Edward Frenkel on Abstraction

This was a talk he gave on March 13 at the UNESCO International Day of Mathematics 2026. 

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See the whole thing here, or here:

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They didn't invite me, but here's my address: 

Abstraction (and the objective nature of mathematics) comes from our abilities as living beings to communicate with each other in language and, most crucially, to be able to talk about language itself, and thereby construct schemes which allow us to describe translations between different ways to describe the same thing. The objective mathematical world that we imagine to be "out there" is in fact something (that same thing we are describing to each other) that emerges from our activities in describing our own communication with each other. So there is in fact just one fundamental mathematical object from which all others are derived. Here is one way to describe it:

RULES <- RULE | RULE ?ws? RULES 

RULE <- SYM ?ws? '<-' ?ws? SYMSLIST 

SYMSLIST <- SYMS | SYMS ?ws? '|' ?ws? SYMSLIST 

SYMS <- SYM | SYM ?ws? SYMS 

SYM <- '"' ?notdquote? '"' | "'" ?notsquote? "'" | ?AZs? | '?' ?azAZs? '?'

See Richard Clegg Explaining What's Wrong With Computer Science and Daniel Tubbenhauer on An Unknotter. See also About Logic with Andrej Bauer for a really great example of it happening in real life. 

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