Every learning path in one place: the foundations of the sciences, a finance track, and the road to cybersecurity and security research. Each path lives in a public repository with checklists and free resources; this page is the map.

How to study

Five methods, from the research on learning: retrieval practice (close the book, write what you remember), spaced repetition (review at growing intervals with flashcards), the Feynman technique (explain it in plain words; where you stall is the gap), problems over pages (do the exercises), and connect subjects (statistics links to economics, energy to chemistry). The why, with sources: How to study.

For each topic: watch a video for the picture, read the book section for the details, do practice problems for the skill, then write one plain-words paragraph.

Polymath foundations: 50 topics

The core of five subjects, ten topics each, all with free resources (checklist, where to learn each topic).

Subject Topics Start with
Math algebra, geometry, trigonometry, functions, calculus, probability, statistics, logarithms, proofs, problem solving OpenStax books, 3Blue1Brown, MIT OpenCourseWare
Physics vectors, kinematics, Newton’s laws, forces, energy, momentum, electricity, magnetism, waves and optics College Physics 2e, PhET simulations
Chemistry atoms, periodic trends, bonding, stoichiometry, reactions, thermochemistry, kinetics, equilibrium, acids and bases, organic Chemistry 2e, MIT 5.111SC
Biology cells, genetics, DNA and RNA, evolution, anatomy, physiology, photosynthesis, respiration, ecology, homeostasis Biology 2e, MIT 7.01SC
Social studies world history, geography, ideologies, economics, government, globalization, nationalism, international relations, source analysis, critical thinking World History, Our World in Data

Order: math first (the language of the sciences), physics alongside calculus, then probability and statistics (needed for AI, security and economics), then chemistry, biology and social studies.

Engineering

Ten topics to master for each of seven branches (mechanical, electrical, aerospace, civil, chemical, biomedical, software) and the software side of robotics (track, resources). Calculus and physics come first for every branch.

Finance

What to master for investment banking, private equity, trading and wealth management, plus who to read (track, resources). Start with economics and statistics, then accounting and valuation (Damodaran’s free NYU class).

Cybersecurity and AI security

Path What it is
Roadmap five stages over 12–18 months, from foundations to AI security
Modules 01–15 networking, systems, crypto, web, identity, detection, cloud, forensics, OSINT, OPSEC, radio, blockchain
AI security track attacks on AI systems and defending against AI attackers
Becoming a security researcher the skill tree, a staged path to first CVEs, disclosure
Threat intel staying current, incident deep dives

Building software

Guide Topic
GitHub Actions and DevOps automation, CI/CD, the DevOps loop
Command-line field guide Git, the shell, regex, secrets
Programming languages meta which languages lead, and the go-to language for each field

All guides: the research index.