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{{Short description|2016 book by Marcus du Sautoy}}
{{Infobox book
| name =      What We Cannot Know
| image =     What We Cannot Know.jpg
| alt =       What We Cannot Know
| caption =   Front cover
| author =    [[Biography:Marcus du Sautoy|Marcus du Sautoy]]
| subject =   [[Philosophy:Epistemology|Epistemology]]
| pub_date =  19 May 2016
| publisher = HarperCollins
| pages =     320
| isbn =      9780007576661
}}
'''''What We Cannot Know: Explorations at the Edge of Knowledge''''' is a 2016 popular science book by the British mathematician [[Biography:Marcus du Sautoy|Marcus du Sautoy]]. He poses questions from science and mathematics and attempts to identify whether they are known, currently unknown or may be impossible to ever know.

==Background==
The author, British mathematician [[Biography:Marcus du Sautoy|Marcus du Sautoy]], succeeded [[Biography:Richard Dawkins|Richard Dawkins]] as Simonyi Professor for the Public Understanding of Science. His contributions to [[Science communication|science communication]] include television documentaries and a co-hosting role on ''Dara Ó Briain: School of Hard Sums''.<ref name="Undark"/>

Du Sautoy said that the book took three years to write. He was inspired to explore unknowns in science by considering provable unknowns in mathematics: for instance, Gödel's first incompleteness theorem states that in any (sufficiently sophisticated) logical system, there are true statements about positive whole numbers that cannot be proven true. In analogy, du Sautoy says that there are unknown questions around [[Philosophy:Consciousness|consciousness]] because every person is limited to their own consciousness (like a [[Formal system|formal system]] is limited to its axioms).<ref>{{cite web|url=https://iai.tv/articles/what-we-cannot-know-auid-787|title=What We Cannot Know|last=du Sautoy|first=Marcus|date=2 March 2017|accessdate=26 November 2022}}</ref> Another mathematical analogy du Sautoy made is that [[Euclid's theorem]]—that there are infinitely many [[Prime number|prime number]]s—is a finite proof of a fact about [[Infinity|infinity]]. Du Sautoy imagines that, in physics, some proof of infinitude of the [[Astronomy:Universe|universe]] could be similarly possible.<ref>{{cite web|url=https://www.prospectmagazine.co.uk/magazine/if-i-ruled-the-world-mathematics-euclid|title=If I ruled the world: Marcus du Sautoy|work=Prospect|last=du Sautoy|first=Marcus|author-link=Marcus du Sautoy|date=19 May 2016|accessdate=26 November 2022}}</ref>

The book was published on 19 May 2016.<ref>{{cite web|url=https://www.waterstones.com/book/what-we-cannot-know/marcus-du-sautoy/9780007576661|title=What We Cannot Know|publisher=Waterstones|accessdate=26 November 2022}}</ref>

==Synopsis==
Du Sautoy identifies seven "edges" of human knowledge, through consideration of physical objects. For instance, he questions whether it is possible to know what side a die will land on prior to rolling, using [[Probability|probability]] and [[Chaos theory|chaos theory]] in his analysis. He explores philosophical and scientific concepts of [[Time|time]] and [[Philosophy:Consciousness|consciousness]]. Other topics include [[Biology:Evolutionary biology|evolutionary biology]] and [[Physics:Particle physics|particle physics]]. As well as unknown questions, he illustrates known facts from quantum physics and [[Astronomy:Astronomy|astronomy]].

Du Sautoy connects the unknowns of human knowledge to [[Religion:God|God]], recalling that a radio interviewer defined God to him as "something which transcends human understanding". He ultimately rejects belief in a deity himself. He illustrates topics with examples from his own life, such as his practice of the trumpet and cello.

==Reception==
In ''Undark Magazine'', science communicator John Durant praised that du Sautoy's book is "honestly self-deprecating" and that he manages to be "amiable and entertaining" without exaggerating scientific fact.<ref name="Undark">{{cite web|url=https://undark.org/2016/07/22/book-review-what-we-cannot-know-marcus-du-sautoy/|title=Book Review: What We Cannot Know|work=Undark Magazine|last=Durant|first=John|date=22 July 2016|accessdate=26 November 2022}}</ref> Similarly, Nicola Davis of ''{{wipe|The Guardian}}'' praised that du Sautoy "exposes with humility his own confusions, apprehensions and concerns", but criticised that he "somewhat limply concludes" that what humans cannot know may remain unknown.<ref>{{cite web|url=https://www.theguardian.com/books/2016/may/15/what-we-cannot-know-marcus-du-sautoy-review|title=What We Cannot Know by Marcus du Sautoy – review|work={{wipe|The Guardian}}|last=Davis|first=Nicola|date=15 May 2016|accessdate=26 November 2022}}</ref> In contrast, a writer for ''[[Finance:The Economist|The Economist]]'' found the conclusion to be "optimistic" and saw the book as "fascinating".<ref>{{cite news|title=Circle in a Circle; The Boundaries of Science|newspaper=[[Finance:The Economist|The Economist]]|volume=419|issue=8994|pages=84–87|year=2016}}</ref> Barbara Kiser reviewed the book for ''Nature'' as a "finely synthesized study" in which du Sautoy takes readers on a "dazzling journey".<ref>{{cite journal|title=''What We Cannot Know'' (Review)|journal=Nature|last=Kiser|first=Barbara|volume=533|issue=7603|year=2016|page=319|doi=10.1038/533319a |s2cid=4449643 |doi-access=free}}</ref>

Rob Kingston recommended it as a science book of 2016 for ''The Times''.<ref>{{cite web|url=https://www.thetimes.co.uk/article/books-of-the-year-science-ks30mj7dj|title=Books of the year: science|last=Kingston|first=Rob|work=The Times|date=27 November 2016|accessdate=26 November 2022}}</ref> The University of Limerick's Centre for Teaching and Learning listed it as one of seven books that they encouraged students to read in 2020.<ref>{{cite news|title=Seven must-read books for freshers|work=Irish Independent|date=12 September 2020}}</ref>

==References==
{{reflist}}

[[Category:Books about philosophy of mathematics]]

{{Sourceattribution|What We Cannot Know}}