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The Gravity of Math: How Geometry Rules the Universe
One of the preeminent mathematicians of the past half century shows how physics and math were combined to give us the theory of gravity and the dizzying array of ideas and insights that has come from it
Mathematics is far more than just the language of science. It is a critical underpinning of nature. The famed physicist Albert Einstein demonstrated this in 1915 when he showed that gravity—long considered an attractive force between massive objects—was actually a manifestation of the curvature, or geometry, of space and time. But in making this towering intellectual leap, Einstein needed the help of several mathematicians, including Marcel Grossmann, who introduced him to the geometrical framework upon which his theory rests.
In The Gravity of Math, Steve Nadis and Shing-Tung Yau consider how math can drive and sometimes even anticipate discoveries in physics. Examining phenomena like black holes, gravitational waves, and the Big Bang, Nadis and Yau Why do mathematical statements, derived solely from logic, provide the best descriptions of our physical world?
The Gravity of Math offers an insightful and compelling look into the power of mathematics—whose reach, like that of gravity, can extend to the edge of the universe.
Mathematics is far more than just the language of science. It is a critical underpinning of nature. The famed physicist Albert Einstein demonstrated this in 1915 when he showed that gravity—long considered an attractive force between massive objects—was actually a manifestation of the curvature, or geometry, of space and time. But in making this towering intellectual leap, Einstein needed the help of several mathematicians, including Marcel Grossmann, who introduced him to the geometrical framework upon which his theory rests.
In The Gravity of Math, Steve Nadis and Shing-Tung Yau consider how math can drive and sometimes even anticipate discoveries in physics. Examining phenomena like black holes, gravitational waves, and the Big Bang, Nadis and Yau Why do mathematical statements, derived solely from logic, provide the best descriptions of our physical world?
The Gravity of Math offers an insightful and compelling look into the power of mathematics—whose reach, like that of gravity, can extend to the edge of the universe.
272 pages, Hardcover
Published April 16, 2024
29 people are currently reading
151 people want to read
About the author
Steve Nadis
8 books5 followersSteve Nadis is a Contributing Editor to Astronomy Magazine. He has published articles in Nature, Science, Scientific American, New Scientist, Sky&Telescope, The Atlantic Monthly, and other journals. He has written or contributed to more than two dozen books. A former staff researcher for the Union of Concerned Scientists, Nadis has also been a research fellow at MIT and a consultant to the World Resources Institute, the Woods Hole Oceanographic Institution, and WGBH/NOVA. He lives in Cambridge, Massachusetts.
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Displaying 1 - 13 of 13 reviews
July 31, 2024
One of my majors in college was math, and I took a lot of extra math courses on top of what was required for the degree, so this book is right up my alley. If you're not into math, you might not find this book as interesting. Although the authors do a good job of keeping the descriptions at a level where a lay person can at least follow along, if not completely understand the concepts at hand. It's kind of a history of mathematics over the last 100 years or so, as told by physicists. And the accounts of Einstein struggling with the math were fascinating - especially if you have always assumed that he was a genius at everything. (Spoiler alert: he wasn't.)
March 30, 2024
I am not sure who the target audience of this book is. As a math student who's currently doing there master degree and who only has a mild interest in history, I can say that it's not me.
It says in the description that "The Gravity of Math offers an insightful and compelling look into the power of mathematics […]" and I suppose it does? But without actually doing any maths. It explained the most basic concepts like what a vector is or rotation symmetry in detail but everything above that is just superficially touched upon. If you already know some differential geometry you get some nice connections to physics out of it but definitely no new maths. If you don't know anything about it however, I feel like this will just confuse you.
But then what exactly is this book about? Well, The history of gravity really. It's just 250 pages of this mathematician did that in this year, then this physicist did that, than this one did that, and then in the next year this mathematician did that and so on. And frankly, I don't care.
I wanted maths, I got history. Did I learn some things? Yeah, sure. But it was also quite boring.
