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Proof: The Art and Science of Certainty

Description:

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.  


Editorial Reviews

Review

“Adam Kucharski's new book Proof is a life raft in a sea of fake news and misinformation.”―Jacob Aron, New Scientist

“A wide-ranging study on separating facts from fiction, truth from lies, and evidence from presumptions.” ―
Kirkus

"Kucharski explains why getting at the truth of just about anything is incredibly hard. There's fascinating technical detail here, and a moral: the more we appreciate how hard proof is to come by, the better we can bridge the widening gulf between experts and skeptics."―
Simon Ings, New Scientist

"Adam Kucharski has a knack of making complex problems sound simple - and exciting. A book that made me smile and feel clever."―
Peter Frankopan, author of The Silk Roads

"A vivid, intelligent and wide-ranging book about how we know what we know. Adam Kucharski is a brilliant and entertaining guide."―
Tim Harford, author of How To Make The World Add Up

“Adam Kucharski is that rarest of beasts: a true mathematical expert who can also write beautiful accessible, human prose.
Proof is a profound and utterly absorbing exploration of the limits and power of proof and truth, both in mathematics, logic, and the quest for certainty that we find ourselves on, whether we’re running the country of trying to decide on what to do with a medical test result. Kucharski elegantly explores how proof is not just a mathematical concept but a vital tool in decision-making, justice, and survival—it’s brilliant.”―Chris van Tulleken, author of Ultra-Processed People

"In an increasingly complex world, where we're beset by information, misinformation, and endlessly required to make decisions about it all, Kucharski shines a brilliant and clarifying light through the muddle. Proof is a puzzle-solver's delight; the essential guide we need to make sense of what and who to trust, and the risks therein."―
Gaia Vince, author of Nomad Century

About the Author

Adam Kucharski is a professor at the London School of Hygiene and Tropical Medicine, where he works on analysis of infectious disease outbreaks, work that won him the 2023 Adams Prize for mathematics. He regularly appears in print and broadcast media and is the author of The Perfect Bet and The Rules of Contagion. He lives in Hertfordshire, UK. 

Reviews:

5.0 out of 5 stars How to find the truth

W.L. · July 13, 2025

(function() { P.when('cr-A', 'ready').execute(function(A) { if(typeof A.toggleExpanderAriaLabel === 'function') { A.toggleExpanderAriaLabel('review_text_read_more', 'Read more of this review', 'Read less of this review'); } }); })(); .review-text-read-more-expander:focus-visible { outline: 2px solid #2162a1; outline-offset: 2px; border-radius: 5px; } This is a great book. I believe so strongly in this book that I bought copies for my son and daughter and have recommended it to most of my friends and acquaintances.The subject is really how to find the truth and how to convince others of the truth. The search for truth has a long history. The book begins with the attempts to use Euclid's method to find the truth by starting with some agreed upon "truths." In particular, this is why the U.S. Constitution contains the phrase " we hold these truths to be self evident..."The history of the search for methods to determine the truth continues with a chapter devoted to the attempts to, at least, derive Mathematics by Euclid's method--from agreed upon axioms. This collapses in the 1930's. The story is very well told.The book continues with entertaining discussions of the law--how convinced must a jury be to convict. This is followed by a fascinating review of the development, use, and shameful errors of statistics.There is much more but I do not want to summarize the book. I want to convince you to read it.I fervently believe that anyone who teaches statistics at any level read this book. What they learn will improve their teaching.Everyone else would benefit from reading this book. It will be somewhat more challenging for people who have no background in math or science but they will learn a great deal and be entertained while they learn.

5.0 out of 5 stars It’s a good description of this or that.

J.M. · September 7, 2025

It a wonderful thought provoking description of how logical analysis of what should be avoided but instead walk right into the mess.

4.0 out of 5 stars Examples a Bit Narrow

T.H. · June 11, 2025

I like books about math and about proof, in particular. Though this book is not what I expected it to be, it is interesting, nonetheless.Though Professor Kucharski does take a brief look back at the long history of mathematical proof, he focuses his attention mainly on the last two centuries, with the foundations of statistics and what that means for mathematical certainty. There’s a lot of discussion of p-values and the kinds of judgements investigators make to back up assertions. There are discussions about how misinformation spreads. As an epidemiologist, a majority of this book references his work in studying the COVID outbreak. It is a useful example because he is clearly working in his area of expertise; however, I was not very interested in this which caused me to struggle somewhat making it through.In the end, though this book is timely and has points of interest, it isn’t quite what I was looking for in a study of proof. I think if the examples would have covered a wider range of fields, I would have appreciated Professor Kucharski’s expertise more. Still, for someone interested in the analysis of infectious disease outbreaks, this is the book for you.

5.0 out of 5 stars Good examples.

b. · August 12, 2025

Gives all kinds of examples of telling whether something is true or not.

