Elements of Mathematics: From First Principles for Data Scientists, AI Engineers and Quants

Advanced mathematics from first principles, for data scientists, AI engineers and quants. No prerequisites assumed, nothing dumbed down.

1. 0. The map in one hour

   Hilbert space, manifold, measure, homology, transport plan. One sentence each, one paragraph each, and what each one lets you do that you could not do before. No proofs and no prerequisites: this is the map, so that everything after it has somewhere to attach.

2. 1. The number that broke arithmetic

   The Greeks proved a number existed that they could not write down, and it wrecked their programme. The repair took 2,200 years and is the single property every convergence proof in this series quietly uses. Then the modern version of the same problem: why 0.1 + 0.2 is not 0.3, and why the textbook variance formula should not go into production.

3. 100. Appendix: derivations and definitions

   A growing reference for the mathematical objects the series uses but which sit outside the flow. Each entry is self-contained, so they can be read on their own or skipped entirely.