This book, published in 2007, is a discussion of various mathematical experiments in Number Theory using the computer. The main computational tool used is the sophisticated package PARI-GP. Maybe the best way to describe the book in more detail is to just quote its preface. Preface -------- There is a long and distinguished tradition in mathematics, perhaps even more pronounced in number theory, whereas a chance discovery of a pattern or identity between numbers arising from unrelated calculations leads to the development of whole new fields (this is precisely how Gauss phrases it in a diary entry).

This project got started at a fabulous workshop held in Benasque, Spain (in the mountains, a few hours drive from Barcelona) in 2009. I wrote this post in my blog after returning from another workshop there on p-adic analysis in 2007. In my own notes I added: The place is truly amazing. Mountains falling over you as you walk down the street. The plan of the 2009 workshop was to explore ways to compute exotic L-functions, not arising from elliptic curves or usual modular forms.

I gave some version of this lecture on the Mathematics of the football/soccer ball several times, in different places and in various languages. Florence 20/05/2024 Gonit Sora (online) 14/06/2021 Form their website: Gonit Sora is a multi lingual (English and Assamese) web magazine devoted to publishing well written and original articles related to science in general and mathematics in particular. One of its founders and current editor is Manjil P. Saikia, a former ICTP Diploma student, who invited me to give this online talk.