Thumbnails of mathematical terms

The following essay treats of the art of mathematical definition:

https://worldofdrjustice.blogspot.com/2014/01/what-is-mathematics-expanded.html

Here are some recent additions:

Ergodicity means, roughly, that … very long sample paths … end up resembling each other.

-- Nassim Taleb, Fooled by Randomness (2004), p. 59

Ergodicity, … that time will eliminate the annoying effects of randomness.

-- Nassim Taleb, Fooled by Randomness (2004), p. 144

Holonomy is a measure of how tangent vectors on a particular surface  get twisted up as you attempt to parallel-transport them on a loop.

-- Shing-Tung Yau, The Shape of Inner Space (2010), p. 129

The Lie Bracket of X and Y … informally … represents the net direction of motion if one first moves an infinitesimal amount in the X direction, then in the Y direction, then back in the XS direction and back in the Y direction, in that order.

-- Mark Ronan, “Lie Theory”, in Timothy Gowers, ed., The Princeton Companion to Mathematics (2008), p. 231

Logic

… [C. S.] Pierce’s last papers on logic, a subject which he defined rather surprisingly as ‘the stable establishment of beliefs’.

-- I. Grattan-Guinness, The Search for Mathematical Roots 1870 - 1940 (2000), p. 174

Logic is the infancy of mathematics, or conversely, mathematics is the maturity of logic.

-- Bertrand Russell, 1957, quoted in I. Grattan-Guinness, The Search for Mathematical Roots 1870 - 1940 (2000), p. 315

Spinors are analogues of tangent vectors.

-- Shing-Tung Yau, The Shape of Inner Space (2010), p. 131