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Seemingly Impossible Swift Programs
Bit sequences (infinite) being used to prove the equality of functions in the domain of bits (not all functions, but a surprising subset of them).
Programming  Functional  Mathematics  Haskell  Swift 
yesterday by svieira
The HoTT Book | Homotopy Type Theory
Homotopy Type Theory:
Univalent Foundations of Mathematics
The Univalent Foundations Program
Institute for Advanced Study
types  typeTheory  math  mathematics  book  free 
yesterday by dicewitch
Alan Turing, On computable numbers | Joel David Hamkins
What I was extremely surprised to find, however, and what I want to tell you about today, is that despite the title of the article, Turing adopts an incorrect approach to the theory of computable numbers. His central definition is what is now usually regarded as a mistaken way to proceed with this concept.

Let me explain. Turing defines that a computable real number is one whose decimal (or binary) expansion can be enumerated by a finite procedure, by what we now call a Turing machine. You can see this in the very first sentence of his paper, and he elaborates on and confirms this definition in detail later on in the paper.
computability  mathematics  number-theory  algorithms  rather-interesting  history-of-science  representation  to-write-about  ReQ 
2 days ago by Vaguery

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