Some remarks about pure and applied mathematics Mathematics is - PDF document

Some remarks about pure and applied mathematics

Mathematics is nourished and strengthened when it makes contact with significant ap- plications. • symbiotic relationship of mathematics and physics; • mathematization of biology • tools for operations research, economics and finance (simplex method, game theory, stochas- tic differential equations...) • growing importance of quantitative methods, statistics, in the social sciences, medecine, en- vironmental studies... Mathematics increasingly pervades all aspects of human activity and knowledge. For mathe- matics, this is a welcome development! 1

Mathematics is made up of a number of vi- tal core areas (algebra, analysis, geometry, topology, logic and foundations...) often referred to as “pure mathematics”. These areas are (for the most part) developped for their own sake , without regard for eventual applications. Why pure mathematics? 2

The defense of Gustav Jacobi “ Monsieur Fourier avait l’opinion que le but principal des math´ ematiques ´ etait l’utilit´ e publique et l’explication des ph´ enom` enes naturels. Un philosophe tel que lui aurait dˆ u savoir que le but unique de la Science, c’est l’honneur de l’esprit humain et que, sous ce titre, une ques- tion de nombres vaut bien une question de syst` eme du monde.” 3

A more utilitarian defense A vibrant and healthy core is precisely what makes it possible for mathematics to con- tribute significantly to other disciplines. Could we conceive of... • Nanotechnology, without quantum mechan- ics? Quantum mechanics, without Hilbert Spaces and the spectral theorem? • Genomics, without sophisticated pattern match- ing and genetic algorithms? • Computer security, without cryptography? Cryptography, without number theory? • Environmental studies, without powerful math- ematical models? Models, without partial dif- ferential equations? • Inventory control, without operations research? Operations research, without linear algebra? 4

Conclusion In order to further develop its burgeoning ties with other disciplines, while maintaining its tra- ditional strengths in the core areas, the mathematics department really ought to be Growing . Yet is has been shrinking . 5

Why is that? 6