This book is my quest to explore the ultimate nature of reality, from the microcosm to our universe and beyond. If you join me by reading it and discussing with me on Facebook, then it will be our quest!

    2014 Book Tour:
Jan. 7: Launch!
Jan. 13: New York
Jan. 14: Philadelphia
Jan. 15: Brooklyn
Jan. 20: Menlo Park
Jan. 21: San Francisco
Jan. 22: Santa Cruz
Jan. 23: Seattle & Redmond
Jan. 27: Cambridge
Jan. 30: London
Feb. 5: Boston
May 20: Arlington
June 30: Paris
July 8: Stockholm
Aug 20: Reddit AMA

"Our Mathematical Universe boldly confronts one of the deepest questions at the fertile interface of physics and philosophy: why is mathematics so spectacularly successful at describing the cosmos? Through lively writing and wonderfully accessible explanations, Max Tegmark—one of the world's leading theoretical physicists—guides the reader to a possible answer, and reveals how, if it's right, our understanding of reality itself would be radically altered." —Prof. Brian Greene, physicist, author of The Elegant Universe and The Hidden Reality

"Daring, Radical. Innovative. A game changer. If Dr. Tegmark is correct, this represents a paradigm shift in the relationship between physics and mathematics, forcing us to rewrite our textbooks. A must read for anyone deeply concerned about our universe." —Prof. Michio Kaku, author of Physics of the Future

"Tegmark offers a fresh and fascinating perspective on the fabric of physical reality and life itself. He helps us see ourselves in a cosmic context that highlights the grand opportunities for the future of life in our universe." —Ray Kurzweil, author of The Singularity is Near

"Readers of varied backgrounds will enjoy this book. Almost anyone will find something to learn here, much to ponder, and perhaps something to disagree with." —Prof. Edward Witten, physicist, Fields Medalist & Milner Laureate

"This inspirational book written by a true expert presents an explosive mixture of physics, mathematics and philosophy which may alter your views on reality." —Prof. Andrei Linde, physicist, Gruber & Milner Laureate for development of inflationary cosmology

"Galileo famously said that the universe is written in the language of mathematics. Now Max Tegmark says that the universe IS mathematics. You don't have to necessarily agree, to enjoy this fascinating journey into the nature of reality." —Prof. Mario Livio, astrophysicist, author of Brilliant Blunders and Is God a Mathematician?

"Scientists and lay aficionados alike will find Tegmark's book packed with information and very thought provoking. You may recoil from his thesis, but nearly every page will make you wish you could debate the issues face—to—face with him." —Prof. Julian Barbour, physicist, author of The End of Time

"In Our Mathematical Universe, renowned cosmologist Max Tegmark takes us on a whirlwind tour of the universe, past, present—and other. With lucid language and clear examples, Tegmark provides us with the master measure of not only of our cosmos, but of all possible universes. The universe may be lonely, but it is not alone." —Prof. Seth Lloyd, Professor of quantum mechanical engineering, MIT, author of Programming the Universe

"Max Tegmark leads his readers, clearly and accessibly, right to the frontiers of speculative cosmology —and indeed far beyond." —Prof. Martin Rees, Astronomer Royal, cosmology pioneer, author of Our Final Hour

"A lucid, engaging account of the various many—universes theories of fundamental physics that are currently being considered, from the multiverse of quantum theory to Tegmark's own grand vision." —Prof. David Deutsch, physicist, Dirac Laureate for pioneering quantum computing

"Hisnande och provokativt om de yttersta frågorna. En nödvändig bok för dig som någon gång funderat på varifrån allt kommer." —Prof. Ulf Danielsson, physicist, author of Den bästa av världar

Editorial Reviews

New York Times: "This is science writing at its best - dynamic, dramatic and accessible.[...] 'Our Mathematical Universe' is nothing if not impressive. Brilliantly argued and beautifully written, it is never less than thought-provoking about the greatest mysteries of our existence." —Amir Alexander, The New York Times (full review here)

Publishers Weekly: "Tegmark offers a fascinating exploration of multiverse theories, each one offering new ways to explain `quantum weirdness' and other mysteries that have plagued physicists, culminating in the idea that our physical world is `a giant mathematical object' shaped by geometry and symmetry. Tegmark's writing is lucid, enthusiastic, and outright entertaining, a thoroughly accessible discussion leavened with anecdotes and the pure joy of a scientist at work." —Publishers Weekly (starred review)

