Related papers: A Note on a Recent Conjecture in Mathematics Magaz…
Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…
Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.
We highlight the different uses of the word 'likelihood' that have arisen in statistics and meteorology, and make the recommendation that one of these uses should be dropped to prevent confusion and misunderstanding.
It is shown that a natural notion of congruence permutability for quasivarieties already implies ``being a variety''. The result follows immediately from [3] and the sole aim of this note is to state it explicitly, together with a…
In this note, we give some new families of two-stage spaces for which the torus rank conjecture is affirmed.
The article gives a survey of mathematical proofs that rely on computer calculations and formal proofs.
In a recent talk of Robbert Fokkink, some conjectures related to the infinite Tribonacci word were stated by the speaker and the audience. In this note we show how to prove (or disprove) the claims easily in a "purely mechanical" fashion,…
The papers mentioned in the bibliography lead to this new hypothesis which constitutes a wide panorama of the physical reality. Its coherence and its simplicity are virtues that make interesant to gaze upon it.
This is an extension and background to a talk I gave on 9 October 2013 to the Brown Graduate Student Seminar, called `A friendly intro to sieves with a look towards recent progress on the twin primes conjecture.' During the talk, I mention…
The simultaneous appearance in May 2003 of four books on the Riemann hypothesis (RH) provoked these reflections. We briefly discuss whether the RH should be added as a new axiom, or whether a proof of the RH might involve the notion of…
A method is presented for using the consistent part of inconsistent axiomatic systems.
These are my notes for a talk at the The Tate Conjecture workshop at the American Institute of Mathematics in Palo Alto, CA, July 23--July 27, 2007, somewhat revised and expanded. The intent of the talk was to review what is known and to…
We provide the results of pattern recognition experiments on mathematical expressions. We give a few examples of conjectured results. None of which was thoroughly checked for novelty. We did not attempt to prove all the relations found and…
An open problem in numerical analysis is to explain why molecular dynamics works. The difficulty is that numerical trajectories are only accurate for very short times, whereas the simulations are performed over long time intervals. It is…
In this short note we present a family of counterexamples to the King's conjecture.
We introduce a new criterion which if satisfied implies the Riemann hypothesis.
The article presents the proof of Casas-Alvero conjecture.
These brief notes record our puzzles and findings surrounding Givental's recent conjecture which expresses higher genus Gromov-Witten invariants in terms of the genus-0 data. We limit our considerations to the case of a projective line,…
In this note a two sided bound on the tail probability of sums of independent, and either symmetric or nonnegative, random variables is obtained. We utilize a recent result by Lata{\l}a on bounds on moments of such sums. We also give a new…
In this note we shall give a new proof to a quadrature formulae due to Newton.