Proof : the art and science of certainty / Adam Kucharski.

By:

Kucharski, Adam (Mathematician) [author.]

Material type: Text

text

Media type:

unmediated

Carrier type:

volume

ISBN:

9781541606692

Subject(s):

Genre/Form:

Popular works.

LOC classification:

QA9.54 .K83 2025

Summary: "An award-winning mathematician shows how we prove what's true, and what to do when we can't. How do we establish what we believe? And how can we be certain that what we believe is true? And how do we convince other people that it is true? For thousands of years, from the ancient Greeks to the Arabic golden age to the modern world, science has used different methods--logical, empirical, intuitive, and more--to separate fact from fiction. But it all had the same goal: find perfect evidence and be rewarded with universal truth. As mathematician Adam Kucharski shows, however, there is far more to proof than axioms, theories, and laws: when demonstrating that a new medical treatment works, persuading a jury of someone's guilt, or deciding whether you trust a self-driving car, the weighing up of evidence is far from simple. To discover proof, we must reach into a thicket of errors and biases and embrace uncertainty--and never more so than when existing methods fail. Spanning mathematics, science, politics, philosophy, and economics, this book offers the ultimate exploration of how we can find our way to proof--and, just as importantly, of how to go forward when supposed facts falter"-- Provided by publisher.

List(s) this item appears in: New Adult Nonfiction

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Holdings
Item type	Current library	Collection	Shelving location	Call number	Status	Date due	Barcode	Item holds
Adult Book	Phillipsburg Free Public Library	Adult Non-Fiction	New Books	511.36 KUC	Available		36748002616813

Total holds: 0

Enhanced descriptions from Syndetics:

An award-winning mathematician--he "made me smile and made me feel clever" (Peter Frankopan)--shows how we prove what's true, and what to do when we can't

How do we establish what we believe? And how can we be certain that what we believe is true? And how do we convince other people that it is true? For thousands of years, from the ancient Greeks to the Arabic golden age to the modern world, science has used different methods--logical, empirical, intuitive, and more--to separate fact from fiction. But it all had the same goal: find perfect evidence and be rewarded with universal truth.

As mathematician Adam Kucharski shows, however, there is far more to proof than axioms, theories, and laws: when demonstrating that a new medical treatment works, persuading a jury of someone's guilt, or deciding whether you trust a self-driving car, the weighing up of evidence is far from simple. To discover proof, we must reach into a thicket of errors and biases and embrace uncertainty--and never more so than when existing methods fail.

Spanning mathematics, science, politics, philosophy, and economics, this book offers the ultimate exploration of how we can find our way to proof--and, just as importantly, of how to go forward when supposed facts falter.

Includes bibliographical references (pages 309-342) and index.

"An award-winning mathematician shows how we prove what's true, and what to do when we can't. How do we establish what we believe? And how can we be certain that what we believe is true? And how do we convince other people that it is true? For thousands of years, from the ancient Greeks to the Arabic golden age to the modern world, science has used different methods--logical, empirical, intuitive, and more--to separate fact from fiction. But it all had the same goal: find perfect evidence and be rewarded with universal truth. As mathematician Adam Kucharski shows, however, there is far more to proof than axioms, theories, and laws: when demonstrating that a new medical treatment works, persuading a jury of someone's guilt, or deciding whether you trust a self-driving car, the weighing up of evidence is far from simple. To discover proof, we must reach into a thicket of errors and biases and embrace uncertainty--and never more so than when existing methods fail. Spanning mathematics, science, politics, philosophy, and economics, this book offers the ultimate exploration of how we can find our way to proof--and, just as importantly, of how to go forward when supposed facts falter"-- Provided by publisher.

Table of contents provided by Syndetics

Introduction (1)
Chapter 1 The National Axioms (11)
Chapter 2 Logic Makes Mathematical Monsters (29)
Chapter 3 One Hundred Guilty and One Innocent (65)
Chapter 4 Tasting Statistical Tea and Brewing Scientific Beer (97)
Chapter 5 Paradigm Rifts (153)
Chapter 6 Big Lies (213)
Chapter 7 In Machines We Trust (257)
Chapter 8 How Much Do We Lose? (299)
Acknowledgments (307)
Notes (309)
Index (343)

Reviews provided by Syndetics

Publishers Weekly Review

"Even mathematical notions of proof not always as robust... as they might seem," according to this thought-provoking analysis. Kucharski (The Rules of Contagion), an epidemiology professor at the London School of Hygiene and Tropical Medicine, uses historical examples to explore the challenges of establishing objective truths through math and science. For instance, he discusses how Abraham Lincoln's efforts to use Euclidian logic to prove that slavery was at odds with America's founding principles failed because such reasoning requires both parties to agree on certain foundational axioms, which Lincoln's pro-slavery opponents didn't subscribe to. Modern science determines what counts as a statistically significant result based on an "arbitrary" cutoff, Kucharski contends, describing how in the 1920s statistician Ronald Fisher first proposed disregarding findings if "the probability of obtaining a result that extreme by chance" is more than 5% because that figure was just large enough to validate his recent research. Lamenting how scientists have exploited this threshold, Kucharski notes that for every 10 experiments, "there's a 40 percent chance that one will cross the traditional... cutoff purely by chance," leading some researchers to repeat experiments until they get the desired result and omit mention of the unsuccessful iterations in publication. The straightforward prose renders the quirks of research methodology approachable for lay readers. This edifies. (May)

Kirkus Book Review

A data specialist investigates the long search for truth and certainty. We live in an era of fake news, bickering experts, and information overload. This raises a key question: How do we know what to believe? Kucharski is a mathematician who specializes in epidemiology, and his 2020 bookThe Rules of Contagion: Why Things Spread--And Why They Stop brought together his expertise in trend analysis, social behavior, and disease treatment. In his new book, he casts a broader net, aiming to establish how truth is uncovered in science, law, politics, philosophy, and many other areas of human endeavor. He starts with Euclid and other classical thinkers who tried to find universal truths through the principles of mathematics and geometry, and he explains how their concepts provided the foundations of Western logic and rationalism. The development of calculus added another dimension. But all these ideas broke down in the face of increasing social complexity and new discoveries. Computer models and algorithms seemed to offer solutions but were eventually revealed as prone to bias, errors, and data limitations. Kucharski does a good job of exposing the flaws in these approaches and sees the "unknown unknowns" as the main obstacle on the path to truth. The book does not offer much advice about how to extract nuggets of truth from mountains of verbiage, but the best option, the author says, is to keep an open mind. He concludes: "We must seek out every useful fragment of data, gather every relevant tool, searching wider and climbing further. Finding the good foundations among the bad. Dodging dogma and falsehoods. Then perhaps, just perhaps, we'll reach the truth in time." A wide-ranging study on separating facts from fiction, truth from lies, and evidence from presumptions. Copyright (c) Kirkus Reviews, used with permission.