Norman Wildberger - How Physicists do Maths

For context, see A skeptical look at the Special Relativity narrative

See Steven Weinberg on Aristotle and Modern Science, Another Introduction to Geometric Algebra and Wikipedia's Introduction to gauge theory.

See Algebraic Topology of Finite Topological Spaces and Applications by Jonathan A. Barmak The first chapter of this is surprisingly readable, and would be understandable too, to someone who is familiar with CW complexes and Homotopy theory in general.

See also How to Divide Without Floating Point Arithmetic and Norman Wildberger's Sociology of Mathematics.

See also Daniel Tubbenhauer and Holly Krieger on The Riemann Hypothesis.

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Maybe that number should be called Z? See Doron Zeilberger - An Ultra-Finitistic Foundation of Probability (Foundations of Probability seminar November 19, 2018:)

See Opinion 165: The MASTERPIECE "Ten Great Ideas about Chance" by Persi Diaconis and Brian Skyrms is Fascinating for (at least) two reasons: It tells you a lot about Probability (and Statistics) But It also tells you a lot about Humans and their "Infinitary Religion".

See the book Ten Great Ideas about Chance by Persi Diaconis and Brian Skyrms.

Persi Diaconis and Brian Skyrms begin with Gerolamo Cardano, a sixteenth-century physician, mathematician, and professional gambler who helped develop the idea that chance actually can be measured. They describe how later thinkers showed how the judgment of chance also can be measured, how frequency is related to chance, and how chance, judgment, and frequency could be unified. Diaconis and Skyrms explain how Thomas Bayes laid the foundation of modern statistics, and they explore David Hume’s problem of induction, Andrey Kolmogorov’s general mathematical framework for probability, the application of computability to chance, and why chance is essential to modern physics. A final idea—that we are psychologically predisposed to error when judging chance—is taken up through the work of Daniel Kahneman and Amos Tversky.

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When we (finite individual human beings) make representations, for example, on computer gaphic displays, we typically have a matrix of (non-negative) integer pixel values. So we should never need to do anything other than exact arithmetic all the way through the process. When we make such representations we need to be able to expand the whole process model to achieve a certain fidelity of representation: See Trying to Make a Sci-Fi Movie and Sense Perception v. Sense:

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