It says in the description that "The Gravity of Math offers an insightful and compelling look into the power of mathematics […]" and I suppose it does? But without actually doing any maths. It explained the most basic concepts like what a vector is or rotation symmetry in detail but everything above that is just superficially touched upon. If you already know some differential geometry you get some nice connections to physics out of it but definitely no new maths. If you don't know anything about it however, I feel like this will just confuse you.
But then what exactly is this book about? Well, The history of gravity really. It's just 250 pages of this mathematician did that in this year, then this physicist did that, than this one did that, and then in the next year this mathematician did that and so on. And frankly, I don't care.
I wanted maths, I got history. Did I learn some things? Yeah, sure. But it was also quite boring.
June 3, 2024
A great introduction into relativity. I really enjoyed the science history mixed in with technical information. I did not follow all of the math but that should not dissuade anyone. I enjoyed how it highlighted the strong connection between mathematicians and physicist and supported a wholistic understanding of both to solve problems.
October 16, 2024
Richard Feynman was apparently not a believer in the value of mathematics to the science of physics, having said, "If all mathematics disappeared today, physics would be set back exactly one week." The authors of this book would disagree, and they set out to show just how central mathematics, geometry in particular, is to our understanding of the universe.
I've read a number of books that set out to explain Einstein's relativity and the relative universe we inhabit, but this is the first one that tells the story with a focus on the geometry and math Einstein and those who work in this area rely on. This approach ends up being one of the most satisfying and helpful explanations of the subject.
The geometry here is presented for a layperson's understanding, so few formulas and no assumptions about when you last cracked a math textbook. You have to slow down at times to parse some of the mathematical English, but focusing on the math behind relativity really gave me a much better understanding than any of the books I've read that tried to leave the math out. The first chapter was probably the best, from the perspective of showing how geometry is at the heart of understanding relativity. The discussion of Minkowski spacetime was illuminating. Once you understand that, so much of what follows can be understood more deeply than if you skipped the math entirely.
For me, the only weak chapter was Chapter 7 on the nature of mass. It was a surprise to learn that despite E = MC2 we don't really have an adequate description of what "mass" actually is. This chapter shows how researchers are trying to cure that inadequacy. Apparently this quest is necessary to prove that a universe must be mass positive, which would mean energy positive.
The problem with the chapter is mainly that the questions it raises are not answered and instead we sort of wade into a work in progress. There are lots of names mentioned and credit is given for this step forward and that step forward to such an extent that it feels a little bit like inside baseball, of interest only to the academics in the field. There is also rather a lot of effort to establish the centrality of Shing-tung Yau, one of the authors, in this area. We are not only told about his own papers but that such-and-such scientist discussed his ideas with Yau before publishing, such-and-such graduate students was one of Yau's graduate students, and so on. It was a bit much, I thought.
The book moves on to discuss the quest for unification, which Einstein spent 30 years on without measurable success. It is a good place to end the discussion of how geometry rules the universe. Symmetry and string theory are discussed and I think I understood both a bit more clearly because of the geometric focus throughout the book. The discussion is not long or detailed, but it helps to show how these things grew out of Einstein's work and the work of those who have come after.
Geometry turns out to provide a way to understanding relativity, not only for Einstein, but for a reader like me.
I've read a number of books that set out to explain Einstein's relativity and the relative universe we inhabit, but this is the first one that tells the story with a focus on the geometry and math Einstein and those who work in this area rely on. This approach ends up being one of the most satisfying and helpful explanations of the subject.
The geometry here is presented for a layperson's understanding, so few formulas and no assumptions about when you last cracked a math textbook. You have to slow down at times to parse some of the mathematical English, but focusing on the math behind relativity really gave me a much better understanding than any of the books I've read that tried to leave the math out. The first chapter was probably the best, from the perspective of showing how geometry is at the heart of understanding relativity. The discussion of Minkowski spacetime was illuminating. Once you understand that, so much of what follows can be understood more deeply than if you skipped the math entirely.
