What is good mathematics?

This article, dedicated, with admiration to Reuben Hersh, for his forthcoming 90th birthday, argues that mathematics today is not yet a science, but that it is high time that it should become one.

Remarks on mathematical proof and the practice of mathematics.

Mathematical research is often motivated by the desire to reach a beautiful result or to prove it in an elegant way. Mathematician's work is thus strongly influenced by his aesthetic judgments. However, the criteria these judgments are based on remain unclear. In this article, we focus on the concept of mathematical beauty, as one of the central aesthetic concepts in mathematics. We argue that beauty in mathematics reveals connections between apparently non-related problems o...

This article discusses epistemological problems in the philosophy of mathematics and issues concerning the reliability of the mathematical literature.

In this paper, I explore what mathematical research can tell us about ourselves, and our role in the world, using examples from my own experience. The paper is a sequel to my piece "Mathematics is a Quest for Truth", published in the Notices of the American Mathematical Society in 2014.

An opiniated essay on what pure mathematics is and why the adjective "pure" in "pure mathematics" is not a good choice.

In this short essay, I shall try to find a way to humanize mathematics. I shall give some mathematical remarks concerning that. I shall give some brief comments to my past works from the point of view of this paper.

This paper establishes grounds for deeper exploration into the question of dual nature of mathematics as an abstract discipline and as a concrete science. It is argued, as one of the consequences of the discussion, that the division into "pure" and "applied" mathematics is artificial. The criterion of creativity and applicability outside of the original context is used as a litmus test. It is emphasized that great societies and cultural environments produce great mathematics ...

A sketch of some of the fundamental notions related to the nature of knowledge is offered, with special focus on the role of mathematics and my own opinions. No single idea exposed here is entirely original; indeed, this topic has been explored by legions of philosophers, mathematicians, and scientists throughout history -- I listed a few related books among the references. I look forward to observations and criticisms that may serve to improve this exposition.

In the words of the esteemed mathematician Paul Erd\"os, the mathematician's task is to \emph{prove and conjecture}. These two processes form the bedrock of all mathematical endeavours, and in the recent years, the mathematical community has increasingly sought the assistance of computers to bolster these tasks. This paper is a testament to that pursuit; it presents a robust framework enabling a computer to automatically generate conjectures - particularly those conjectures t...