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The Universe Speaks in Numbers: How Modern Math Reveals Nature's Deepest Secrets
How math helps us solve the universe's deepest mysteriesOne of the great insights of science is that the universe has an underlying order. The supreme goal of physicists is to understand this order through laws that describe the behavior of the most basic particles and the forces between them. For centuries, we have searched for these laws by studying the results of experiments. Since the 1970s, however, experiments at the world's most powerful atom-smashers have offered few new clues. So some of the world's leading physicists have looked to a different source of modern mathematics. These physicists are sometimes accused of doing 'fairy-tale physics', unrelated to the real world. But in The Universe Speaks in Numbers, award-winning science writer and biographer Farmelo argues that the physics they are doing is based squarely on the well-established principles of quantum theory and relativity, and part of a tradition dating back to Isaac Newton. With unprecedented access to some of the world's greatest scientific minds, Farmelo offers a vivid, behind-the-scenes account of the blossoming relationship between mathematics and physics and the research that could revolutionize our understanding of reality.A masterful account of the some of the most groundbreaking ideas in physics in the past four decades. The Universe Speaks in Numbers is essential reading for anyone interested in the quest to discover the fundamental laws of nature.
291 pages, Kindle Edition
First published April 30, 2019
About the author
Graham Farmelo
10 books79 followersGraham Farmelo is a senior research fellow at the Science Museum, London and associate professor of physics at Northeastern University, US.
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August 26, 2019
Theoretical physics has taken something of a hammering lately with books such as Sabine Hossenfelder's Lost in Math. The suggestion from these earlier titles is that theoretical physics is so obsessed with mathematics that many theoretical physicists spend their careers working on theory that doesn't actually apply to the universe, because the maths is interesting. Even experimental physics can be tainted, as the driver for new expenditure in experiments, such as the proposed new collider at CERN, is not driven by discoveries but by these mathematically-directed theories. Graham Farmelo presents the opposite view here: that this speculative mathematical work is, in fact, a great success.
As I am very much in the Hossenfelder camp, I expected to find Farmelo's book rather irritating, as it's effectively a love letter to mathematically-obsessed theoretical physics - but in reality (an entertaining phrase, given the context) I found it both interesting and enjoyable. Farmelo has a clear enthusiasm for the wonders of higher abstract mathematics and takes us through the history of the transformation of physics from being driven by experiment and observation to being driven by mathematical theory with a light touch and some fascinating detail.
However, much though I enjoyed The Universe Speaks in Numbers, it hasn't changed my position. The book's subtitle is 'how modern maths reveals nature's deepest secrets' - but the problem is that it is failing to do so. We discover lots of new and interesting mathematics - with the physicists actually revealing new maths that surprised the mathematicians - but hardly anything that has come out of this mathematical work that has carried physics forward in the last 40 years. Modern maths isn't revealing nature's deepest secrets, it is revealing some of the secrets of more maths, and that isn't what physics should be about.
I think I can pinpoint where the worldview goes adrift from reality on page 127 of the book. Farmelo comments 'Most of [the remainder of the book] is not conventional science, in which theorists make predictions that experimenters test; rather, it is speculative science, still under development and often not yet susceptible to observational tests. But it is science nonetheless...' - I'm afraid I can't agree. Speculation isn't science. It may become science, so isn't necessarily worthless scientifically speaking, but it certainly isn't science at the moment, and hasn't succeeded in making the leap in several decades.
For example, as Hossenfelder points out in her book, string theory works best if the cosmological constant value that reflects the expansion or contraction of the universe is negative. Unfortunately it's actually positive, but most string theorists spend their time working with a negative cosmological constant. It makes for beautiful mathematics - but has nothing to do with our universe. It isn't science, it's maths.
I haven't lost hope for physics, where there is still plenty of excellent work going on. However, I don't share Farmelo's enthusiasm for building mathematical towers in the sky, piling speculation on speculation. This doesn't however, distract from the fact that this is an excellent summary of the current position and how we got here, and Farmelo manages to put the state of theoretical physics across without alienating someone with a very different view, which surely is an excellent achievement.
As I am very much in the Hossenfelder camp, I expected to find Farmelo's book rather irritating, as it's effectively a love letter to mathematically-obsessed theoretical physics - but in reality (an entertaining phrase, given the context) I found it both interesting and enjoyable. Farmelo has a clear enthusiasm for the wonders of higher abstract mathematics and takes us through the history of the transformation of physics from being driven by experiment and observation to being driven by mathematical theory with a light touch and some fascinating detail.
However, much though I enjoyed The Universe Speaks in Numbers, it hasn't changed my position. The book's subtitle is 'how modern maths reveals nature's deepest secrets' - but the problem is that it is failing to do so. We discover lots of new and interesting mathematics - with the physicists actually revealing new maths that surprised the mathematicians - but hardly anything that has come out of this mathematical work that has carried physics forward in the last 40 years. Modern maths isn't revealing nature's deepest secrets, it is revealing some of the secrets of more maths, and that isn't what physics should be about.
I think I can pinpoint where the worldview goes adrift from reality on page 127 of the book. Farmelo comments 'Most of [the remainder of the book] is not conventional science, in which theorists make predictions that experimenters test; rather, it is speculative science, still under development and often not yet susceptible to observational tests. But it is science nonetheless...' - I'm afraid I can't agree. Speculation isn't science. It may become science, so isn't necessarily worthless scientifically speaking, but it certainly isn't science at the moment, and hasn't succeeded in making the leap in several decades.
For example, as Hossenfelder points out in her book, string theory works best if the cosmological constant value that reflects the expansion or contraction of the universe is negative. Unfortunately it's actually positive, but most string theorists spend their time working with a negative cosmological constant. It makes for beautiful mathematics - but has nothing to do with our universe. It isn't science, it's maths.
I haven't lost hope for physics, where there is still plenty of excellent work going on. However, I don't share Farmelo's enthusiasm for building mathematical towers in the sky, piling speculation on speculation. This doesn't however, distract from the fact that this is an excellent summary of the current position and how we got here, and Farmelo manages to put the state of theoretical physics across without alienating someone with a very different view, which surely is an excellent achievement.