Booklist:"Lively and lucid, the narrative invites general readers into debates over computer models for brain function, over scientific explanations of consciousness, and over prospects for finding advanced life in other galaxies. Though he reflects soberly on the perils of nuclear war and of hostile artificial intelligence, Tegmark concludes with a bracingly upbeat call for scientifically minded activists who recognize a rare opportunity to make our special planet a force for cosmic progress. An exhilarating adventure for bold readers." —Bryce Cristensen, Booklist (starred review)

BBC Focus: "MAX TEGMARK IS a professor of physics at MIT and a leading expert on theories of the Universe. But he's also arguably the nearest we have to a successor to Richard Feynman, the bongo-playing, wise-cracking physicist who proved it is possible to be smart, savvy and subversive at the same time. Tegmark has carved out a career as a physicist willing to ponder mind-boggling issues like the existence of multiple universes, yet without being dismissed as a crackpot by his peers. As he admits in this engrossing account of his career and thinking, this has enabled him to stay under the radar of the scientific establishment. But now `Mad Max' has been given the freedom of an entire book. And he hasn't wasted it. Around half of it is a lucid tour d'horizon of what we know about the Universe. The rest is an exhilarating expedition far beyond conventional thinking, in search of the true meaning of reality. Don't be fooled: Tegmark is a very smart physicist, not a hand-waving philosopher, so the going gets tough in parts. But his insights and conclusions are staggering - and perhaps even crazy enough to be true." —Robert Matthews, BBC Focus magazine

Nature: See the full review here; it's too long to fit in this spot, but here are some of my favorite snippets from it: "Cosmologist Max Tegmark has written an engaging and accessible book, Our Mathematical Universe, that grapples with this multiverse scenario. He aims initially at the scientifically literate public, but seeks to take us to - and, indeed, beyond - the frontiers of accepted knowledge. His explication of these ideas is more ambitious and individualistic than books on this topic by Leonard Susskind and Alex Vilenkin, for instance. [...] Tegmark's book captures two trends in contemporary science writing: scientific autobiography and the popular book as manifesto, expressing a body of personal scientific ideas ill-suited to traditional academic journals." [...] Fortunately, he is an engaging host. [...] This is a valuable book, written in a deceptively simple style but not afraid to make significant demands on its readers, especially once the multiverse level gets turned up to four. It is impressive how far Tegmark can carry you until, like a cartoon character running off a cliff, you wonder whether there is anything holding you up." —Andrew Liddle, Nature

Wall Street Journal: "Our Mathematical Universe" is a fascinating and well-executed dramatic argument from a talented expositor" —Peter Woit, The Wall Street Journal (full review here)

Biographile: See the full review here; it's too long to fit in this spot, but here are some of my favorite excerpts: "Just a few years ago, the idea of multiple universes was seen as a crackpot idea, not even on the margins of respectability. As Tegmark relays in his new book Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, he was discouraged from devoting his academic attention to it. But now, thanks in large part to Tegmark and his pursuit of controversial ideas, the concept of multiple universes (or a multiverse) is considered likely by many experts in the field.[...] Tegmark explains with charismatic enthusiasm why it matters [...] Tegmark's clear, engaging prose style can take you down these exciting and unexpected pathways of thought without making you feel lost. [...] in Our Mathematical Universe, we meet a revolutionary cosmology physicist who is hell bent on figuring out if that theory is true, how to prove it, how to use it, and what it means for the world as we know it." —Nathan Gelgud, Biographile

Financial Times: See the full review here; it's too long to fit in this spot, but here are some of my favorite excerpts: "Today multiple universes are scientifically respectable, thanks to the work of Tegmark as much as anyone. [...] Physics could do with more characters like Tegmark. He combines an imaginative intellect and a charismatic presence with a determination to promote his subject [...] enough will be comprehensible for non-scientific readers to enjoy an amazing ride through the rich landscape of contemporary cosmology. There are many interesting diversions from the main argument, from an assessment of threats to human civilisation (such as a 30 per cent risk of nuclear war) to the chance of intelligent life elsewhere in our galaxy (lower than astrobiologists like to think). Written in a lively and slightly quirky style, it should engage any reader interested in the infinite variety of nature." —Clive Cookson, Financial Times

