Search

 

PressCNRS international magazine

Table of contents

Mark van Atten

Rethinking mathematics

van atten

© R. Rucker


Mark van Atten is startled when interrupted by a noise or someone from the outside world. But that rarely happens at the Institute for the History and Philosophy of Science and Technology (IHPST),1 where he spends most of his days reading. At the Institute, silence has become almost mandatory, in sharp contrast to the busy streets of the surrounding Paris Latin Quarter. There, van Atten continues to live the life of a true thinker, almost untouched by the passage of time; at 32, he looks 10 years younger. His stature is impressive but his shy and reserved manners can't conceal a kind nature. Wearing a typical English public-school navy blazer, you might even try to second-guess his origins. But there again, you'd be wrong. The man is Dutch.

A specialist in Husserlian phenomenology,2 van Atten's current research demonstrates the importance of philosophy of mind to the foundations of mathematics. And what he was reading when you startled him could well have been Brouwer and Gödel, for him the two key figures who “revolutionized logic and mathematics at the start of the 20th century: Gödel created the field of mathematical logic, while Brouwer was the first to develop a mathematical system known as intuitionism.” Like Plato, Gödel believed that mathematical objects exist independently of our minds and can be discovered. For Brouwer, on the other hand, mathematical reality cannot be separated from the self and its constructs. Both mathematicians looked to philosophy for solutions when their theoretical work came to a dead end. Van Atten is now studying how their different philosophical starting-points led them to different forms of mathematics.

Van Atten started his career studying cognitive models of the mind through the study of neural networks, leading him to a Master's degree in artificial intelligence at the University of Utrecht. It was there that he encountered Dirk van Dalen, a major Brouwer expert, and decided to abandon artificial intelligence to pursue philosophy. “While you can study mathematics from the perspective of cognitive science, such research will always be more empirical than conceptual,” he declares, proving his dislike of easy answers. Van Atten brilliantly defended his thesis in 1999, an investigation of choice sequences (a mathematical concept introduced by Brouwer) and their philosophical justification. The thesis was bolstered by van Dalen's advice and a year at the Harvard philosophy department studying with Charles Parsons. This was then followed by a postdoc at Utrecht and Louvain, but in spite of this extensive experience, his own country could not offer him a permanent research position. CNRS, however, did just that.

In 2003, van Atten successfully entered CNRS' official competition for research positions and joined the Institute for the History and Philosophy of Science and Technology in Paris. He'll be the first to tell you that the city itself has presented unparalleled opportunities for his research, making it possible for him to interact with today's major foreign philosophers in English, French, German or Dutch. But he won't deny that the city also lets him indulge his fondness for Asian and French cinema, and that he has become accustomed to his solitary walks through the city streets where he can pursue the ramifications of his ideas.

 

Stéphanie Bia

Notes :

1. CNRS / Université de Paris-I / Ecole Normale Supérieure joint lab.
View web site
2. Phenomenology addresses the question of how it is possible for a subjective mind to grasp objective realities such as the truths of mathematics.

Contacts :

Mark van Atten
Institut d'histoire et de philosophie des sciences et des techniques, Paris.
mark.vanatten@univ-paris1.fr


Top

Back to homepageContactcredits