Related papers: How long is a Proof? - A short note

The paper is withdrawn by the author due to an oversimplified and misleading approach which was taken initially as a starting point.

Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.

The paper has benn withdrawn because the computation of the external virial contains an error which invalidate the main result.

In the short note, we describe a sampling construction that yields a sequence of graphons converging to a prescribed limit graphon in 1-norm. This convergence is stronger than the convergence in the cut norm, usually used to study graphon…

We give examples of calculi that extend Gentzen's sequent calculus LK by unsound quantifier inferences in such a way that (i) derivations lead only to true sequents, and (ii) proofs therein are non-elementarily shorter than LK-proofs.

Proofs that a smooth morphism is flat available in the literature are long and difficult. We give a short proof of this fact.

These informal notes are concerned with sums and averages in various situations in analysis.

The Halting Problem is ill-conceived and ill-defined.

These notes are a self-contained short proof of the stability of persistence diagrams.

Large language models demonstrate promising long context processing capabilities, with recent models touting context windows close to one million tokens. However, the evaluations supporting these claims often involve simple retrieval tasks…

Withdrawn due to error. See D. Lowe, L. Susskind and J. Uglum, hep-th/9402136, for correct treatment. Apologies to all recipients.

This paper has been withdrawn by the author due to the presented idea is wrong.

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…

This note is the written version of conversations with young colleagues on unofficial history, general ideas, unexpected facts and open problems concerning tilting theory.

Mathematical proofs should be paired with formal proofs, whenever feasible.

We give a pen and paper and (comparatively) much simpler proof to verify of the Four Colour Theorem.

In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.

These Course Notes provide an introduction to mathematical proofs for undergraduate students transitioning from computational calculus to abstract mathematics. Topics include propositional logic, proof techniques, mathematical induction,…

Significance tests are probably the most extended form of inference in empirical research, and significance is often interpreted as providing greater informational content than non-significance. In this article we show, however, that…

The aim of this work is to understand the retraction phenomenon in the arts and humanities domain through an analysis of the retraction notices: formal documents stating and describing the retraction of a particular publication. The…