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

• f human activity and knowledge. For mathe-

matics, this is a welcome development!

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Mathematics is made up of a number of vi- tal core areas (algebra, analysis, geometry, topology, logic and foundations...)

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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?

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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.”

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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?

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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.

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Why is that?

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