For me, the only weak chapter was Chapter 7 on the nature of mass. It was a surprise to learn that despite E = MC2 we don't really have an adequate description of what "mass" actually is. This chapter shows how researchers are trying to cure that inadequacy. Apparently this quest is necessary to prove that a universe must be mass positive, which would mean energy positive.
The problem with the chapter is mainly that the questions it raises are not answered and instead we sort of wade into a work in progress. There are lots of names mentioned and credit is given for this step forward and that step forward to such an extent that it feels a little bit like inside baseball, of interest only to the academics in the field. There is also rather a lot of effort to establish the centrality of Shing-tung Yau, one of the authors, in this area. We are not only told about his own papers but that such-and-such scientist discussed his ideas with Yau before publishing, such-and-such graduate students was one of Yau's graduate students, and so on. It was a bit much, I thought.
The book moves on to discuss the quest for unification, which Einstein spent 30 years on without measurable success. It is a good place to end the discussion of how geometry rules the universe. Symmetry and string theory are discussed and I think I understood both a bit more clearly because of the geometric focus throughout the book. The discussion is not long or detailed, but it helps to show how these things grew out of Einstein's work and the work of those who have come after.
Geometry turns out to provide a way to understanding relativity, not only for Einstein, but for a reader like me.
August 30, 2024
Geometry and physics
Geometry and mathematical statements derived from logic provide the best theoretical descriptions of our physical world. Einstein’s theory of general relativity describes gravity as the curvature of spacetime caused by massive objects. Mathematically, this is expressed through complex equations using tensors and geometry which is not just a language, it’s the very fabric of our universe. Geometrical analyses are also used to study the shape and curvature of spaces, similar to relativistic description of the curvature of spacetime.
A circle can be drawn with any center on a flat two-dimensional surface, this is called Euclidean geometry. But on a spherical surface such as the planet Earth, no true parallel lines exist. For instance, all lines of longitude on Earth eventually intersect at the North and South Poles. Because earth is spherical. Therefore, this requires non-Euclidean geometry. This book largely focuses on gravity and relativity to illustrate the importance of geometry, i.e., the non-Euclidean geometry. The readers must note that this is about geometry and gravity (spacetime bending). Math is hard enough to appreciate, and geometry generates less interest for an average reader. I did not find this book interesting since there are many books in the market that describe relativity in a much better way.
Geometry and mathematical statements derived from logic provide the best theoretical descriptions of our physical world. Einstein’s theory of general relativity describes gravity as the curvature of spacetime caused by massive objects. Mathematically, this is expressed through complex equations using tensors and geometry which is not just a language, it’s the very fabric of our universe. Geometrical analyses are also used to study the shape and curvature of spaces, similar to relativistic description of the curvature of spacetime.
A circle can be drawn with any center on a flat two-dimensional surface, this is called Euclidean geometry. But on a spherical surface such as the planet Earth, no true parallel lines exist. For instance, all lines of longitude on Earth eventually intersect at the North and South Poles. Because earth is spherical. Therefore, this requires non-Euclidean geometry. This book largely focuses on gravity and relativity to illustrate the importance of geometry, i.e., the non-Euclidean geometry. The readers must note that this is about geometry and gravity (spacetime bending). Math is hard enough to appreciate, and geometry generates less interest for an average reader. I did not find this book interesting since there are many books in the market that describe relativity in a much better way.
March 12, 2025
It isn't bad, but I had trouble understanding it as it went along, and as my understanding began to slip, it's hard to regain that grip.
Bad metaphor by me notwithstanding, the authors are mathematicians who are arguing of the role that math has played in physics breakthroughs beginning with Einstein and onward. Einstein was initially disinterested in math, but he needed some way to explain his thoughts on relativity, and the non-Euclidian geometry of people like Bernhard Reimann gave him the tools to explain and flesh out his concepts. (It wasn't easy, as it still took Einstein several years to do so). Afterwards, mathematicians provide proofs for black holes before the science was there for it. You get talk on gravity waves and the mass of the universe and trying to create a unified theory of forces and -- I'm talking far more broadly because beginning with gravity waves I started having trouble following. I readily admit that is most likely more an indictment of me than of the book, but nevertheless I didn't get as much out of the back half.