April 30, 2020
I wanted a book on why the universe seems to be explicable in terms of math at a deeper philosophical level. Instead I got a decent history of physics that covers some familiar ground (the birth of relativity and quantum mechanics) and some unfamiliar ground (recent mathematical advances in gauge theory), with the combination of capsule biographies and light explanations that are not enough to fully explain.
What made the book a little more than that was the overarching narrative about the different styles of physics, experimental, theoreticians responding to experiments, and theoreticians who treat mathematical beauty as an end unto itself. Graham Farmelo argues that Einstein and Dirac were exemplars of this last approach and their modern heirs are string theorists who are working entirely unmoored from experiments or even commonsense reality, but Farmelo is still betting on them because of the mathematical beauty of their approach. Over the course of the story, Farmelo describes a period of falling out between math and physics and how they came back together again that I had not previously been aware of.
Overall, interesting but the main argument is more asserted and proven and less new and creative than I would have hoped. I might have to try Our Mathematical Universe: My Quest for the Ultimate Nature of Reality.
What made the book a little more than that was the overarching narrative about the different styles of physics, experimental, theoreticians responding to experiments, and theoreticians who treat mathematical beauty as an end unto itself. Graham Farmelo argues that Einstein and Dirac were exemplars of this last approach and their modern heirs are string theorists who are working entirely unmoored from experiments or even commonsense reality, but Farmelo is still betting on them because of the mathematical beauty of their approach. Over the course of the story, Farmelo describes a period of falling out between math and physics and how they came back together again that I had not previously been aware of.
Overall, interesting but the main argument is more asserted and proven and less new and creative than I would have hoped. I might have to try Our Mathematical Universe: My Quest for the Ultimate Nature of Reality.
October 27, 2019
This is a book-length defense of the idea that it is good and proper that physicists are creating theories based more on pure mathematics than on physical experiments. It is a position I don't really agree with, though the author makes a compelling case that this approach has worked before, and has a good chance of working again. The actual math in modern physics would be far, far above my head, as well as over the head of almost all readers, so no attempt is made to fully describe it. There is more focus on the history of the ideas, people involved, and on how physicists and mathematicians are finally starting to see value in each other's work.
One of the cool things that keeps coming up in new theories is 'dualities'. Many theories can be expressed in terms of completely different concepts but in the end can be proven to be mathematically equivalent.
One of the cool things that keeps coming up in new theories is 'dualities'. Many theories can be expressed in terms of completely different concepts but in the end can be proven to be mathematically equivalent.
September 28, 2020
This book is a remarkably mediocre consideration of the idea that the fundamental truths of nature are mathematical. It then takes that premise and projects it forward to support the idea that math can predict physical law. This to me is simply an over aggressive reading into the idea that mathematical beauty in some way indicates truth. The book also takes the questionable step of calling string theory science when at best it's either a secondary model with no novel data or is in some sort of pre-science phase.
The book glosses over the handwaving that comes up when you try to reconcile physics with mathematics and ignores things like the complexity of setting a gauge for a gauge theory, the infinite series that are Feynmann diagrams and the requirement of convergence in perturbation theory. Additionally, it overlooks the grand sweep of cases where the "more beautiful" option was simply wrong whether it be the value of the fine structure constant or any number of times the wrong equation was used because it was more beautiful.
This book is unsatisfying and offers little to nothing to the reader.
The book glosses over the handwaving that comes up when you try to reconcile physics with mathematics and ignores things like the complexity of setting a gauge for a gauge theory, the infinite series that are Feynmann diagrams and the requirement of convergence in perturbation theory. Additionally, it overlooks the grand sweep of cases where the "more beautiful" option was simply wrong whether it be the value of the fine structure constant or any number of times the wrong equation was used because it was more beautiful.
This book is unsatisfying and offers little to nothing to the reader.
May 2, 2022
Ants cannot count.
After a quick book review, we will come back to ants (!) to see where the book arguments may fall short.
In many ways, the title is a misnomer. The author takes on a highly challenging topic in trying to defend theoretical physics against the experimental one. In academic circles and popular books, theoreticians have taken a severe beating in recent years for their inability to come up with anything proven or provable of late.
Of course, the book primarily relies on the massive successes of the theoreticians until the mid-twentieth century. However, the book's best parts are when the author discusses lesser-discussed progress and achievements since. It is clear that theoreticians still have a role to play, but is it forever or as substantial as it has historically been? The author takes a strong position on this question. However, one can make different types of arguments to discuss otherwise.
Using financial theory analogies, this reviewer can see three different theories on mathematics and the universe: a weak form, a strong form, and an even stronger one.
In the most superfluous version, one would assume the universe to keep evolving based on a set of rules along a continuum - notwithstanding the quantized nature. This mechanism can be captured through symbols, methods, and equations of mathematics, which is also a rule-based field.
One does not dwell too much on why math works but accepts that it does. And the believers could use this to argue why it is possible for someone (or a group of someone) sitting in a room to come up with ideas on how the universe works simply through deductive reasoning in her mind. History is replete with examples - well discussed in the book - of the greatest human brains achieving this over the last five hundred years. Their sitting-behind-desk-analysis led to transformative insights that not only were proven by the best experimenters later but led them on what and where to look.
The strong form is based on propositions (led by luminaries like Dirac) that any mathematical discoveries we make will have some real-world applications in our efforts to understand the universe. Starting from geometry to trigonometry, calculus, probability theories, and all the way to non-Euclidean geometry, complex numbers, topology, and set theory have all found utility in physics. It is almost as if Mathematicians cannot find a pure work that has no application for the physicians. Some may even go on to say that our mathematical universe has to manifest anything possible in mathematics. However, until we find a perfect, Platonic circle, the arguments are better limited to applications rather than manifestations!
