Related papers: Did Hypatia Know about Negative Numbers?
We define a new class of numbers based on the first occurrence of certain patterns of zeros and ones in the expansion of irracional numbers in a given basis and call them Sagan numbers, since they were first mentioned, in a special case, by…
Telegraphic notes on the historical bibliography of the Gamma function and Eulerian integrals. Correction to some classical references. Some topics of the interest of the author. We provide some extensive (but not exhaustive) bibliography.…
Are time-travels possible? is the past still existing? and is the future already existing? We try to give an answer to these an other questions concerning the properties of time and the close connection (but deep physical difference)…
Any rational number can be written as the sum of distinct unit fractions. In this survey paper we review some of the many interesting questions concerning such 'Egyptian fraction' decompositions, and recent progress concerning them.
Although the cosmic concordance cosmology is quite successful in fitting data, fine tuning and coincidence problems apparently weaken it. We review several possibilities to ease its problems, by considering various kinds of dynamical Dark…
Two sides of cosmological constant problem are discussed: a mysterious compensation of all contributions to vacuum energy with the accuracy of 100-50 orders of magnitude and a surprising equality of a constant vacuum energy density to the…
We present a different combinatorial interpretations of Lucas and Gibonacci numbers. Using these interpretations we prove several new identities, and simplify the proofs of several known identities. Some open problems are discussed towards…
This paper finds a symmetry relation (between quantiles of a random variable and its negative) that is intuitively appealing. We show this symmetry is quite useful in finding new relations for quantiles, in particular an equivariance…
The "Millennium Prize Problems" have a place in the history of mathematics. Here we tell some little-known anecdotes from the perspective of the planner of that project. These stories are far from their end; more likely they are just at…
I am presenting a first-ever scientific collection of short sayings on probability and statistics expressed by most various men of science, many classics included, from antiquity to Kepler to our time. Quite understandably, the reader will…
This is the extended version of a Comment submitted to Physical Review Letters. I first point out the inappropriateness of publishing a Letter unrelated to physics. Next, I give experimental results showing that the technique used in the…
This is a short historical note concerning the evolution of Wetzel's problem and Erdos' solution.
This analysis which uses new mathematical methods aims at proving the Riemann hypothesis and figuring out an approximate base for imaginary non-trivial zeros of zeta function at very large numbers, in order to determine the path that those…
We collect a number of open questions concerning Diophantine equations, Diophantine Approximation and transcendental numbers. Revised version: corrected typos and added references.
This paper presents a little reflection about the Sleeping Beauty Problem, maybe contributing to shed light on it and perhaps helping to find a simple and elegant solution that could definitively resolve the controversies about it.
The study examines the relationship between Ball's magic numbers and reverses divisors. These numbers are the source of beautiful and curious properties. Activities related to numbers can be a fun way to motivate mathematics students, while…
In this pedestrian approach I give my personal point of view on the various problems posed by dark matter in the universe. After a brief historical overview I discuss the various solutions stemming from high energy particle physics, and the…
The aim of this paper is to investigate some properties, recurrence relations and identities involving degenerate hyperharmonic numbers, hyperharmonic numbers and degenerate harmonic numbers. In particular, we derive an explicit expression…
We prove that there is at least one irrationnal among the nine numbers zeta(5), zeta(7),..., zeta(21).
We present here a note which synthesizes our previous ideas concerning some problems in cosmology, and the numerical correspondences between the physical constants that we could deduce.