One random thing: the authors are pretty high on string theory. That's interesting, because from what little I know, that's on the outs in the world of physics. Well, maybe it's still more en vogue with mathetmaticians. Or maybe what little I know on the matter is even less than I think here.
Bad metaphor by me notwithstanding, the authors are mathematicians who are arguing of the role that math has played in physics breakthroughs beginning with Einstein and onward. Einstein was initially disinterested in math, but he needed some way to explain his thoughts on relativity, and the non-Euclidian geometry of people like Bernhard Reimann gave him the tools to explain and flesh out his concepts. (It wasn't easy, as it still took Einstein several years to do so). Afterwards, mathematicians provide proofs for black holes before the science was there for it. You get talk on gravity waves and the mass of the universe and trying to create a unified theory of forces and -- I'm talking far more broadly because beginning with gravity waves I started having trouble following. I readily admit that is most likely more an indictment of me than of the book, but nevertheless I didn't get as much out of the back half.
One random thing: the authors are pretty high on string theory. That's interesting, because from what little I know, that's on the outs in the world of physics. Well, maybe it's still more en vogue with mathetmaticians. Or maybe what little I know on the matter is even less than I think here.
January 11, 2025
This well written book tells the story of the developent of general relativity and the important mathematical results that aided and evolved from the development. As a retired mathematics professor (though nowhere near Shing-Tun Yau's level) I have heard and encountered most of the mathematical ideas and topics during my career. While I don't feel I learned much new from the book, it does give me directions to look to learn more about this fascinating topic.
Overall, the authors describe an amazing team and decades long effort to advance and test the ideas of relativity and to learn so much more about the universe in which we live. A great book!
Overall, the authors describe an amazing team and decades long effort to advance and test the ideas of relativity and to learn so much more about the universe in which we live. A great book!
May 26, 2025
Albert Einstein was a brilliant physicist but, when he first published his ground-breaking theories, did not have much regard for math. However, when he reached an impasse, he realized that he needed a little help from his friends, especially those gifted in mathematics. This book is the story of the mathematics and mathematicians who have been so critical to the development of the general theory of relativity. We sometimes think of this theory as the result of Einstein’s marvelous insight into the nature of reality. The book reminds us of just how much hard work has gone into understanding spacetime. An extremely lucid narrative of a very complex topic.
June 21, 2025
For a book on math, I thought there would be more math. I am a math major about to take some advanced geometry classes so I thought this book would be a good entry point into some of the concepts. This book should be labeled as a history book since it walks us through the whole history of relativity following Einstein then other successors that contributed to bring the theory to where it is today. I thought it was interesting to hear about the history and progression of the theory with mathematical concepts woven in, but the book just wasn’t quite what I expected. It’s a fine read if you like math and history.
August 4, 2024
This is the story of Einstein's development of the field equations and general relativity, leading to the subsequent discovery of black holes, gravitational waves, going all the way to current open problems in the field. The narrative flows beautifully and the anecdotes brought the many interesting characters to life. The parallel mathematical development of the ideas in Einstein’s field equations by David Hilbert illuminated the evolving relationship between mathematics and physics.
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August 4, 2024Thought I would like this one but couldn't get into it so just read the first and last 50 pages or so. Interesting interplay between pure math and the physics of cosmology. And that Einstein did not care for math early on but did a total 180 later.
September 30, 2024
With the clear, not for the expert explanations this book teaches you the field equation and the wrinkles of modern physics. It focuses particularly on geometry's role as if God did not have a choice after all. Truly enjoied the read
October 24, 2024
Good but technical
It was much more technical than anticipated, I enjoyed the bits I understood. A terrific history of physics and math.
It was much more technical than anticipated, I enjoyed the bits I understood. A terrific history of physics and math.
Displaying 1 - 13 of 13 reviews