The strongest form would nullify everything above in a way. As Godel proved, mathematics is axiomatic and perennially incomplete. Depending on how one sets the unprovable axioms, there are uncountable, if not infinite, number of mathematics possible. The world we observe cannot validate whatever any mathematician says, or theoretician hypothesises. One must ignore Godel to believe that every mathematical idea will have some utility.
The problem gets worse. Our brains have capacity limits. There may be no reduction in the pace of mathematical discoveries so far, but there has to come a time when a set of human brains can no longer disentangle a more complex set of equations. The world does not have to be based on rules that are human-understandable. Theoretically, the world could be running on a mathematical equation that is based on a billion axioms rather than one we have deployed in theories like string theory. Like ants, there is a limit to our mathematical abilities, and one day our experimental physicians - with their ever-improving toolkit - will be far ahead of what theoreticians could come up with.
Theoretical physics - as done by our scientists - is severely constrained by human brain capacity. This is in contrast to the experimental sciences, whose ability to collect and process data seems to be growing rapidly, if not exponentially. Yes, one may use artificial intelligence to leapfrog mathematical theories too. Still, if they are not decipherable by human brains, they would appear more like the evidence-based, empirical work of experimentalists.
To elucidate this point further, let's assume the universe runs on a mathematical equation that is about a thousand times bigger when expressed through symbols than the standard model with a few thousand arbitrary constants. Such an equation - we are supposing - would not only explain all the motions but also exactly describe the water flowing through a capillary to the formation of genes and the DNA or even the capriciousness of politicians! An ever-evolving intelligent system, like our machines, may be able to unearth a larger and larger slice of such an equation over time. The unearthing would be extraordinarily slow, if not impossible, for a stagnant or slowly-changing construct like the human brain.
There is always a chance that the equation of the universe is shorter and a theoretician arrives at it through deductive analysis, or a slice of it, before experimenters but the chances are definitionally vanishing given the complexities achieved. More importantly, until any such constructs - whether constructed by humans or machines - are verified, they will appear more like dogmas than the statements of the world.
All this does not mean theoreticians have no place in the world of sciences. They absolutely do. But, if they become too exotic with ideas that cannot be verified for long, they will continue to come under pressure regardless of their glorious history.
After a quick book review, we will come back to ants (!) to see where the book arguments may fall short.
In many ways, the title is a misnomer. The author takes on a highly challenging topic in trying to defend theoretical physics against the experimental one. In academic circles and popular books, theoreticians have taken a severe beating in recent years for their inability to come up with anything proven or provable of late.
Of course, the book primarily relies on the massive successes of the theoreticians until the mid-twentieth century. However, the book's best parts are when the author discusses lesser-discussed progress and achievements since. It is clear that theoreticians still have a role to play, but is it forever or as substantial as it has historically been? The author takes a strong position on this question. However, one can make different types of arguments to discuss otherwise.
Using financial theory analogies, this reviewer can see three different theories on mathematics and the universe: a weak form, a strong form, and an even stronger one.
In the most superfluous version, one would assume the universe to keep evolving based on a set of rules along a continuum - notwithstanding the quantized nature. This mechanism can be captured through symbols, methods, and equations of mathematics, which is also a rule-based field.
One does not dwell too much on why math works but accepts that it does. And the believers could use this to argue why it is possible for someone (or a group of someone) sitting in a room to come up with ideas on how the universe works simply through deductive reasoning in her mind. History is replete with examples - well discussed in the book - of the greatest human brains achieving this over the last five hundred years. Their sitting-behind-desk-analysis led to transformative insights that not only were proven by the best experimenters later but led them on what and where to look.
The strong form is based on propositions (led by luminaries like Dirac) that any mathematical discoveries we make will have some real-world applications in our efforts to understand the universe. Starting from geometry to trigonometry, calculus, probability theories, and all the way to non-Euclidean geometry, complex numbers, topology, and set theory have all found utility in physics. It is almost as if Mathematicians cannot find a pure work that has no application for the physicians. Some may even go on to say that our mathematical universe has to manifest anything possible in mathematics. However, until we find a perfect, Platonic circle, the arguments are better limited to applications rather than manifestations!
The strongest form would nullify everything above in a way. As Godel proved, mathematics is axiomatic and perennially incomplete. Depending on how one sets the unprovable axioms, there are uncountable, if not infinite, number of mathematics possible. The world we observe cannot validate whatever any mathematician says, or theoretician hypothesises. One must ignore Godel to believe that every mathematical idea will have some utility.
The problem gets worse. Our brains have capacity limits. There may be no reduction in the pace of mathematical discoveries so far, but there has to come a time when a set of human brains can no longer disentangle a more complex set of equations. The world does not have to be based on rules that are human-understandable. Theoretically, the world could be running on a mathematical equation that is based on a billion axioms rather than one we have deployed in theories like string theory. Like ants, there is a limit to our mathematical abilities, and one day our experimental physicians - with their ever-improving toolkit - will be far ahead of what theoreticians could come up with.
Theoretical physics - as done by our scientists - is severely constrained by human brain capacity. This is in contrast to the experimental sciences, whose ability to collect and process data seems to be growing rapidly, if not exponentially. Yes, one may use artificial intelligence to leapfrog mathematical theories too. Still, if they are not decipherable by human brains, they would appear more like the evidence-based, empirical work of experimentalists.
To elucidate this point further, let's assume the universe runs on a mathematical equation that is about a thousand times bigger when expressed through symbols than the standard model with a few thousand arbitrary constants. Such an equation - we are supposing - would not only explain all the motions but also exactly describe the water flowing through a capillary to the formation of genes and the DNA or even the capriciousness of politicians! An ever-evolving intelligent system, like our machines, may be able to unearth a larger and larger slice of such an equation over time. The unearthing would be extraordinarily slow, if not impossible, for a stagnant or slowly-changing construct like the human brain.
There is always a chance that the equation of the universe is shorter and a theoretician arrives at it through deductive analysis, or a slice of it, before experimenters but the chances are definitionally vanishing given the complexities achieved. More importantly, until any such constructs - whether constructed by humans or machines - are verified, they will appear more like dogmas than the statements of the world.