5.0 out of 5 stars Its flaws do not threaten my 5* rating

D.D. · May 17, 2025

This is a splendid book. It looks at various forms of proof. Mathematical proofs are often (but not always) the most rigourous forms of proof, but many other forms are presented and analysed.It would probably help to have a mathematical background, but I'd be willing to recommend the book to people of sufficient intelligence, even if they lacked such a background.Its greatest strength lies in how comprehensive it is. Quite apart from the ample mathematical and geometrical proofs, we are taken into the world of judicial and political proof as well as epidemology and artificial intelligence.I have to identify a particular flaw, or set of flaws. My biggest complaint about contemporary non-fiction is the overload of first-person singular pronouns. This author is seriously guilty on this point. I really wish Kindle had a facility for counting these. The degree of self-reference in the book is quite painful.If the book had not been otherwise so wonderful, my rating would have been 4* at best. However, my admiratiion for the overall content allows me to keep the 5* rating, despite the flaws.

5.0 out of 5 stars Brilliant, badly needed book

T. · August 20, 2025

Researchers and everyone who cares about science (that should be every human being) should read this book! Kucharski grounds some profound points using a conversational tone and fascinating historical accounts. His diagrams are ingenious and clear (p.124 on controlled experiment; p.215 he shows ladders of true and false causality, the latter due to false information). I’ll be rereading this book many times.

3.0 out of 5 stars How to explain odds n real life

R.S. · August 13, 2025

Fascinating interview in Topol ground truths and Ted talksIn MrEducation science people desire proof but not so easy. Understanding the math of difficult things fun. Ptint a little small so hard for my eyes, but worth

Interesting

J.M.c.c. · September 25, 2025

(function() { P.when('cr-A', 'ready').execute(function(A) { if(typeof A.toggleExpanderAriaLabel === 'function') { A.toggleExpanderAriaLabel('review_text_read_more', 'Read more of this review', 'Read less of this review'); } }); })(); .review-text-read-more-expander:focus-visible { outline: 2px solid #2162a1; outline-offset: 2px; border-radius: 5px; } For me, it is one of the best science books of the year. Interesting reflections about what is considered 'proof' along time and diciplines. I have missed more explanations at some points, particularly regarding science, and specially those branches unrelated to medicine, but overall, a good books, with many examples and anecdotes that allows a light reading

Great insight into something we all should be more aware off

A.K. · June 20, 2025

I loved this book. I first heard about it on a podcast and got intrigued. My issue with non-fiction books is that you normally get all you need from the first 20% of a book. But Mr. Kucharksi manages to keep the book relevant and interesting from the first to the last page. I have actually started to get the book as a gift to a few of my friends and colleagues.

Engaging and informing

S.R. · June 20, 2025

Fantastic book. I often struggle with non-fiction reads, but Kucharski knows how to tell a story as well as inform, and it's really engaging. Next one please!

Interesting, but didn’t talk much about proof

U. · May 12, 2025

Typical pop-sci book with stories and anecdotes but the actual content about proof could be condensed into 3-4 pages. The rest is just filler.

You will enjoy this book!

A. · March 28, 2025

With extensive in depth and wide-ranging research, Adam connects fascinating stories and events from different times and places to show how we are sometimes led to believe something that we should not. His skilful explanations lead us to the conclusion that rather than just being cynical to the point that we don’t believe anything anymore, we need to instead slow down to think carefully and critically about how we know what we know. If you are interested in learning about what we can or cannot believe about the world around us, you will enjoy this book!

Proof: The Art and Science of Certainty

Product ID: U1541606698
Condition: New

4.4

AED17928

Price includes VAT & Import Duties
Type: Hardcover
Availability: In Stock

Quantity:

|

Order today to get by 7-14 business days

Delivery fee of AED 20. Free for orders above AED 200.

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Imported From: United States

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Similar items from “Logic”

Proof: The Art and Science of Certainty

Product ID: U1541606698
Condition: New

4.4

Proof: The Art and Science of Certainty-0
Type: Hardcover

AED17928

Price includes VAT & Import Duties
Availability: In Stock

Quantity:

|

Order today to get by 7-14 business days

Delivery fee of AED 20. Free for orders above AED 200.

Returns & Warranty policies

Imported From: United States

At BOLO, we work hard to ensure the products you receive are new, genuine, and sourced from reputable suppliers.

BOLO is not an authorized or official retailer for most brands, nor are we affiliated with manufacturers unless specifically stated on a product page. Instead, we source verified sellers, authorized distributors or directly from the manufacturer.

Each product undergoes thorough inspection and verification at our consolidation and fulfilment centers to ensure it meets our strict authenticity and quality standards before being shipped and delivered to you.