New Scientist: See the full review here; it's too long to fit in this spot, but here are some of my favorite excerpts: "The book is an excellent guide to recent developments in quantum cosmology and the ongoing debate over theories of parallel universes. [...] Perhaps this book is proof that the two personalities needed for science - the speculative and sceptic - can readily exist in one individual." —Mark Buchanan, New Scientist

The Independent: See the full review here; it's too long to fit in this spot, but here are some of my favorite excerpts: "In Our Mathematical Universe, Max Tegmark - a distinguished cosmologist - gives a lucid rundown of the current state of knowledge on the origin, present state, and fate of the universe(s). [...] It is immensely illuminating on the reach of current cosmological theories. [...] From time to time, Tegmark engagingly admits that such ideas sound like nonsense, but he makes the crucial point that if a theory makes good predictions you have to follow all of the consequences. [...] His concluding chapter on the risks humanity faces is wise and bracing: he believes we "are alone in our Universe" but are capable of tackling terrible threats from cosmic accidents, or self-induced nuclear or climatic catastrophes. He doesn't cite poets but his philosophy adds up to an updated 21st-century version of Thomas Hardy's 'If way to the better there be, it exacts a full look at the worst'." —Peter Forbes, The Independent

The Times: See the full review here; it's too long to fit in this spot, but here are some of my favorite excerpts: "mind-bending book about the cosmos" [...] "Tegmark's achievement is to explain what on earth he is talking about in language any reasonably attentive reader will understand. He is a professor at MIT, and clearly a fine teacher as well as thinker. He tackles the big, interrelated questions of cosmology and subatomic physics much more intelligibly than, say, Stephen Hawking." —Giles Whittell, The Times

The Guardian: See the full review here; it's too long to fit in this spot, but here are some of my favorite excerpt: "Max Tegmark's doorstopper of a book takes aim at three great puzzles: how large is reality? What is everything made of? Why is our universe the way it is? Tegmark, a professor of physics at MIT, writes at the cutting edge of cosmology and quantum theory in friendly and relaxed prose, full of entertaining anecdotes and down-to-earth analogies." —Brian Rotman, The Guardian

The Pittsburg Post-Gazette: See the full review here; it's too long to fit in this spot, but here are some of my favorite excerpts: "Our Mathematical Universe is a delightful book in which the Swedish-born author, now at MIT, takes readers on a roller coaster ride through cosmology, quantum mechanics, parallel universes, sub-atomic particles and the future of humanity. It is quite an adventure with many time-outs along the way" [...] Our Mathematical Universe" gives keen insight into someone who asks questions for the pure joy of answering them." —Stephen Hirtle, The Pittsburg Post-Gazette

The New York Times: See the full review here; it's too long to fit in this spot, but here are some of my favorite excerpts: "an informative survey of exciting recent developments in astrophysics and quantum theory [...] Tegmark participated in some of these pioneering developments, and he enlivens his story with personal anecdotes. [...] Tegmark does an excellent job explaining this and other puzzles in a way accessible to nonspecialists. Packed with clever metaphors, this section illuminates an important area on the cutting edge of modern physics." —Edward Frenkel, The New York Times Sunday Book Review

Availability of the book

The book is now available on Amazon. I'm excited that it's coming out in many countries and languages:
CountryPublisherPlanned launch
United States Random House/Knopf  (buy) January 7 2014
United KingdomPenguin  (buy) January 2014
FranceDunod  (buy)April 16, 2014
SwedenVolante  (buy) May 17, 2014
RussiaCorpusSummer 2014
RomaniaEditura ASCRSummer 2014
JapanKodanshaSummer 2014
GreeceTravlosSeptember 2014
GermanyUllsteinFall 2014
SpainAntoni BoschFall 2014
ItalyBollati BoringhieriFall 2014
PolandProszynski-I-SkaTBD
TurkeyTubitakTBD
South KoreaEast Asia PublishingTBD
ChinaCheers PublishingTBD


Contents of the book

This book is my personal quest for the ultimate nature of reality, which I hope you'll enjoy seeing through my eyes. Together, we'll explore the clues that I personally find the most fascinating, and try to figure out what it all means. Here's how I've organized the book:

After two consecutive journeys of exploration, one outward and one inwards, we step back and ask what it all means. We end by returning home and asking what this means for us humans and the future of life in our cosmos, and what we personally can do about it - which is more than one might think!

