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Mathematics, seen in the right light, possesses not only truth but also supreme beauty, a cold and austere beauty, like that of sculpture. (Bertrand Russell, from Mysticism and Logic).
Until the moment I started reading this book, I could hardly fully understand this statement. Despite loving scientific disciplines, it was not at all easy to see the world of mathematics as something "beautiful", a form of art just like sculpture, music, and painting. From a distance, at least, that world of numbers, functions, formulas, theorems seems utterly devoid of any delight, often a matter unto itself.
The theory of numbers allowed me to see mathematics from a completely new and fascinating perspective: the captivating element of this branch of mathematics is that most of the issues (many still unresolved) appear really simple. Anyone who can count is able to understand them.
The other side of the coin, alas, is the extreme difficulty in solving these truly elementary problems that have driven generations of mathematicians crazy. An example? Almost everyone knows what a prime number is, and many could list a few in a short time, but the criterion (seemingly random) by which Nature has placed these fundamental atoms is still a mystery, the greatest unresolved one for now (and in my opinion forever).
Simon Singh, a world-renowned university professor, tells us the story that led to the proof of Fermat's Last Theorem, a story that lasted 358 years, beginning with Pierre de Fermat's mocking note in the margin (he stated the conjecture but added that he didn't have enough space to prove it) and ending in 1995 with Andrew Wiles: it must be said that he put the last piece of a journey that saw the greatest mathematicians go mad and get closer and closer to what for a long time has been the mathematical enigma par excellence.
To give credit to all these great minds, the author has the excellent idea of retracing the history of mathematics with a captivating story, full of curiosities but above all very clear and simple, so that anyone who knows at least the basics of arithmetic can appreciate the work and be fascinated and amused by it.
Starting with Pythagoras and the great Greek mathematicians, continuing with Euler, Gauss, Descartes, Riemann, Gödel, Turing, and concluding with Wiles, we are introduced to the geniuses and what they experienced and suffered in pursuing the discipline, along with numerous anecdotes.
Did you know that Pythagoras, faithful to his idea that everything could be expressed in terms of whole numbers, drowned one of his students who showed an interest in irrational numbers? Or that Gauss, in elementary school, formulated a general equation to quickly calculate the sum of numbers from 1 to N, thus rendering the professor's punishment futile?
Andrew Wiles finally reached the finish line, using mathematical concepts and structures developed in the twentieth century so complex that we can certainly affirm that Pierre De Fermat issued a challenge he was not at all capable of addressing.
Mathematics, as the pages turn, becomes more and more our friend, and even though very few individuals in the world could easily handle modular forms and elliptic equations, sympathy for these minds grows exponentially. From bookworms, they become artists in their own right.
Is or is not mathematics the only discipline that is completely independent of experience, a wonder that manifests itself solely in the mind?
This is precisely the beauty of mathematics, its perfection as an ideal reality, is unattainable: we can be sure that Wiles' proof can never be falsified; it will remain solid and carved until the end of time.
Devouring the book to the last page, the conclusion is one: mathematicians belong to another species, bizarre, misunderstood, brilliant, ambitious to achieve the prize of eternity: the stability created by mathematical proof leads to authentic immortality. Perhaps thousands of years from now, the texts of Shakespeare or Manzoni, or Dante's Comedy, will be forgotten, but the achievements of mathematics will forever be the treasure of humanity.
God created the integers, all else is the work of man. (Kronecker)
(if you find the book in English, I highly recommend it, some concepts are made lighter and more intuitive compared to Italian grammar)
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