All this does not mean theoreticians have no place in the world of sciences. They absolutely do. But, if they become too exotic with ideas that cannot be verified for long, they will continue to come under pressure regardless of their glorious history.
December 5, 2023
إذا كنت بعيد عن النقاش العلمي الذي يدور بين العلماء بالفيزياء النظرية فهذا الكتاب ليس موجه لك. فبعض الكتب والمقالات تظهر أن علماء الفيزياء النظرية وصلوا إلى أبواب مغلقة تحد تطور هذا العلم. فمن جهة فالتوفيق بين نظرية النسبية الخاصة ونظرية الكم للوصول لنظرية كل شيء وصل لطريق مغلق ولم يستطع العلماء إلى الآن أن يأتوا بنظرية فيزيائية جامعة للأكون الضخمة وللأكوان فائقة الصغر، ومن جهة أخرى فالتطور بالفيزياء النظرية لم يصاحبه تطور بالفيزياء التجريبية لاختبار النظريات الفيزيائية المقدمة، هنا المأزق، فإذا كان تعريف العلم هو انتاج نظرية قابلة للدحض أو التأكيد من خلال التجربة فما الذي ي��عل هذه النظريات غير المجربة وبعضها غير قابل للتجريب أن تعتبر علما؟ لذا كثير من العلماء النظريين إلتفتوا للرياضيات وأهملوا الجانب التطبيقي، عندها خرجت لنا بعض النظريات جذابة رياضي�� وغير معقولة واقعيا كنظرية الأكوان المتعددة ونظرية الأوتار الفائقة والتي إلى الآن لا يوجد طريقة لختبار صحتها. عندها بعض الفيزيائيين أبدوا تحفظهم على هذا التوجه والذي يهتم بجمال النظرية الرياضية على واقعية النظرية، مثلا كتاب :Lost in Math: How Beauty Leads Physics Astray.
هذا الكتاب هو رد نوعا ما على هذه المشكلة فالكتاب يتابع تاريخ الفيزياء مع التركيز على أهمية الرياضيات بفك غموض بعض الظواهر الفيزيائية. طبعا الجميع يعرف أهمية الرياضيات للفيزياء وبقية العلوم، لكن النقاش هنا هو أهمية الرياضيت لتقدم العلم وقدرة بعض أفرع الرياضيات على حل المشاكل الفيزيائية تجريديا وبلا تجربة. فالمؤلف للوصول لفكرته هذه يطيل التفصيل في الأحداث الفيزيائية من خمسينيات القرن الماضي وحتى الآن والتي اشتهر فيها العالم بول ديراك وإصراره على أن العالم يبحث عن الجمال الرياضي في عمله البحثي وإلا لا يواصل عمله. المؤلف واضح بتوجهه بأن الرياضيات عندها القدرة على حل المشاكل الرياضية وأننا لا يجب أن ننتظر التجربة لتلحق بها.
الكتاب عموما جيد ولكن إذا لم يهمك هذا النقاش فيوجد كتب أخرى أفضل منه.
هذا الكتاب هو رد نوعا ما على هذه المشكلة فالكتاب يتابع تاريخ الفيزياء مع التركيز على أهمية الرياضيات بفك غموض بعض الظواهر الفيزيائية. طبعا الجميع يعرف أهمية الرياضيات للفيزياء وبقية العلوم، لكن النقاش هنا هو أهمية الرياضيت لتقدم العلم وقدرة بعض أفرع الرياضيات على حل المشاكل الفيزيائية تجريديا وبلا تجربة. فالمؤلف للوصول لفكرته هذه يطيل التفصيل في الأحداث الفيزيائية من خمسينيات القرن الماضي وحتى الآن والتي اشتهر فيها العالم بول ديراك وإصراره على أن العالم يبحث عن الجمال الرياضي في عمله البحثي وإلا لا يواصل عمله. المؤلف واضح بتوجهه بأن الرياضيات عندها القدرة على حل المشاكل الرياضية وأننا لا يجب أن ننتظر التجربة لتلحق بها.
الكتاب عموما جيد ولكن إذا لم يهمك هذا النقاش فيوجد كتب أخرى أفضل منه.
July 24, 2019
A significant subject has been upheld and presented in a very lucid way. This book is mostly a historical account till recent times on the nature of relation/interface between physics and mathematics over the time with the study of mathematics supporting the theories of physics and more recently physics benefitting mathematical development. This book highlights the very strong interdependence of each of the disciplines on each other and both of these having theories dual to each other.
The intricate relation between physics and mathematics was not so easy to underpin or to describe over the time since revolutionary discoveries of our physical world was brought about by the pioneers like Copernicus, Kepler and Galileo. Although among the ancient Greeks were notable figures who embraced the significant importance of mathematics to our physical world, like Pythagoras/Pythagorean school, Plato and Archimedes, it was not until the great Sir Isaac Newton that a systematic analysis of Mathematical Principles for Natural World was laid down wide open to appreciate its significance.
Since then the paths of the study of mathematics and physics have intertwined and also separated when these two aspects of Natural world was studied with distinct set of ways.
Mathematicians followed strict logic and militant rigour to bring about solid unshakable proofs. Mathematicans believed in a Platonic existence of the axioms, theorems and principles which they discover with their rigourous methods.
Whereas physicists relied on observations and measurement within the uncertainties of error, reasoning and intuition and ofcourse these being supported by a mathematical base for understanding its consistency. The stringent rigour was not essential for every physical theories, if it is supported well by experimental facts.
Two great revolutions : The Quantum theory and Special relativity sprouted out mostly supported by experimental results and intelligent reasoning with intuition of the luminaries like Planck, Einstein, Lorentz, Poincaré to name a few. Even the great Micheal Faraday was an excellent experimenter who gifted us with the idea of fields about seven decades before relativity and quantum theory's inception. However James Clerk Maxwell superbly incorporated Faraday's ideas in his mathematical tour de force to lay bare the nature of electromagnetism and its mathematical structure.
