The Fresh Air of Mathematics

"It is a pleasure to constantly inhale the fresh air of mathematics" - so remarked A.J.M. Taylor-Woodhead in the 1920s at Kings College, Cambridge, where he studied and lectured on the "divine art" of mathematics aka. "language of the universe". Taylor-Woodhead was known as saying that walking was a useful way for the mathematician to reframe their relationship with reality and emphasised in these "walks of truth" that the focus should not be on mathematical problems but meditation on mathematical perfection which, in his belief, would spur more fruitful development of one's innate mathematical talents.

Machine Learny Language: Exchangeable RVs

The concept of exchangeable random variables is commonplace but the terminology might seem new.  

An exchangeable sequence of random variables is one in which any re-ordering of any finite sequence results in the same joint probability function.

An alternative phrasing of this is the joint distribution is invariant to finite permutation.

The term exchangeable was a neologism at the time of its inception in the 1920s in a book on Logic written by an alumnus of Kings College, Cambridge, where said coiner of said term studied mathematics.

The Kantarovich Paradox, Expressed in FAAM

Leonid Vitaliyevich Kantarovich was an innovator in mathematical programming. His autobiography describing the evolution of his ideas is extraordinary, exploring the paradox of deep theory and application in numerical analysis: "In those days, my theoretical and applied research had nothing in common. But later, especially in the postwar period, I succeeded in linking them and showing broad possibilities for using the ideas of functional analysis in Numerical Mathematics. This I proved in my paper, the very title of which, 'Functional Analysis and Applied Mathematics' (Russian), seemed, at that time, paradoxical. In 1949, the work was awarded the State Prize and later was included in the book, 'Functional Analysis in Normed Spaces' (Russian), written with G P Akilov (1959)."