If you ever have concerns regarding the authenticity of a product purchased from us, please contact Bolo Support. We will review your inquiry promptly and, if necessary, provide documentation verifying authenticity or offer a suitable resolution.

Your trust is our top priority, and we are committed to maintaining transparency and integrity in every transaction.

All product information, images, descriptions, and reviews originate from the manufacturer or from trusted sellers overseas. BOLO is not affiliated with, endorsed by, or an authorized retailer for most brands listed on our website unless stated otherwise.

While we strive to display accurate information, variations in packaging, labeling, instructions, or formulation may occasionally occur due to regional differences or supplier updates. For detailed or manufacturer-specific information, please contact the brand directly or reach out to BOLO Support for assistance.

Unless otherwise stated, all prices displayed on the product page include applicable taxes and import duties.

BOLO operates in accordance with the laws and regulations of United Arab Emirates. Any items found to be restricted or prohibited for sale within the UAE will be cancelled prior to shipment. We take proactive measures to ensure that only products permitted for sale in United Arab Emirates are listed on our website.

All items are shipped by air, and any products classified as “Dangerous Goods (DG)” under IATA regulations will be removed from the order and cancelled.

All orders are processed manually, and we make every effort to process them promptly once confirmed. Products cancelled due to the above reasons will be permanently removed from listings across the website.

Description:

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.  


Editorial Reviews

Review

“Adam Kucharski's new book Proof is a life raft in a sea of fake news and misinformation.”―Jacob Aron, New Scientist

“A wide-ranging study on separating facts from fiction, truth from lies, and evidence from presumptions.” ―
Kirkus

"Kucharski explains why getting at the truth of just about anything is incredibly hard. There's fascinating technical detail here, and a moral: the more we appreciate how hard proof is to come by, the better we can bridge the widening gulf between experts and skeptics."―
Simon Ings, New Scientist

"Adam Kucharski has a knack of making complex problems sound simple - and exciting. A book that made me smile and feel clever."―
Peter Frankopan, author of The Silk Roads

"A vivid, intelligent and wide-ranging book about how we know what we know. Adam Kucharski is a brilliant and entertaining guide."―
Tim Harford, author of How To Make The World Add Up

“Adam Kucharski is that rarest of beasts: a true mathematical expert who can also write beautiful accessible, human prose.
Proof is a profound and utterly absorbing exploration of the limits and power of proof and truth, both in mathematics, logic, and the quest for certainty that we find ourselves on, whether we’re running the country of trying to decide on what to do with a medical test result. Kucharski elegantly explores how proof is not just a mathematical concept but a vital tool in decision-making, justice, and survival—it’s brilliant.”―Chris van Tulleken, author of Ultra-Processed People

"In an increasingly complex world, where we're beset by information, misinformation, and endlessly required to make decisions about it all, Kucharski shines a brilliant and clarifying light through the muddle. Proof is a puzzle-solver's delight; the essential guide we need to make sense of what and who to trust, and the risks therein."―
Gaia Vince, author of Nomad Century

About the Author

Adam Kucharski is a professor at the London School of Hygiene and Tropical Medicine, where he works on analysis of infectious disease outbreaks, work that won him the 2023 Adams Prize for mathematics. He regularly appears in print and broadcast media and is the author of The Perfect Bet and The Rules of Contagion. He lives in Hertfordshire, UK. 

Reviews:

5.0 out of 5 stars How to find the truth

W.L. · July 13, 2025

(function() { P.when('cr-A', 'ready').execute(function(A) { if(typeof A.toggleExpanderAriaLabel === 'function') { A.toggleExpanderAriaLabel('review_text_read_more', 'Read more of this review', 'Read less of this review'); } }); })(); .review-text-read-more-expander:focus-visible { outline: 2px solid #2162a1; outline-offset: 2px; border-radius: 5px; } This is a great book. I believe so strongly in this book that I bought copies for my son and daughter and have recommended it to most of my friends and acquaintances.The subject is really how to find the truth and how to convince others of the truth. The search for truth has a long history. The book begins with the attempts to use Euclid's method to find the truth by starting with some agreed upon "truths." In particular, this is why the U.S. Constitution contains the phrase " we hold these truths to be self evident..."The history of the search for methods to determine the truth continues with a chapter devoted to the attempts to, at least, derive Mathematics by Euclid's method--from agreed upon axioms. This collapses in the 1930's. The story is very well told.The book continues with entertaining discussions of the law--how convinced must a jury be to convict. This is followed by a fascinating review of the development, use, and shameful errors of statistics.There is much more but I do not want to summarize the book. I want to convince you to read it.I fervently believe that anyone who teaches statistics at any level read this book. What they learn will improve their teaching.Everyone else would benefit from reading this book. It will be somewhat more challenging for people who have no background in math or science but they will learn a great deal and be entertained while they learn.