However the dedicated study of mathematics progressed steadily over time with not any significant input from physicists since the days of Euclid among the Greeks and later on through Fermat, Euler, Lagrange,Cauchy, Gauss, Riemann to name some of the great mathematicians.
However Newton's detailed work in the late 17th century and the masterstroke of Einstein in 1915 to wrought upon the description of gravity in terms of geometry reminded a severely close relation between these two disciplines of study. From then on the history is teeming with such examples where theories in physics did progress when new mathematical principles were used. Developments in quantum mechanics in the 1920s culminated in the celebrated Dirac Equation for electron using important mathematics like matrices, complex numbers and Clifford algebra which pointed towards a totally non-intuitive discovery of the positron.
Two noteworthy lectures in the 1930s, one given by Einstein and the other by Dirac, highlighted the importance of mathematics to new discoveries in physics and both believed in concentrating on mathematics more, than always hunting for experimental results.
The conventional approach for mathematics was having no interdependence on physical theories and on the other hand physicists relied on assumptions and theories developed on reasoning of experimental results within uncertainties. So even after such massive work done, as mentioned above , the two disciplines derailed into a long separation after the second world war. Totally unlike what Einstein and Dirac suggested , this phase disappointed many great thinkers like Freeman Dyson and robbed them of hope of a merger of these two jewels.
But eventually significant discoveries over the time not only revived the old spirit of physics being progressed by developing mathematics but this time mathematics was benefitted by physics with insights of physicists which out of the blue breathed with mathematical forms. The attempt to unify all forces of nature gave birth to the String Theory which was fertile for new mathematical developments. Even the successful Gauge theory was found to possess wonderful connection with Mathematics. The scattering amplitude for collision of hadrons to study the nature of strong force gave rise to the modern jewel namely Amplituhedron by Nima Arkani Hamed and J.Trnka. This sophisticated piece of work imbibed the geometric form of positive Grassmanian which have its description boiled down to whole numbers. Thus the title of the book.
It's worth reading to understand this wonderful relationship of Physics and Mathematics.
The intricate relation between physics and mathematics was not so easy to underpin or to describe over the time since revolutionary discoveries of our physical world was brought about by the pioneers like Copernicus, Kepler and Galileo. Although among the ancient Greeks were notable figures who embraced the significant importance of mathematics to our physical world, like Pythagoras/Pythagorean school, Plato and Archimedes, it was not until the great Sir Isaac Newton that a systematic analysis of Mathematical Principles for Natural World was laid down wide open to appreciate its significance.
Since then the paths of the study of mathematics and physics have intertwined and also separated when these two aspects of Natural world was studied with distinct set of ways.
Mathematicians followed strict logic and militant rigour to bring about solid unshakable proofs. Mathematicans believed in a Platonic existence of the axioms, theorems and principles which they discover with their rigourous methods.
Whereas physicists relied on observations and measurement within the uncertainties of error, reasoning and intuition and ofcourse these being supported by a mathematical base for understanding its consistency. The stringent rigour was not essential for every physical theories, if it is supported well by experimental facts.
Two great revolutions : The Quantum theory and Special relativity sprouted out mostly supported by experimental results and intelligent reasoning with intuition of the luminaries like Planck, Einstein, Lorentz, Poincaré to name a few. Even the great Micheal Faraday was an excellent experimenter who gifted us with the idea of fields about seven decades before relativity and quantum theory's inception. However James Clerk Maxwell superbly incorporated Faraday's ideas in his mathematical tour de force to lay bare the nature of electromagnetism and its mathematical structure.
However the dedicated study of mathematics progressed steadily over time with not any significant input from physicists since the days of Euclid among the Greeks and later on through Fermat, Euler, Lagrange,Cauchy, Gauss, Riemann to name some of the great mathematicians.
However Newton's detailed work in the late 17th century and the masterstroke of Einstein in 1915 to wrought upon the description of gravity in terms of geometry reminded a severely close relation between these two disciplines of study. From then on the history is teeming with such examples where theories in physics did progress when new mathematical principles were used. Developments in quantum mechanics in the 1920s culminated in the celebrated Dirac Equation for electron using important mathematics like matrices, complex numbers and Clifford algebra which pointed towards a totally non-intuitive discovery of the positron.
Two noteworthy lectures in the 1930s, one given by Einstein and the other by Dirac, highlighted the importance of mathematics to new discoveries in physics and both believed in concentrating on mathematics more, than always hunting for experimental results.
The conventional approach for mathematics was having no interdependence on physical theories and on the other hand physicists relied on assumptions and theories developed on reasoning of experimental results within uncertainties. So even after such massive work done, as mentioned above , the two disciplines derailed into a long separation after the second world war. Totally unlike what Einstein and Dirac suggested , this phase disappointed many great thinkers like Freeman Dyson and robbed them of hope of a merger of these two jewels.
But eventually significant discoveries over the time not only revived the old spirit of physics being progressed by developing mathematics but this time mathematics was benefitted by physics with insights of physicists which out of the blue breathed with mathematical forms. The attempt to unify all forces of nature gave birth to the String Theory which was fertile for new mathematical developments. Even the successful Gauge theory was found to possess wonderful connection with Mathematics. The scattering amplitude for collision of hadrons to study the nature of strong force gave rise to the modern jewel namely Amplituhedron by Nima Arkani Hamed and J.Trnka. This sophisticated piece of work imbibed the geometric form of positive Grassmanian which have its description boiled down to whole numbers. Thus the title of the book.
It's worth reading to understand this wonderful relationship of Physics and Mathematics.
May 29, 2023
Exactly what I wanted. Captivating. Makes me want to be a mathematician or physicist. Captures the beauty and excitement of these fields and their interaction.
July 16, 2023
I couldn’t bring myself to finish this book. I read all but the last 20 pages and conclusion. It was quite interesting , and as a college freshman I was able to understand most of it until the 50s/60s. It is all like a retelling of physics history, abbreviated of course. However at some point in the last century it becomes less explanations and more just oversimplified of very complex theories. I didn’t like reading that, since I wasn’t learning anything, or understanding what exactly was so thrilling and new. I also don’t know all too much anout the field, maybe a bit more than the average person, but honestly the title had given me a lot more to hope for. It just felt like one big essay.
