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:

"
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 thoughtprovoking 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 bongoplaying, wisecracking 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 mindboggling 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 handwaving 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 illsuited 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 wellexecuted 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 nonscientific 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 selfinduced nuclear or climatic catastrophes. He doesn't cite poets but his philosophy adds up to an updated 21stcentury 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:
"mindbending 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 downtoearth analogies."
—Brian Rotman,
The Guardian
The Pittsburg PostGazette:
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 Swedishborn author, now at MIT, takes readers on a roller coaster ride through cosmology, quantum mechanics, parallel universes, subatomic particles and the future of humanity. It is quite an adventure with many timeouts 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 PostGazette
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
"representerar verkligen dagens fysik och inte gårdagens. Den är pedagogisk, avantgardistisk och oförvägen."
—Lars Gustavsson,
Sydsvenska Dagbladet
"très imaginatif et propose une description stupéfiante de la réalité"
—David Larousserie,
Le Monde
Availability of the book
The book is now available on
Amazon.
I'm excited that it's coming out in many countries and languages:
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 claims of gravitational gravitational waves by
the south polebased 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 uptodate and selfcontained account of
what it's all about. Here are some of the questions answered:
 What does the theory of inflation really predict?
 What physics does it assume?
 Doesn't creation of the matter around us from almost nothing violate energy conservation?
 How could an infinite space get created in a finite time?
 How is this linked to the BICEP2 signal?
 What remarkable prize did Alan Guth win in 2005?
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 (she's currently editing more that I hope to post here soon):
.
Here's my guest appearance on Minutephysics (chapters 1012 explore this at much greater depth):
.
Here's a TEDxtalk about consciousness (I go into greater depth on this in Chapter 11):
.
Podcasts about the book
Articles about the book
 Discover magazine, December 2013 issue (excerpts from Chapter 10; paywall disappears December 3 2013)
 Discover magazine (interview with me about a key idea from 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:
 Cosmological inflation generically implies Level I multiverse
 Inflation + string landscape generically implies Level II multiverse
 Unitary quantum mechanics implies Level III multiverse
 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+1dimensional pseudoRiemannian 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+1dimensional pseudoRiemannian 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 superadvanced 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 nonmathematical 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 coorganized 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 illdefined, 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
(pseudoRiemannian manifolds, CalabiYau manifolds, Hilbert spaces, etc.) are actually inconsistent or illdefined.
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 mathphysics 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.
.

.

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 groundup, 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 groundup and carefully exploring its wild implications. Here are some brief introductions I've written:
Here's some further reading:
 The book with Hugh Everett's original Ph.D. thesis, widely lambasted but rarely read,
is in my opinion an excellent pedagogical piece. Although it's sadly out of print, you can download it for free
here.

You'll find a useful set of ManyWorld links in
the
Stanford Encyclopedia of Philosophy.
 There's an excellent 2009 book on the quantum many worlds interpretation containing chapters from many of its best known advocates
and critics.
 You'll find a fascinating free biography of Everett by Eugene Shikhovtsev
here.
 Peter Byrne has recently written the definitive Everett biography