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Experimental mathematics in the 1990s: The second loss of certainty?

Henrik Kragh Sørensen
Torsdag, 8 april, 2010, at 16:15, in Aud. D3 (1531-215)

In most traditional accounts, experiments - one of the corner-stones of modern natural sciences - have had no place in mathematics. However, during the 1990s, with the advent of high-speed computers and sophisticated software packages a new experimental flavour was brought to parts of mathematics leading to the gradual formation of a branch of so-called “experimental mathematics” with its own research problems, methodology, conferences, and journals.

In my talk, I first briefly outline some of the roles computers came to play in mathematics. I then consider some of the institutionalizing processes of “experimental mathematics” in the 1990s with special emphasis on the journal of the same name and the group around CECM and the Borwein brothers in Vancouver. As examples, I illustrate the PSLQ algorithm and the so-called BBP formula for individual digits of $\pi$. This brings me to discuss the type of experiments involved and address some of the controversies over the role of proof and certainty in mathematics that were raised in the columns of mathematical journals during that decade. These discussions lead to a brief consideration of the notions of discipline and style in the case of experimental mathematics during the 1990s highlighting two conclusions. First, the protagonists of experimental mathematics certainly adopted and exploited a particular style for both epistemic and non-epistemic purposes. Second, although it was supported by institutionalization and infrastructure, experimental mathematics did not develop into a mathematical discipline of its own in the 1990s, partly because of the cross-disciplinarity of its subject matter and partly because it became increasingly integrated with existing disciplines and branches of mathematics.

Kontaktperson: Bent Ørsted