June 19, 2022
Farmelo argues for the importance of the interconnection between theoretical science and mathematical research. This is far more of a history book (detailing discoveries made simply cognitively and then backed up by physical findings, and then leading into the world of string theory) than a book about actual math or physics; most of the idea depicted here are quickly glossed over, so I am unilluminated about their actual content or importance, particularly in the more baroque later chapters. Nevertheless, I enjoyed the book, and think anyone interested in history of philosophy of science likely would as well.
May 3, 2023
Audio book
My expectations were completely different from what the book actually is. I was hoping for more scientifically oriented physics book, explaining details of theories.
This was mostly history of physics of who said what and when!
Unfortunately I was bored half way in the book.
My expectations were completely different from what the book actually is. I was hoping for more scientifically oriented physics book, explaining details of theories.
This was mostly history of physics of who said what and when!
Unfortunately I was bored half way in the book.
May 18, 2024
A love letter to mathematical theory, yet it is neither about mathematics nor does it use mathematics. As far as I can tell, it is a philosophical work about the nature of scientific speculation. Big disappointment.
July 17, 2022
Did I enjoy listening to this, following along, and returning to many of the historical anecdotes in this recording? Definitely. Historical mathematicians, physicists, and philosophers (often overlapping) were presented as dynamic thinkers, which is certainly true. The many theories and developments were set in respective contexts of time and in relation to theories and developments from came before; often I learned of often competing, sometimes complementing concurrent contributions. Did I understand all of the references to mathematics and physics? Admittedly, no, as I laughed various times to references of "all school children will recall" -- and I did indeed recall after a review here -- as I heard properties and laws. Still, despite not clearly understanding all the mechanics of Modern Math, I came to more deeply appreciate the science and art of numbers, cause-effect, and the thinkers who advance this discipline. I will return to this again in the future, learning a bit more and enjoying this yet again.
July 8, 2023
Interesting and insightful, plus the writing flows very well. This book talks about both the past and present of physics and mathematical research.
October 22, 2021
Not your everyday light reading, but super interesting. It only took me three times to understand the difference between particle physics and string theory 🙃
July 5, 2019
Agreed you should never judge a book by its cover, but this would be more aptly titled "A History of the Relationship Between Maths and Physics, with a few stories thrown in". Would've liked either a bit more detail on the maths, or else something entirely for the general reader, felt this sat somewhere in the middle.
June 28, 2021
I enjoyed this book and it answered many questions I had, such as "has string theory ever been demonstrated by experimental results?" I actually liked to early portions of the book more than the latter and more recent work in fundamental physics, which I think was written more as a comprehensive review for workers in the field than for the general public, even if they have some background in mathematics. I found the latter chapters to be too abstract to be as informative as I would have liked. And after thinking about this book for a day or so after finishing it, I came to the conclusion that physicists are much more conflicted than their colleagues in other scientific disciplines and even in engineering about the role of advanced mathematics in the development of their field. Engineers just take it for granted that most new advances, either in generating new analysis theories or even in the development of advanced fabrication methods, will naturally incorporate math (and even new mathematical principles, if they are called for).
August 26, 2020
I found this book extremely fascinating however I am sure that if I hadn’t majored in Math for my undergrad I would have been horribly bored by the topics covered. This book details the long standing mercurial relationship between the mathematical community and the physics community. I loved learning how all of the theories we use on a daily basis came to be. I loved learning about all the quirky mathematicians and physicists throughout history and what they actually contributed to what we know today. This book gave me a deeper admiration for the beauty and aesthetic of both mathematics and physics. I found the layout of the book confusing at times since it wasn’t chronological. Overall, for a math book, it was extremely intriguing!
February 21, 2020
Undoubtedly one of the best books I have read on Physics and Maths in the last few years. The unification of these two branches is an ongoing journey. It is fascinating to witness the frontiers being scaled and the collaboration between the pure mathematicians and the equally pure physicists. Einstein and Paul Dirac shine their lights and lend their shoulders for others to see farther. Completely illuminating.
Phenomenal effort and a must read.
Phenomenal effort and a must read.
January 31, 2022
not what I expected
I thought this book was going to live up to its title and show how math reveals nature. Instead it was a narrative history if the intersection of advanced math and physics. Don’t get me wrong , it’s an interesting story, but it’s a story , not a technical book. It talked about things like gauge theory, but it didn’t make an effort to explain what gauge theory is all about. Oh well.
I thought this book was going to live up to its title and show how math reveals nature. Instead it was a narrative history if the intersection of advanced math and physics. Don’t get me wrong , it’s an interesting story, but it’s a story , not a technical book. It talked about things like gauge theory, but it didn’t make an effort to explain what gauge theory is all about. Oh well.
December 15, 2021
I’d give this book 6 stars!
Although I believe one must be a mathematical physicist to understand and appreciate the integration of both the higher level math as it relates to physics. Absolutely fascinating.
Although I believe one must be a mathematical physicist to understand and appreciate the integration of both the higher level math as it relates to physics. Absolutely fascinating.
July 18, 2021
Extraordinary! Best popular science ever!
May 25, 2020
Couldn't put it down.
February 6, 2021
This was absolutely wonderful. I love physics, cosmology, mathematics -- you name it. I'm always looking for a good book, but often what I find are explications-- yet again -- of special relativity or quantum physics discoveries of nearly a century ago. The first half of this book did approach those topics from a slightly different direction (i.e., a focus on the mathematics), but I skipped those because I was already familiar with them. But the second half was an up-to-the-minute of publication story about significant progress that's being made in the new field of physical mathematics. It was wonderful. Many thanks to Goodreads to IRL friend Chris Opsal for suggesting it!
I skipped about the first half, because I've read many summaries of the mathematical and physical components of the discovery of special and general relativity, etc. But the second half, bringing the story up to the present day, was absolutely wonderful and included much material I had not seen. It was refreshing to see string theory presented in an objective way, by neither proponents nor skeptics, but simply people saying, here is the math, and here is what has and hasn't been tested experimentally.
