Can mathematics explain everything in the universe? Are there mathematical laws that govern the entire universe? What is the relationship between mathematics and the universe? Is mathematics an invention or a discovery? Professor Yasushi Suto of the University of Tokyo is a leading cosmologist worldwide, studying the structure of the universe and the evolution of galaxies.
In "Mathematics of the Universe," the author shows readers the surprising fact that our universe is governed by mathematical laws.
The laws of the universe are expressed in astonishingly specific terms through mathematics.
Kepler's laws and Newton's law of universal gravitation, which accurately describe the motion of planets and objects, are expressed in mathematical equations.
Einstein's equation E=mc2 contains knowledge about all kinds of energy transformations, from the tiny world of atomic nuclei to the explosions that occur in the vastness of space.

"Mathematics of the Universe" introduces mathematics as a language that most concretely and accurately expresses the world we live in.
It explains when the laws of the universe began to be expressed in mathematics, why mathematics is the best language to describe our universe, and how scientists use mathematics to read and write the secrets of the universe.
However, this does not mean that the book deals with the specific meaning of complex mathematical equations or that it aims to help readers understand mathematical equations.
Just as you would appreciate a work of art, you should be able to appreciate the beauty of formulas and realize that anyone can express this world through formulas.

When appreciating art or music, everyone can enjoy it at their own level, even if the experiences of experts and amateurs are different.
That is the universal value of art.
Science, like art, can be understood and enjoyed in each person's own way.
The more you know about math or science, the more deeply you will be moved by it, but you don't necessarily have to study math or science in depth.
As I've said before, science, like art, should be enjoyed in a variety of ways.
--- p.30

The reason I'm introducing these seemingly complex formulas is to build up your immunity to them, like a kind of vaccine.
One thing you need to understand is that there are laws that govern this world, and while they may seem complex, they can be expressed in simple formulas.
Many physicists, including myself, consider this equation to be one of the most elegant in physics.
There is no need to mention Einstein's great achievements, such as discovering equations that explain the laws of the world.
Above all, Einstein's insight and efforts to penetrate the existence of laws and express them in concrete formulas are truly moving.
That's why we say that Einstein "discovered" the general theory of relativity rather than "invented" it.
--- p.49

If we calculate the influence of other planets on Mercury's perihelion movement using Newton's law, it would be 532" (about 0.147°), including Venus 276.38", Earth 91.41", and Neptune 0.04".
This means that only about 93 percent of actual observations can be explained by Newton's laws.
Whenever I lecture on general relativity, I always say that we must be cautious when it comes to claims that Newton's laws are wrong.
In fact, in most fields except astronomy, reliable results can be obtained using only Newton's laws without general relativity.
Newton's laws are among the most complete laws in physics.
Physics is the process of updating existing known laws of physics with better ones.
Although it is not yet clear whether we can rigorously describe this world with the laws of physics that can be described mathematically, Newton's laws and general relativity are examples of the progress of physics.
--- p.83

Mathematics is really important to properly express the laws of physics.
Without fields of mathematics like calculus and Riemannian geometry, it would be impossible to even imagine properly expressing the laws of physics as we know them.
If mathematics had nothing to do with the natural world, we would probably think it was just some brilliant invention by some genius mathematician.
So we can see that mathematics was not invented by someone, but rather discovered in nature.
When we think about this fact, we can see anew how great a role mathematics plays as a language for explaining the world.
--- p.98

In his book Brilliant Blunders, American astrophysicist Mario Livio (1945~) conducted a detailed literature review and concluded that Einstein's claim that the biggest mistake of his life was made originated from a fictional conversation created by Gamo.
Since Gamo was known for enjoying jokes, it is highly likely that this remark by Einstein was also Gamo's creation.
However, according to a scientific history paper based on the testimony of several physicists who said that Gamow and Einstein spoke directly, this may not have been Gamow's invention, but rather an actual statement made by Einstein.
Although there is still debate about what Einstein thought of the cosmological constant, it seems clear that he was not particularly fascinated by it.
Yet it is ironic that the cosmological constant plays such an important role in modern cosmology.
--- p.118

Just as expanding a gas without heating it lowers its temperature and density, the universe works on the same principle.
Conversely, if we imagined going back in time, the universe would contract instead of expand, so its temperature and density would increase.
If this trend continues, at some point the temperature and density of the universe could theoretically reach infinity.
This point is defined as the beginning of the universe, that is, the origin of time (t=0).
But in reality, it is likely that the currently known laws of physics will break down before the density reaches infinity.
In any case, it is clear that as we get closer to t=0, the universe will reach an extremely high temperature and high density state.
This very state is called the 'Big Bang', and it is not that some single point in the universe exploded.
--- p.128~129

Black holes are among the most intriguing celestial objects predicted by general relativity.
The possibility of black holes can be mathematically derived using Einstein's equations.
Surprisingly, however, the person who first mathematically derived the existence of black holes was not Einstein, but the German astronomer Karl Schwarzschild (1873-1916).
When World War I began in 1914, Schwarzschild volunteered for the German Army.
When the general theory of relativity was published in 1915, he was so fascinated by the theory while serving in the military in Russia that he sent a letter to Einstein informing him of the important discovery.
This discovery is the 'Schwarzschild Sea', which became the basis for black hole research.
--- p.196

Since the laws of physics were mathematically described, theoretical predictions and experimental verification with high accuracy became possible, and models with errors could be easily discarded.
If the laws of physics had to be expressed only in vague sentences or assertions rather than in mathematics, not only would quantitative verification be impossible, but it would also be difficult to accurately understand the movements of the natural world.
The universality of mathematically described laws tells us that physical laws are discovered, not invented.
It also means that science is exploring the fundamental truths of nature.

--- p.226