历史与综述

It is well-known to be impossible to trisect an arbitrary angle and duplicate an arbitrary cube by a ruler and a compass. On the other hand, it is known from the ancient times that these constructions can be performed when it is allowed to…

A proof of the Quadratic Reciprocity Law is presented using a Lemma of Gauss, the theory of finite fields and the Frobenius automorfism.

This is my article on Tate's work for the second volume in the book series on the Abel Prize winners. True to the epigraph, I have attempted to explain it in the context of the "great reformulation".

This paper has been withdrawn by the author. In this article I review W\"ust's recent handbook on mathematical physics from a philosophical standpoint. It emerges a structural approach to mathematics which evidences the utility of logic in…

The article provides an historical survey of the early contributions on the applications of fractional calculus in linear viscoelasticty. The period under examination covers four decades, since 1930's up to 1970's and authors are from both…

I present and discuss a puzzle about wizards invented by John H. Conway.

A trip through some of the standard examples of dimensional analysis and scaling, with further thoughts on yacht prices, growing up, mice, bears and marsupials.

Cauchy's contribution to the foundations of analysis is often viewed through the lens of developments that occurred some decades later, namely the formalisation of analysis on the basis of the epsilon-delta doctrine in the context of an…

The legacy of Jordan's canonical form on Poincar\'e's algebraic practices. This paper proposes a transversal overview on Henri Poincar\'e's early works (1878-1885). Our investigations start with a case study of a short note published by…

We study the eleven points in the plane of a given triangle, whose pedal triangles are similar to the given one. We prove that the six points whose pedal triangles are positively oriented, lie on a single circle, while the five points,…

Poincar\'e's approach to the three body problem has often been celebrated as a starting point of chaos theory in relation to the investigation of dynamical systems. Yet, Poincar\'e's strategy can also be analyzed as molded on - or casted in…

Here we weave together interviews conducted by the author with three prominent figures in the world of Ramanujan's mathematics, George Andrews, Bruce Berndt and Ken Ono. The article describes Andrews's discovery of the "lost" notebook,…

Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of heigher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hibert-style Axiomatic Method. The new notion of Axiomatic…

In a recent paper G. Bhatnagar has given simple proofs of some of Ramanujan's continued fractions. In this note we show that some variants of these continued fractions are generating functions of q-Schroeder-like numbers.

This paper is a greatly expanded version of a talk I gave in April 2009 at KunenFest. It describes Ken's work in algebra, particularly using automated deduction tools.

This is a brief overview of the role of mathematicians in the so-called "Luzin Case" as well as some analysis of the mathematical and humanitarian roots of the affair.

Mathematical challenges punctuate the history of early modern mathematics. While cultural historians have attempted to contextualize these challenges among contemporary practices, in particular duels or advertisements in a competitive…

Prosopography is usually used to globally describe a large population of ordinary subjects. It is thus opposed to biography, as a genre devoted to exceptional individuals. I show in this article how to use prosopography to study a single…

The notion of difference between two quantities plays a basic role in mathematics, consequently in all branches of human activity where the mathematics is applied. However the long stand question is: what is the difference between three (or…

A short biographical note on the life and works of K. Ramachandra, one of the leading mathematicians in the field of analytic number theory in the second half of the twentieth century.