The notion of using pure mathematics as well as experimental results to guide physics research started with Einstein's attempt to find a combined theory of gravity and electromagnetism (3).
I was delighted to learn of "instantons" of which I had not heard before. According to Gerard t'Hooft, "it's best to think of instantons not as particles but as events that happen at points in space-time" (136). And there is experimental evidence: the mass of eta mesons (one of the lightest particles, with no spin), "could be understood only if eta mesons featured in the underlying theory."
About the usefulness of mathematical concepts for understanding scattering amplitudes, "Karl Jacobs told me that the results of the scattering-amplitudes revolution were 'essential for us to pin down the Higgs particle with high precision.'" (243).
"Arkani-Hamed and Trnka then returned to their project, which at long last seemed to be coming to fruition. It took almost a year before they were sure that the pieces of the gluons' scattering amplitude comprised what they described as the 'positve space.' During the following summer, they finally understood that they were in fact looking at an abstract object composed of piecesof the positive Grassmannian that fit perfectly together like tiles, to form a multisided geometric object - a polytope." (244).
Weinberg argues that the partnership with mathematicians has occurred because there is so little new experimental data for them to work on -- that they work with mathematics "faute de mieux." However, he is glad that they *have* kept working, quoting Winston Churchill's advice, "keep buggering on."
As always, I was especially interested in references to female scientists:
Cecile de Witt, who organized, with John Wheeler, a conference to bring together phsyicists and mathematicians -- in 1967
Lauren Williams, an expert on positive Grassmanians who has built her career working 'at the crossroads of pure and applied mathematics,' said of the amplituhedron that "it is such a beautiful object that it has to be something worth working on" (245)
Fabiola Gianotti, CERN's director general, "refuses to be downhearted. Even after the experimenters at the LHC have spent years preparing to open one of nature's cupboards only to find it empty of new particles, she said in 2018, 'There's still time for surprises -- no one knows what will show up in the next few years.'" She is confident that they can still support the design of next-generation particle accelerators and detectors, and that there will always be a "need for high-energy accelerators probing the smallest constituents of matter."
I skipped about the first half, because I've read many summaries of the mathematical and physical components of the discovery of special and general relativity, etc. But the second half, bringing the story up to the present day, was absolutely wonderful and included much material I had not seen. It was refreshing to see string theory presented in an objective way, by neither proponents nor skeptics, but simply people saying, here is the math, and here is what has and hasn't been tested experimentally.
The notion of using pure mathematics as well as experimental results to guide physics research started with Einstein's attempt to find a combined theory of gravity and electromagnetism (3).
I was delighted to learn of "instantons" of which I had not heard before. According to Gerard t'Hooft, "it's best to think of instantons not as particles but as events that happen at points in space-time" (136). And there is experimental evidence: the mass of eta mesons (one of the lightest particles, with no spin), "could be understood only if eta mesons featured in the underlying theory."
About the usefulness of mathematical concepts for understanding scattering amplitudes, "Karl Jacobs told me that the results of the scattering-amplitudes revolution were 'essential for us to pin down the Higgs particle with high precision.'" (243).
"Arkani-Hamed and Trnka then returned to their project, which at long last seemed to be coming to fruition. It took almost a year before they were sure that the pieces of the gluons' scattering amplitude comprised what they described as the 'positve space.' During the following summer, they finally understood that they were in fact looking at an abstract object composed of piecesof the positive Grassmannian that fit perfectly together like tiles, to form a multisided geometric object - a polytope." (244).
Weinberg argues that the partnership with mathematicians has occurred because there is so little new experimental data for them to work on -- that they work with mathematics "faute de mieux." However, he is glad that they *have* kept working, quoting Winston Churchill's advice, "keep buggering on."
As always, I was especially interested in references to female scientists:
Cecile de Witt, who organized, with John Wheeler, a conference to bring together phsyicists and mathematicians -- in 1967
Lauren Williams, an expert on positive Grassmanians who has built her career working 'at the crossroads of pure and applied mathematics,' said of the amplituhedron that "it is such a beautiful object that it has to be something worth working on" (245)
Fabiola Gianotti, CERN's director general, "refuses to be downhearted. Even after the experimenters at the LHC have spent years preparing to open one of nature's cupboards only to find it empty of new particles, she said in 2018, 'There's still time for surprises -- no one knows what will show up in the next few years.'" She is confident that they can still support the design of next-generation particle accelerators and detectors, and that there will always be a "need for high-energy accelerators probing the smallest constituents of matter."
June 14, 2023
I have rarely read a book that makes such a complicated subject so engaging. Using just the right amount of creative description, Farmelo presents the history of theoretical physics beginning with Isaac Newton, Pierre-Simon Laplace and James Clerk Maxwell, before moving on to well-known names like Heisenberg, Planck and Einstein. Best of all, this book contains very few mathematical equations, instead describing the work of each scientist in a manner which is accessible to any interested reader.
This book is sure to introduce you to a few names you have never heard of before, unless you are a physicist of mathematician, in which case this book is not for you. By presenting a broad overview of the subject, Farmelo builds a case that the most fundamental laws of nature are mathematical. The early chapters set up what we already know: there are atoms, and atoms have electrons. Maxwell realized that electricity and magnetism were related, and was one of the first people to develop equations describing how it worked. Then Paul Dirac figured out that the underlying principles of electrodynamics had a lot in common with abstract mathematics. And these individuals were not natural philosophers, just hard working guys trying to make the math easier to do.
Physics and mathematics went their separate ways in the 1950s, but the discoveries from one camp kept complimenting work in the other. Sometimes it was a competition, sometimes they challenged one another, and scientists trained as physicists or mathematicians had their own culture that sometimes struggled to communicate. Farmelo includes discoveries that have been made as recently as 2015 and projects what he expects scientists to work on in the future. The completed narrative describes the greatest human minds working together to discover the underlying order of the cosmos.
This book is sure to introduce you to a few names you have never heard of before, unless you are a physicist of mathematician, in which case this book is not for you. By presenting a broad overview of the subject, Farmelo builds a case that the most fundamental laws of nature are mathematical. The early chapters set up what we already know: there are atoms, and atoms have electrons. Maxwell realized that electricity and magnetism were related, and was one of the first people to develop equations describing how it worked. Then Paul Dirac figured out that the underlying principles of electrodynamics had a lot in common with abstract mathematics. And these individuals were not natural philosophers, just hard working guys trying to make the math easier to do.
Physics and mathematics went their separate ways in the 1950s, but the discoveries from one camp kept complimenting work in the other. Sometimes it was a competition, sometimes they challenged one another, and scientists trained as physicists or mathematicians had their own culture that sometimes struggled to communicate. Farmelo includes discoveries that have been made as recently as 2015 and projects what he expects scientists to work on in the future. The completed narrative describes the greatest human minds working together to discover the underlying order of the cosmos.
August 30, 2020
This is basically a history of physics, and the interplay between math and physics (which I never knew were really considered to be very separate subjects once you get into theoretical physics). I found Einstein's thought experiments most fascinating--I'd known a bit about this before, but the fact that he specifically eschewed higher level math until he needed it to elucidate general relativity was interesting. Paul Dirac, one of Einstein's contemporaries, followed in his footsteps of thought experiments as well. This was unprecedented, since historically, all scientific advancements had been made through testing hypotheses via experimentation. Dirac gave a speech to a lay audience explaining the concept of thought experiments, in which he argued that when a concept is well and truly understood, not only should one not be dependent upon experimental data, but if the experimental data contradicts the expected findings of the thought experiment, one should doubt the data, rather than the expectation. (Makes sense, when considering how often experiments can go awry due to unanticipated variables.)
When the story got to theoretical particles like boson-higgs and what not, it went over my head, but I still found the overall story of the progress of theoretical physics fascinating.
When the story got to theoretical particles like boson-higgs and what not, it went over my head, but I still found the overall story of the progress of theoretical physics fascinating.
August 30, 2019
The conceit here is nothing new to physics folk: Math is unnaturally good at describing the universe. So much so that many Physicists wonder if mathematics holds the answers (over experimentation and other types of modeling). This book was very much a historical exposition of the merging and synthesis of math and theoretical physics. At times interesting but also at times a bit tedious I found. Ultimately, there was not a lot of unpacking around the idea of math-as-a-tool vs. math-as-ultimate-truth even though I though it would be a central theme of the book.
Personally, I'm with Where Mathematics Come From: How the Embodied Mind Brings Mathematics into BeingGeorge Lakoff on mathematics: math is a language invented inside us, not a truth "out there". It's so useful precisely because it is the language of logic and absolutes.
Great quote by Maxwell:"...the great tragedy of science - the slaying of beautiful hypothesis by an ugly fact."
Personally, I'm with Where Mathematics Come From: How the Embodied Mind Brings Mathematics into BeingGeorge Lakoff on mathematics: math is a language invented inside us, not a truth "out there". It's so useful precisely because it is the language of logic and absolutes.
Great quote by Maxwell:"...the great tragedy of science - the slaying of beautiful hypothesis by an ugly fact."
December 11, 2019
Breezy romp though the mathematical abstractions that helped make physics into the formidable, envy-inducing, philosophy-adducing Prima Donna of natural sciences. From Newton to Witten, the book attempts to show that the pursuit of mathematically "beautiful" patterns (i.e. numerical approximations and their "unreasonable effectiveness" at explaining physical observations) and their internal consistency ("symmetry") has helped physics achieve it's preeminence and predicts, nay advocates, this line of attack (a view strongly endorsed by Dirac, the subject of Farmelo's stellar previous book).
I was always stuck by the fact that around 1925, Heisenberg's (haphazard) use of matrix multiplication (known to math since the 1700's) for his version of quantum mechanics was considered a "radical" step, but it appears gauge and string theory have finally started paying the favor back, leading to the creation of what Farmelo calls "physical mathematics."
All in all a great source to brush up on jargon and inside references for cocktail party physics.
I was always stuck by the fact that around 1925, Heisenberg's (haphazard) use of matrix multiplication (known to math since the 1700's) for his version of quantum mechanics was considered a "radical" step, but it appears gauge and string theory have finally started paying the favor back, leading to the creation of what Farmelo calls "physical mathematics."
All in all a great source to brush up on jargon and inside references for cocktail party physics.
April 15, 2022
The story is really well knit and the narrative had a steady flow, with the Audible version having an excellent reader. I find this story to be accessible in part to non-mathematicians and non-engineers... in part.
As an engineer, I found the first half to be digestible with a lot of flashbacks from highschool and university, full of buzzwords and names, and the second part to be full of esoteric concepts that I could not even dream of grasp.
After starting listening to the second half, I've decided to go through the whole book in a single continuous run, as I was afraid if I sleep on it, I'll lose the narrative and chain of breakthroughs described that were building one on top of the another.
Only three stars as I found it a great listen but can't see myself picking it up again.
As an engineer, I found the first half to be digestible with a lot of flashbacks from highschool and university, full of buzzwords and names, and the second part to be full of esoteric concepts that I could not even dream of grasp.
After starting listening to the second half, I've decided to go through the whole book in a single continuous run, as I was afraid if I sleep on it, I'll lose the narrative and chain of breakthroughs described that were building one on top of the another.
Only three stars as I found it a great listen but can't see myself picking it up again.
October 18, 2021
This is a glorious ride through some excellent historical research and science. A real delight to get to know and see so many players and their trajectories. It's also a remarkable boon to see math and how it has been loathed and loved in physics. They are now surely inextricably interwoven but that did not come easily over the centuries. It was nearly mystical to see that math actually managed to reveal so many unexpected things revealing a symmetry in it all...the universe. Whoa...thats a weird freak out to grasp and be shown. Groovey cool fun...probably need to read again in a year or two to try and retain more of it. Bravo!
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