Inflation and the BICEP2 discovery

Since the sensational discovery of gravitational gravitational waves by the south pole-based experiment BICEP2 is generating huge interest in inflation, I've decided to post my entire book chapter on inflation here so that you can get an up-to-date and self-contained account of what it's all about. Here are some of the questions answered: Here you go!

If you have further inflation questions after reading this, please ask me about them on Facebook.

Videos about the book

Here's a video my wife Meia made where we ponder the book together:
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She's currently editing some more that I hope to post here soon.

Podcasts about the book



Articles about the book


Discuss the book
I'd love to hear your questions and comments about these fun topics. Please join me on my Facebook by clicking "Like" and post your thoughts. In addition to hopefully answering your questions there, I'm planning to collect answers to the most common questions in the FAQ section below.

Critique
Although I feel very grateful for the large amounts of positive feedback I've received from colleagues, reviewers and others across the web, my book has also received some spirited criticism, centering around the following questions:

Q: Are parallel universes science or mere speculation?
A: First of all, please note that my book does not claim that parallel universes exist. Instead, all my arguments involve what logicians know as "modus ponens": that if X implies Y and X is true, then Y must also be true. Specifically, I argue that if some scientific theory X has enough experimental support for us to take it seriously, then we must take seriously also all its predictions Y, even if these predictions are themselves untestable (involving parallel universes, for example). In other words, I argue that parallel universes are not a scientific theory, but prediction of certain scientific theories. Specifically, I claim that there are four implications:
  1. Cosmological inflation generically implies Level I multiverse
  2. Inflation + string landscape generically implies Level II multiverse
  3. Unitary quantum mechanics implies Level III multiverse
  4. The Mathematical Universe Hypothesis implies Level IV multiverse
On other words, the key point that many critics miss is that parallel universes are not scientific theories, but predictions of certain theories, such as cosmological inflation, which are scientific because they make testable predictions for things that we can observe, such as cosmic microwave background measurements by the Planck satellite. For more details on this, see this blog post of mine. We humans have repeatedly underestimated the size our of cosmos by assuming that everything we could observe at the time was all that existed. No matter how seductively comforting a small reality may feel, we are not free to opt out of scientific predictions just because we don't like them: our job as scientists is not to tell our cosmos how to be, but to follow the trail of experimental evidence wherever it leads us.

Q: Isn't mathematics just a language that we invent rather than discover?
A: This is a famous controversy among mathematicians and philosophers. The way I see it, we humans invent the language of mathematics (the symbols, our human names for the symbols, etc.), but it's important not to confuse this language with the structure of mathematics that I focus on in the book. For example, any civilization interested in Platonic solids would discover that there are precisely 5 of them (the tetrahedron, cube, octahedron, dodecahedron and icosahedron). Whereas they're free to invent whatever names they want for them, they're not free to invent a 6th one - it simply doesn't exist. It's in the same sense that the mathematical structures that are popular in modern physics are discovered rather than invented, from 3+1-dimensional pseudo-Riemannian manifolds to Hilbert spaces.

Q: Aren't you conflating the description with the described when saying that our physical reality *is* mathematical rather than just being *described* by math?
A: This distinction (which I explore in detail in chapters 11 and 12) is crucial both in physics and in mathematics. Our language for describing the planet Neptune (which we obviously invent - we invented a different word for it in Swedish) is of course distinct from the planet itself. Similarly, we humans invent the language of mathematics (the symbols, our human names for the symbols, etc), but it's important not to confuse this language with the structure of mathematics. For example, as mentioned above, any civilization interested in Platonic solids would discover that there are precisely 5 of them (the tetrahedron, cube, octahedron, dodecahedron and icosahedron). Whereas they're free to invent whatever names they want for them, they're *not* free to invent a 6th one - it simply doesn't exist. It's in the same sense that the mathematical structures that are popular in modern physics are discovered rather than invented, from 3+1-dimensional pseudo-Riemannian manifolds to Hilbert spaces. The possibility that I explore in the book is that one of the structures of mathematics (which we can discover but not invent) corresponds to the physical world (which we also discover rather than invent).

Q: Isn't this mathematical universe idea old hat, dating back to Pythagoras?
A: The roots of this idea are indeed very old, and I give ample credit to Pythagoras and Galileo in my book! But they didn't have the benefit of knowing all the amazing mathematical clues that nature has subsequently revealed, from general relativity to quantum mechanics and math behind the Higgs boson, which is why we can now explore the idea and its implications in greater detail.

