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The cover of Proof

Proof

Adam Kucharski, 2025

Learn how mathematics, science, law, and AI build convincing evidence under uncertainty, and why proof depends as much on people as on methods.

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9 parts, about 31 minutes to read.

Why read it

  • Shows that proof is not one ladder to certainty but a set of methods, each suited to different stakes and errors
  • Helps you read a positive test, a trial result or a risk score by asking what error it guards against
  • An epidemiologist moves across mathematics, courtrooms, pandemic modelling and machine learning to compare how each earns trust

Who it is for

  • Professionals who must decide before the evidence is complete
  • Readers confused by conflicting science headlines
  • Students of statistics, law or data science

What the summary covers

  1. Proof begins where certainty runs out3 min
  2. Axioms build systems, but people contest foundations3 min
  3. Mathematical monsters reveal the limits of intuition3 min
  4. Law makes the price of error explicit3 min
  5. Experiments strengthen causal claims without becoming oracles4 min
  6. Live science works by competing explanations and converging signals5 min
  7. Evidence systems fail through incentives, authority, and distrust4 min
  8. Machines replace full explanation with probabilistic assurance4 min
  9. Use the toolkit before proof arrives too late2 min

Recommended by

  • Peter FrankopanAuthor of The Silk Roads
    Adam Kucharski has a knack of making complex problems sound simple
  • Tim HarfordAuthor of How To Make The World Add Up
    A vivid, intelligent and wide-ranging book about how we know what we know.
  • Chris van TullekenAuthor of Ultra Processed People
    Adam Kucharski is that rarest of beasts: a true mathematical expert who can also write beautiful accessible, human prose.

About the author

  • Adam KucharskiProfessor at the London School of Hygiene and Tropical Medicine analysing infectious disease outbreaks
    • PhD in applied mathematics at the University of Cambridge
    • Awarded a Wellcome Trust/Royal Society Sir Henry Dale Fellowship in 2017
    • Shared the 2023 Adams Prize with Anne Cori for modelling the spread of infectious disease outbreaks
    • Author of The Perfect Bet and The Rules of Contagion
    • The Rules of Contagion named a Times, Guardian and FT science book of the year
    • Lives in Hertfordshire, UK

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