26 · Backtesting the Soul

There are certain indicators, certain signals, certain cues you learn to recognise. As you see new maths questions, you train yourself to think of certain "real work" — not staring at the statement, surrendering after seven minutes, and reading the official solution with the emotional satisfaction of a tourist visiting someone else's summit.

Phase zero — diagnostic week. Sit one untouched older exam, 2010–2015, under strict conditions: four 90-minute blocks matching the 2026 structure, no calculator, no internet, no hints, no music, no theatrical productivity rituals. Score yourself harshly. Zero to ten: foundations and proof-writing are weak. Eleven to thirty: some tactical ability, inconsistent. Thirty-one to fifty: strong baseline. Fifty-one to seventy: top-100 trajectory with serious training. Seventy-one to ninety: fellowship-level potential. Ninety-one plus: already near the elite frontier. Don't lie to yourself while grading — Putnam graders are not emotionally invested in your self-concept.

Phase one, months one through four — build the tactical engine. Complete the core sections of Putnam and Beyond and the MIT topic sets. Weekly: fifteen to twenty topic problems, eight to twelve fully written solutions, six to ten MIT seminar problems, two hours reviewing past failures, one timed 90-minute mixed session. Sequence: proof methods and invariants, algebra, number theory, combinatorics, inequalities, sequences and recurrences, analysis, probability, linear algebra, geometry as a secondary track. The standard for moving on: 80% of straightforward exercises, 50–60% of intermediate, 20–30% of hard — without reading solutions prematurely.

Phase two, months five through nine — convert knowledge into retrieval. Stop thinking in chapters; start identifying structures cold. Weekly: twelve to sixteen random historical Putnam problems, two timed sessions, six to eight full proof rewrites, two hours of failure-log review, one oral explanation session. For every problem record: the problem, the topic, the first useful observation, the wrong approaches attempted, the trigger I missed, the shortest viable proof, whether I could re-solve it in ten minutes, and review dates at one day, seven days, thirty days. The crucial field is "the trigger I missed": test small cases, factor before expanding, use parity, define an extremal counterexample, reinterpret combinatorially, integrate by parts, telescope the sum, exploit symmetry, substitute a root of unity, compare dimensions, use expectation rather than enumeration. Your competitive edge is not remembering a thousand solutions — it's recognising a hundred recurring triggers rapidly.

Phase three, months ten through fourteen — full-paper warfare. Every week: one complete blind paper in the four-session format, a full post-mortem the next day, re-solve the missed problems after forty-eight hours, and again after thirty days. Phase four, months fifteen through eighteen — fellowship-level refinement on protected blind papers. Monday: blind 90-minute set. Tuesday: post-mortem and proof rewrite. Wednesday: weak-topic drilling. Thursday: blind set. Friday: post-mortem and spaced review. Saturday: full four-session mock. Sunday: deep review and rest. At this stage every missed problem becomes an asset: extract the method, generate two variations, solve them cold later.