Mathematics surely starts with counting and basic arithmetic; perhaps some
understanding of repetition and regular intervals comes next, but geometry was
surely not far behind. It was surely where mathematics first got formalised and
axiomatised, at least; and several ancient civilisations recognised the
significance of some of its consequences. In this part of my web-site, I
explore some of the basic results of classical geometry, particularly those
involving pictorial proofs (presented using SVG images, for the most part).
More algrebraic treatments of geometry
remain elsewhere.
In a talk How
geometry created modern physics, Yang-Hui He leads us from Greek geometry,
through al-Khowarizmi's invention of algebra (as an abstraction of it),
Descartes' marriage of that to geometry, Leibniz and Newton's (maybe via the
earlier Oxford School – I'm guessing some influence from Archimedes'
proof-methods that measured the sphere, among other things) innovation of the
infinitessimal calculus to the birth of modern physics in Newton's mechanics and
the flowering that followed. Euler weaves a synthesis of all these parts,
preparing the way for Lagrange, Hamilton and the beginnings of vector algebra
and calculus, within which Maxwell builds electrodynamics. Meanwhile, in the
background, the geometers are at work again, working out how to live without
Euclid's fifth postulate. Then Gauss and Riemann gets to start the synthesis of
that with everything that came before, paving the way to describe dynamics on a
smooth manifold, as Maxwell unwittingly forced Einstein to do. Also has a slide
that says elementary particles are Irreducible representations of Lie Group
SU(3)×SU(2)×U(1) – I may want to know more about
that.
Written by Eddy.