FOM: Einstein

[Robert Black]

I think Harvey's last posting (I don't say Harvey himself, because I
suspect that on reflection he will agree with what I am about to say) may
underestimate Einstein's importance for the general intellectual interest
of mathematics.

It's well-known that if you ask Joe Public to name a 20th-century
mathematician, Joe Public will say Einstein, even though Einstein wasn't
really a mathematician at all. But there is a way in which Joe Public is
right.

One of the major differences between, say, 18th-century mathematics and
20th-century mathematics is that modern mathematicians investigate
structures which are quite independent of our 'intuitive' picture of the
world. The point at which this starts is surely non-euclidean geometry, but
I suspect that the key person in this development is not Gauss, Bolyai or
Lobachevsky but rather (for all sorts of reasons) Riemann.

Einstein's use of Riemannian geometry in general relativity provided
something where if not Joe Public at least Joe-Educated-Public could see
how something abstract, counterintuitive and non-vizualizable but logically
coherent could be put to real work.

Let me quote a historian who is certainly not a mathematician but seems to
me to get this exactly right, Eric Hobsbawm, who on pp. 253-4 of _The Age
of Capital_, talking about 19th-century science, says:

'The strange, abstract and logically fantastic world of the mathematicians
remained somewhat isolated both from the general and the scientific public,
perhaps more so than before, since its main contact with both, physics
(through physical technology) appeared at this stage to have less use for
its most advanced and adventurous abstractions than in the great days of
the construction of celestial mechanics. The calculus, without which the
achievements of engineering and communications of the period would have
been impossible, was now far behind the moving frontier of mathematics.
This was perhaps best represented by the greatest mathematician of the
period, Georg Bernhard Riemann (1826-66), whose university teacher's thesis
of 1854 'On the hypotheses which underlie geometry' (published 1868) can no
more be omitted from a discussion of nineteenth-century science than
Newton's _Principia_ can from that of the seventeenth century. [...] Yet
these and other highly original developments did not come into their own
until the new revolutionary age of physics which began at the end of the
century.'

If Hobsbawm is right - and I think he is - then Einstein's use of
Riemannian geometry could reasonably be identified as the point at which
abstract modern mathematics (already developed by others, of course) became
popular.

Robert Black
Dept of Philosophy
University of Nottingham
Nottingham NG7 2RD

tel. 0115-951 5845