You are not dumb, you just lack the prerequisites

Original Article ↗ Hacker News Discussion ↗

Prerequisites and Skill Hierarchies

  • Many commenters agree that struggles in math (and other fields) are often due to missing prerequisites, not inherent stupidity.
  • Math is repeatedly described as a strict skill hierarchy: if lower-level procedures (arithmetic, algebra, trig) aren’t solid, higher-level topics (calculus, proofs, ML) collapse.
  • A common issue: people (and course descriptions) list high-level prerequisites (“know algebra”) without specifying granular skills, so learners overestimate what they actually know.

Top-Down vs Bottom-Up Learning

  • Debate over whether to dive into advanced topics (“trial by fire”) or systematically build foundations.
  • Consensus: top-down is useful for goal-setting and motivation; actual mastery requires bottom-up, especially in math.
  • Some find bottom-up demotivating without a high-level “map”; others find top-down leads to flailing until they circle back to basics.

Talent, IQ, and Motivation

  • Strong disagreement on how far “you just lack prerequisites” goes.
  • One side: most people can reach substantial math competence; motivation, practice habits, and earlier life circumstances (resources, teaching, anxiety) matter more than innate ability.
  • Other side: cognitive differences (IQ, working memory, ADHD, dyscalculia) are real constraints; some people will never get far, even with effort.
  • Several suggest a “soft ceiling”: effort required grows rapidly with abstraction level and differs by person.

Math Education, Gaps, and Anxiety

  • Many stories of being labeled “bad at math” due to early gaps, poor teaching, language issues, or being pushed ahead without mastery.
  • “Gifted kid” arc recurs: coasting on talent, hitting a wall in university, then having to build work ethic and rebuild foundations.
  • Others describe being average or weak in school but later succeeding after deliberate, structured remediation.

Programming and Other Analogies

  • Learning to code is often cited as parallel: either climbing a staircase of basics or jumping into big projects and backfilling knowledge.
  • Social skills, reading research papers, and even life choices (careers, parenting) are framed as having hidden prerequisites too.

Tools, Resources, and Methods

  • Mentioned strategies: recursive reading of paper references, dependency graphs for topics, “parametric books,” spaced practice, immediate feedback systems, and tutoring focused on proofs.
  • Several praise modern platforms (videos, adaptive systems, LLMs) for closing prerequisite gaps by providing patient, on-demand explanations.