Signs of mathematical talent are cues for curiosity, not a diagnosis and not a caste stamp.
Tests measure a sample already shaped by teaching and invitation. False positives are part of the identification problem.
Early cues
- 3–5 — Quantity play — Not just counting — comparing, splitting, noticing errors.
- 6–8 — Self-sought puzzles — Asks for harder problems when the page ends.
- 9–12 — Ceiling on grade tests — All items correct, time left — SMPY’s invitation cue.
- 13–16 — Proof or contest hunger — Two different appetites; both are mathematical.
- Adult — Late formalisation — Some researchers were ordinary school calculators and late proof converts.
Tests & tasks
- Above-level SAT-M / ACT — SMPY/CTY method.
- Olympiad papers — Raw contest craft.
- Dynamic problem with a hint — Vygotsky-style; finds the zone.
- Timed arithmetic only — A thin, biased slice.
Environments
- Problems past the ceiling — Stanley’s practical lever.
- A person who can check proofs — Mentor as catalyst (Gagné).
- физмат / 과학고 / olympiad camps — Dense peers — access still uneven.
- Permission to be stuck — Speed culture hides proof talent.
False positives
- Tutor-polished contest kids — Coaching as gift.
- Fast arithmetic only — A different skill.
- Stereotype match — Who “looks like” last year’s winner.
- One lucky olympiad day — A sample of one.
Mathematical talent: a cue is information. A label without a review date is a caste.