implies a non-commutative version of the Bertini theorem.
Suppose $G$ is a simple group. For any nontrivial elements $g$ and $h$, $g$ can be written as a finite product of conjugates of $h$ or the inverse of $h$. G is called uniformly simple if the length of such an expression is uniformly…
We give a short proof of an improved version of the Effros Open Mapping Principle via a shift-compactness theorem (also with a short proof), involving `sequential analysis' rather than separability, deducing it from the Baire property in a…
The main result can be given a short and elementary proof which has been incorporated into Lemma 3.2 of arXiv:1206.5775
We present an elementary, self-contained proof of Grothendieck's inequality that unifies the real and complex cases and yields both the Krivine and Haagerup bounds, the current best-known explicit bounds for the real and complex…
A very short proof of Kneser's theorem via transversal is given.
In the case of monotone independence, the transparent understanding of the mechanism to validate the central limit theorem (CLT) has been lacking, in sharp contrast to commutative, free and Boolean cases. We have succeeded in clarifying it…
In this paper we give a refinement of the method introduced by Lawrence and Venkatesh and thereby showing that their proof of Mordell's conjecture is uniform up to a uniform bound on the number of Galois representations attached to some…
This paper gives a new elementary proof of the theorem that all vector bundles on $\mathbb P^1$ split into the direct sum of line bundles. The proof is based on the study of divisors associated to germs of sections at the generic point.
We give a simple proof of Voisin's Theorem for general canonical curves of even genus. This completely determines the terms of the minimal free resolution of the coordinate ring of such curves.
A one-line proof of a minimax theorem due to Steinerberger is given.