30d roadmap · 4 milestones
30-Day Math Rating Climb
Like chess ratings: you start near 1500, solve drills matched to your level, and harder problems appear as you improve. Four weeks through the foundations that underpin ML, search evals, and systems reasoning.
Outcome: Raise your per-roadmap ELO by climbing from linear algebra through statistics to calculus — each week unlocks harder drills at your edge.
How to work this roadmap
Treat each milestone as a claim that must be supported by evidence. Before reading, write what you think the mechanism does and where it will fail. After studying the linked concepts, run the drills without copying an answer, preserve the output, and revise the explanation. Move forward when you can connect the milestone goal to a working implementation, benchmark, architecture decision, or reviewable design artifact.
The 30d horizon is a sequencing aid, not a completion badge. Spend more time where your prediction and the observed behavior disagree. Keep a short decision log containing the mechanism selected, alternatives rejected, expected failure mode, measurement used, and remaining uncertainty. Review that log with FSRS prompts so the roadmap produces durable system judgment rather than a temporary tour of terminology.
At the end, explain Raise your per-roadmap ELO by climbing from linear algebra through statistics to calculus — each week unlocks harder drills at your edge. from first principles to a reader outside the domain. A strong explanation should survive follow-up questions about correctness, cost, latency, resource use, security, recovery, and operational visibility. If it cannot, return to the milestone that contains the missing mechanism and build a smaller falsifiable example.
Milestones
Milestone 1
Week 1 — Linear algebra
Vectors, matrices, and the geometric picture behind embeddings and layers.
Concepts
Milestone 2
Week 2 — Probability & description
Uncertainty bookkeeping and summarizing data without lying.
Concepts
Milestone 3
Week 3 — Inference
Confidence intervals and hypothesis tests — the math behind A/B readouts.
Concepts
Milestone 4
Week 4 — Calculus bridge
Gradients and optimization — the runway into gradient descent and training.