Amazing Math

Some of Erdős's work in number theory

Analytic and probabilistic number theory was one of Paul Erdős's favorite subjects. Here is a small selection of his contributions in this field, picked here and there from topics that can still be presented accessibly.

Some conjectures in algebra

Here are a few conjectures proposed by Erdős that, despite some progress, remain unsolved...

Paul Erdős by George Csicsery — Documentaries | Tangente

The great book of problems

The "Book" was a project of Erdős's to bring together the most beautiful known mathematical proofs, several of which had been found by Erdős himself. Although he died shortly before the project was completed, the work was nonetheless published, authored by Aigner and Ziegler. Its successive new editions keep the flame alive.

Collaborating with Paul Erdős — Tenenbaum's Account | Tangente

Much of Paul Erdős's work was carried out jointly with others. Gérald Tenenbaum, one of the French mathematicians who collaborated with him, agreed to discuss the methods of this unconventional mathematician.

To exist is to do mathematics — Erdős | Tangente

Pál Erdős (1913-1996) is renowned for his eccentric behavior, but above all for the brilliance of his ideas. His ingenious methods, off the beaten track, his countless publications, and his constant wandering built the image of a legendary scholar.

More than 600 problems still open

Throughout his life, in papers written either alone or with collaborators, Erdős posed a great many problems. He solved some of them—but far from all.

An iconic photograph

The famous photograph of Paul Erdős and Terence Tao deep in thought has become an iconic image in the recent history of mathematics. But what were these two extraordinary minds thinking about at that moment?

A panorama of set theory | Tangente

Work on the notion of infinity led to paradoxes. This forced mathematicians to formalize set theory. Progressive axiomatization led to the current ZFC system, which nonetheless remains subject to various shortcomings following the work of Kurt Gödel and Paul Cohen.

Four mathemagic tricks

Martin Gardner knew how to blend magic and logic to captivate his readers. A tireless seeker of magic tricks, he explored the "27-card trick" in particular, and created many others besides.

Martin Gardner: Itinerary of a genius | Tangente

Although he is known for his recreational mathematics and his work as a popularizer, Martin Gardner strangely never pursued a course of study in the discipline. Here are the surprising stages of his unusual path.

Cyril Bonin's universe: comics and mathematics | Tangente

Mathematics can hold a special place in an artist's thinking. Cyril Bonin explains how: he is the sole creator—writer, artist and colorist—of a distinctive body of graphic novels.

GIMPS and Mersenne primes | Tangente

If you would like to put your computer to work for research, your name might one day be associated with the discovery of a new Mersenne prime…

A centenarian devoted to magic squares | Tangente

After a busy career in public works engineering, during which he held various positions in Alsace, René Descombes (born in 1924!) has pursued his interest in magic squares since retiring.

The joy of mathematical discovery: amateur mathematicians | Tangente

Christian Boyer, Vincent Thill, Jean Moreau de Saint-Martin and Philippe Fondanaiche—all passionate amateur mathematicians—agreed to answer our questions about how their interest in mathematics began and the activities they have developed in their favorite areas.

They found it

Here are a few amateur mathematicians whose names are associated with recent results.

Recognized amateurs

What is an amateur mathematician? Defining one is no easy task, especially since the concept has undoubtedly evolved over time. Nevertheless, we will look at a few examples, both past and present.

2025: a very square number!

What better way to celebrate the new year than with some delightful mathematical properties of the number 2025? Tangente wishes all its readers a wonderful 2025.

Curious stories of mathematics on video | Tangente

For almost a year, Noëlle Krajcman has been running a TikTok and Instagram channel devoted to mathematical anecdotes.

Ellipse snippets

There are several ways to construct an ellipse. Here are a few.