5.0 out of 5 stars It’s a good description of this or that.

J.M. · September 7, 2025

It a wonderful thought provoking description of how logical analysis of what should be avoided but instead walk right into the mess.

4.0 out of 5 stars Examples a Bit Narrow

T.H. · June 11, 2025

I like books about math and about proof, in particular. Though this book is not what I expected it to be, it is interesting, nonetheless.Though Professor Kucharski does take a brief look back at the long history of mathematical proof, he focuses his attention mainly on the last two centuries, with the foundations of statistics and what that means for mathematical certainty. There’s a lot of discussion of p-values and the kinds of judgements investigators make to back up assertions. There are discussions about how misinformation spreads. As an epidemiologist, a majority of this book references his work in studying the COVID outbreak. It is a useful example because he is clearly working in his area of expertise; however, I was not very interested in this which caused me to struggle somewhat making it through.In the end, though this book is timely and has points of interest, it isn’t quite what I was looking for in a study of proof. I think if the examples would have covered a wider range of fields, I would have appreciated Professor Kucharski’s expertise more. Still, for someone interested in the analysis of infectious disease outbreaks, this is the book for you.

5.0 out of 5 stars Good examples.

b. · August 12, 2025

Gives all kinds of examples of telling whether something is true or not.

5.0 out of 5 stars Its flaws do not threaten my 5* rating

D.D. · May 17, 2025

This is a splendid book. It looks at various forms of proof. Mathematical proofs are often (but not always) the most rigourous forms of proof, but many other forms are presented and analysed.It would probably help to have a mathematical background, but I'd be willing to recommend the book to people of sufficient intelligence, even if they lacked such a background.Its greatest strength lies in how comprehensive it is. Quite apart from the ample mathematical and geometrical proofs, we are taken into the world of judicial and political proof as well as epidemology and artificial intelligence.I have to identify a particular flaw, or set of flaws. My biggest complaint about contemporary non-fiction is the overload of first-person singular pronouns. This author is seriously guilty on this point. I really wish Kindle had a facility for counting these. The degree of self-reference in the book is quite painful.If the book had not been otherwise so wonderful, my rating would have been 4* at best. However, my admiratiion for the overall content allows me to keep the 5* rating, despite the flaws.

5.0 out of 5 stars Brilliant, badly needed book

T. · August 20, 2025

Researchers and everyone who cares about science (that should be every human being) should read this book! Kucharski grounds some profound points using a conversational tone and fascinating historical accounts. His diagrams are ingenious and clear (p.124 on controlled experiment; p.215 he shows ladders of true and false causality, the latter due to false information). I’ll be rereading this book many times.

3.0 out of 5 stars How to explain odds n real life

R.S. · August 13, 2025

Fascinating interview in Topol ground truths and Ted talksIn MrEducation science people desire proof but not so easy. Understanding the math of difficult things fun. Ptint a little small so hard for my eyes, but worth

Interesting

J.M.c.c. · September 25, 2025

(function() { P.when('cr-A', 'ready').execute(function(A) { if(typeof A.toggleExpanderAriaLabel === 'function') { A.toggleExpanderAriaLabel('review_text_read_more', 'Read more of this review', 'Read less of this review'); } }); })(); .review-text-read-more-expander:focus-visible { outline: 2px solid #2162a1; outline-offset: 2px; border-radius: 5px; } For me, it is one of the best science books of the year. Interesting reflections about what is considered 'proof' along time and diciplines. I have missed more explanations at some points, particularly regarding science, and specially those branches unrelated to medicine, but overall, a good books, with many examples and anecdotes that allows a light reading

Great insight into something we all should be more aware off

A.K. · June 20, 2025

I loved this book. I first heard about it on a podcast and got intrigued. My issue with non-fiction books is that you normally get all you need from the first 20% of a book. But Mr. Kucharksi manages to keep the book relevant and interesting from the first to the last page. I have actually started to get the book as a gift to a few of my friends and colleagues.

Engaging and informing

S.R. · June 20, 2025

Fantastic book. I often struggle with non-fiction reads, but Kucharski knows how to tell a story as well as inform, and it's really engaging. Next one please!

Interesting, but didn’t talk much about proof

U. · May 12, 2025

Typical pop-sci book with stories and anecdotes but the actual content about proof could be condensed into 3-4 pages. The rest is just filler.

You will enjoy this book!

A. · March 28, 2025

With extensive in depth and wide-ranging research, Adam connects fascinating stories and events from different times and places to show how we are sometimes led to believe something that we should not. His skilful explanations lead us to the conclusion that rather than just being cynical to the point that we don’t believe anything anymore, we need to instead slow down to think carefully and critically about how we know what we know. If you are interested in learning about what we can or cannot believe about the world around us, you will enjoy this book!

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