Geometry and physics. (English) Zbl 0864.57003

Atiyah, Michael

Math. Gaz. 80, No. 487, 78-82 (1996).

This essay seems to be a summary of the speech the author gave at the Centenary Conference of the Mathematical Association most members of which being mathematics masters in English schools. The main theme is that numerous remarkable recent discoveries in mathematics owe a substantial debt to ideas from quantum physics while the reverse benefits in which discoveries in physics owe a debt to mathematics are more difficult to assess. The essay is remarkable for a few oddities of which the most startling is the following: the author seems to think that continuity is a necessary attribute of geometry which is in stark contradiction with the following definition given by V. S. Varadarajan [Geometry of quantum theory, 2nd ed. (1985; Zbl 0581.46061)]: A geometry is an irreducible complemented modular lattice of finite rank. Also if continuity were a necessary prerequisite of geometry, the word continuous in ‘Continuous geometry’ (1960; Zbl 0171.28003) by J. von Neumann would be redundant. Due to the twin problems of poor pay and growing indiscipline among pupils, school mathematics in England at the present time is in a sorry state and there are few mathematics masters in schools who can comprehend the ideas in the essay. However, any reader will become familiar with the current buzz words in modern topology and mathematical physics.

Reviewer: C.S.Sharma (London)

MSC:

57-03	History of manifolds and cell complexes
83-03	History of relativity and gravitational theory
01A60	History of mathematics in the 20th century

Keywords:

mathematics; continuity; winding number; quantum physics; geometry

Citations:

Zbl 0581.46061; Zbl 0171.28003