Polymath Curriculum

This section is the method the rest of the curriculum runs on: how claims get justified, how arguments get checked, and how theories get tested against the world. It is short by design and sits in Phase 1, alongside the start of the mathematics and programming spine (see III), because everything downstream leans on it.

Mathematics, statistics, computation, and language are the tools every later section leans on: you cannot do quantitative physics without calculus, read a psychology paper without statistics, or build anything without at least one programming language. This section is the curriculum's spine (see III): rather than finishing it before moving on, you carry it alongside the domain sections from Phase 1 through Phase 5, adding tools as the domains need them. In The Assayer (1623), Galileo wrote that "philosophy is written in this grand book, the universe... in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is humanly impossible to understand a single word of it". Three centuries later Eugene Wigner asked why that language keeps working so well beyond the problems it was built for, in his 1960 essay "The Unreasonable Effectiveness of Mathematics in the Natural Sciences".

Physics, chemistry, biology, and earth and cosmos, in that order, each level built on the one below it and adding phenomena the lower level cannot explain on its own. Within each subsection the topics run in historical order, since the sequence of problems is what makes each concept legible; the section as a whole is not chronological, and it is spread across Phases 2 through 5, running alongside the mathematics and computation spine (see III).

This section moves from a single mind to groups to states: how a person thinks, how people organize into societies, and how those societies hold or lose power over time. D.1 comes after B.2 on purpose, because a lot of psychology's classic canon reads differently once you can ask whether a finding replicated. D.3, the history and politics thread, is not confined to one phase: it runs as a background reading track from Phase 1 onward, since dates and narratives don't need calculus as a prerequisite.

Engineering and economics put earlier material to work under real constraints: budgets, materials, other people's incentives. E.3, complex systems, leans on differential equations and programming from section B. E.4 asks how technology has moved through history, which is messier than either a great-inventors or an inevitable-progress story suggests.

This section turns inward: ethics, art, and the question of how the other domains add up to a life. It runs mostly on the reading track, threading through Phases 4 to 6 rather than occupying a block of its own.