Q: Surely "stuff" can't be mathematical?
A: As a thought experiment, imagine that we one day develop super-advanced computers, and that you're a character in a future computer game that's so complex and realistic that you're conscious and mistakenly think you exist in a physically real world made of "stuff". Now you start studying your virtual world like a physicist, and gradually discover that the entities in your world seem to fundamentally have no properties except mathematical properties (since that's how your world is programmed), just as we've discovered here in our world. If you could perceive your virtual world as made of stuff even thought it was purely mathematical, then we need to be open to the possibility that the same might be happening here in our cosmos. Sure, the computer in this example is itself made of stuff, but the feeling that the objects in the game were made of "stuff" was completely illusory and independent of the substrate out of which the computer was built.

Q: Isn't the mathematical universe hypothesis unfalsifiable and hence unscientific?
A: No, it makes the testable prediction that our cosmos has no non-mathematical properties, so if you can prove that some aspect of our cosmos can't be described by mathematics, then you've falsified the hypothesis.

Q: Surely, consciousness can't be described by mathematics?
A: Consciousness is currently not understood through mathematics - nor by any other scientific approach, for that matter. Whether it ever will be is a very interesting question. I co-organized a conference on the Physics of Information recently where we invited the neuroscientists Giulio Tononi, Christoph Koch and Larissa Albantakis to speak, and intriguingly, they do think that the subjective feeling of the color red, the feeling of love, etc., can be understood as complex mathematical shapes related to information processing in the brain. I explore this in chapter 11 of my book. We obviously don't yet know whether their ideas will ultimately prove to be correct or not, but the fact that their research is taken seriously in the neuroscience community means that we can't be 100% sure that consciousness can't ultimately be understood mathematically.

Q: Isn't the matematical universe hypothesis ruled out by Gödel's incompleteness theorem?
A: No, not as far as we know. Given any sufficiently powerful formal system, Gödel showed that we cannot use it to prove its own consistency, but his doesn't mean that it is inconsistent or that we have a problem. Indeed, our cosmos doesn't show any signs of being inconsistent or ill-defined, despite showing hints that it may be a mathematical structure. Moreover, what were we hoping for? If a mathematical system could be used to prove its own consistency, we'd remain unconvinced that it actually was consistent, since an inconsistent system can prove anything. We'd only be somewhat convinced if a simpler system that we have better reason to trust the consistency of could prove the consistency of a more powerful system - unsurprisingly, that's impossible, as Gödel also proved. Of the many mathematicians with whom I'm friends, I've never heard anyone suggest that the mathematical structures that dominate modern physics (pseudo-Riemannian manifolds, Calabi-Yau manifolds, Hilbert spaces, etc.) are actually inconsistent or ill-defined.

Q: Is Max Tegmark a crackpot?
A: That's obviously not for me to answer - you'll find a hilarious analysis of this question here and an even more hilarious classification system here.


Frequently Asked Questions
Coming soon!

Resources
Coming soon! I'm in the process of collecting together videos, articles and other resources that I find helpful for delving deeper into cosmology, quantum mechanics, and the math-physics link, and hope to start posting them below shortly. I'm also planning a special section for kids which will include my two cents worth of advice if you're young, enthusiastic and want to know what do study and what to do if you want to be a scientist when you grow up.

Math/Physics Resources
What's the relation between physics and mathematics? This is one of the key questions I tackle in the book. Here are clips where I talk about this on the BBC and on Morgan Freedman's Through the Wormhole.
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Here are some articles I've written and some interviews with me on the topic:
I find this topic fascinating and spend two whole chapters of the book to finally explaining it properly, from the ground-up, carefully exploring its wild implications. Here are two brief introductions I've written plus an interview: Here's some further reading:
Quantum Resources
Quantum mechanics has been amazingly successful, giving us technologies from lasers to computers - but perhaps also a bigger reality! This BBC/PBS/NOVA movie is my favorite documentary about quantum parallel universes: (Parts 1, 2, 3, 4, 5, 6). Since the late Hugh Everett III is a great hero of mine, I felt truly honored to get to explain his amazing ideas to his rockstar son Mark 7:13 into part 3.
I find this topic fascinating and spend two whole chapters of the book on explaining it from ground-up and carefully exploring its wild implications. Here are some brief introductions I've written: Here's some further reading: