Mathematics is a body of language which expresses knowledge about a real or a hypothetical universe. Some equations are not mathematical theorems but physical laws such as energy - mass equation of relativity, energy - wave equation of quantum physics or the Maxwell equations of classical physics that are deduced by the experimental data rather than derivation from a set of axioms. Algebra, geometry, applied mathematics and analysis bind together in expressing the laws of physics and reality so well that one wonders if God is a mathematician. At the frontiers of theoretical physics such as, string theory, brane physics and supersymmetry, math and physics intertwine so strongly that one has to understand and express what those mathematical formulas say about the intricacies of laws of nature.
The title of the book is misleading, because I first thought that this book is a new kind in that explains what the mathematical equations of physics and cosmology tell us about reality or what the physical constants mean for the universe. It is disappointing in that the author discusses a brief history of laws of levers, Newton's laws, Fermat's last theorem, Euler's theorem, group theory, Fourier series, and theory of chaos and none of them go into any level of detail. There are many books that discuss the historical development and this book serves no real purpose in that regard. Despite this weakness, the chapters on Kepler's law that describes the planetary motion around sun, the chapters on quantum physics and relativity are interesting but still lacks depth.
In the early part of 20 century when principles of quantum physics were proposed, mathematics became the only guide. The entire world quantum physics was not comprehensible. It sounded absurd to talk about wave-particle duality, and the ability of photons to decide that it should behave like wave or particle is dependent on what experiment the observer chooses to perform. Paul Dirac's attempt to reconcile spin angular momentum of an electron with special relativity lead to far reaching consequences that predicted the existence of antiparticles and the existence of bosons and fermions. An empty space contains particles and their antiparticles that pop into existence and pop-out of existence. In quantum physics, particles are treated like quantum fields, which are like electric fields, that pervade all of spacetime and particles are their local manifestations. In other words, a particle may be a fluctuation in the quantum field that may be just temporary or long lasting. The fact that the two fermions cannot have the same quantum state, a consequence of Paul Dirac's equation, which makes an atom to have atomic orbitals that build electron around the nucleus to form various atoms that underlies all of chemistry. There is a very interesting discussion as how Dirac's equation revolutionized modern physics and chemistry.
There are many websites which discusses mathematical equations of physics elegantly, and I recommend NASA's website for educators.
The title of the book is misleading, because I first thought that this book is a new kind in that explains what the mathematical equations of physics and cosmology tell us about reality or what the physical constants mean for the universe. It is disappointing in that the author discusses a brief history of laws of levers, Newton's laws, Fermat's last theorem, Euler's theorem, group theory, Fourier series, and theory of chaos and none of them go into any level of detail. There are many books that discuss the historical development and this book serves no real purpose in that regard. Despite this weakness, the chapters on Kepler's law that describes the planetary motion around sun, the chapters on quantum physics and relativity are interesting but still lacks depth.
In the early part of 20 century when principles of quantum physics were proposed, mathematics became the only guide. The entire world quantum physics was not comprehensible. It sounded absurd to talk about wave-particle duality, and the ability of photons to decide that it should behave like wave or particle is dependent on what experiment the observer chooses to perform. Paul Dirac's attempt to reconcile spin angular momentum of an electron with special relativity lead to far reaching consequences that predicted the existence of antiparticles and the existence of bosons and fermions. An empty space contains particles and their antiparticles that pop into existence and pop-out of existence. In quantum physics, particles are treated like quantum fields, which are like electric fields, that pervade all of spacetime and particles are their local manifestations. In other words, a particle may be a fluctuation in the quantum field that may be just temporary or long lasting. The fact that the two fermions cannot have the same quantum state, a consequence of Paul Dirac's equation, which makes an atom to have atomic orbitals that build electron around the nucleus to form various atoms that underlies all of chemistry. There is a very interesting discussion as how Dirac's equation revolutionized modern physics and chemistry.
There are many websites which discusses mathematical equations of physics elegantly, and I recommend NASA's website for educators.
Reference: The Universe in Zero Words: The Story of Mathematics as Told through Equations by Dana Mackenzie
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