Andrej Bauer's "Five Stages of Accepting Constructive Mathematics"
I remember how much this cheered me up when I first saw it:
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1. Denial, ...
4. Depression, ...
See Plan 9 From Bell Labs and The Console Message Processor.
Conway's Game Of Life, in Conway's Fractran(416 fractions)
Just somebody I share a desk with: see Norman Wildberger's Box Arithmetic.
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5. Acceptance: Does John Conway hate his Game of Life?
6. Death: Conway on Life, Death and The Monster:
7. ... On the Monster Group, and the other 25 Sporadic Simple Groups:
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Life in Life
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A Universal Turing Machine in Conway's Game of Life:
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Carol Wood on The Infinitesimal Monad
Part II
Carol Wood was a student of Abraham Robinson.
... [who] became known for his approach of using the methods of mathematical logic to attack problems in analysis and abstract algebra. He "introduced many of the fundamental notions of model theory". Using these methods, he found a way of using formal logic to show that there are self-consistent nonstandard models of the real number system that include infinite and infinitesimal numbers. Others, such as Wilhelmus Luxemburg, showed that the same results could be achieved using ultrafilters, which made Robinson's work more accessible to mathematicians who lacked training in formal logic. Robinson's book Non-standard Analysis was published in 1966. Robinson was strongly interested in the history and philosophy of mathematics, and often remarked that he wanted to get inside the head of Leibniz, the first mathematician to attempt to articulate clearly the concept of infinitesimal numbers.
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Andrej Bauer - Formalizing invisible mathematics - IPAM at UCLA
He's just a blogger: https://math.andrej.com/
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See Standard ML For The Lady Programmer and Michael Kohlhase and Dennis Müller - The STeX3 Package Collection. Finally, for more on Categorical Equivalence and equality, i.e. idenifying (canonically) isomorphic objects, see the talk Thierry Coquand on Logic and topology in Daniel Tubbenhauer on Algebraic Geometry and Edward Frenkel on The Langlands Program ... On the Tower of Babel: see this ramble I did in Tecate, MX On Mathematics and Abstract Language:
Here is the thing I wrote without using the letter ν: On Tarski's Semantic Definition of Truth "Convention T".
It's important that you print this document double-sided, so that it is on a single sheet of paper, as Putnam will explain in this excellent documentary:
The Origins of Logic in The Organon of Aristotle
See also Thomas Forster on Stratification.
For some insights into Aristotle's principles of logic, see Per Martin Löf's lecture in Daniel Tubbenhauer on Algebraic Geometry and Edward Frenkel on The Langlands Program ... The point being that Aristotle's principal principle of logic is simply that when we use a denoting phrase effectively then we each refer to the same object of thought, even if we spell it differently, Andy Pitts.
For more on Modal Logic, and Deviant Logic in general, see Joan Rand Moschovakis – A Logical Look at Kripke's Idea of Free Choice Sequences.
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