In a letter to his father in 1839, Dostoyevsky wrote that mathematics was a strange science and that is was silly to concern oneself with it. Math is esoteric and secret, perfect and elegant, and – for many of – obscure and puzzling. But reality is fundamentally mathematical. Even the ancient Greeks were aware of this and knew that formulae and theorems were essential tools for understanding the world. “Chaos”, “algorithm”, “infinity”, “numbers”, and “probability” are evocative words that are used in many fields of knowledge and whisper something into our ears even when we care little for mathematics. The books in the series explain mathematics as a sort of alphabet of the world, employ an approach combining philosophy and humanism, and shed light on the role of mathematics in the history of thought. The series offers readers a fascinating adventure leading to a better understanding of the cultural value of mathematics and its impact on civilization.

One, two, three… As children we have all learned the sequence of numbers by heart, but do we really know what numbers are? Or where they come from? Maybe they are a gift from God, as a great mathematician once said. Or perhaps they are a human invention, inspired by innate qualities we share with other animal species. This book tells the story of an extraordinary idea that took shape thousands of years ago in the ancient civilizations of Babylon and Egypt, in China, in the Aztec and Mayan cultures, and then spread throughout the world. On the coasts of Calabria, followers of Pythagoras discovered “unsayable” (that is, irrational) numbers. In India a symbol was invented to represent nothing. Traders and merchants found meaning in negative numbers. And the fertile minds of mathematicians have even found a use for imaginary and transfinite numbers.

Umberto Bottazzini teaches History of Mathematics at the University of Milan and belongs to the editorial boards of the most important international journals dealing with the history of mathematics.

Oltre le colonne d'Ercole
I. Da dove vengono i numeri?
L'«intelligente Hans» e i «cavalli pensanti» di Elberfeld
Ratti, pulcini e altri animali
L'accumulatore numerico
I neonati sanno contare?
I neuroni del numero
II. Come si rappresentano i numeri?
Contare con le mani (e coi piedi)
La perfezione del sette (e del tre)
Tavolette di argilla e papiri
I numeri del tempo
III. L'incommensurabile
Pitagora tra storia e mito
Numeri figurati
«Logos», «alogos»
Terne pitagoriche
Problemi diofantei
IV. La perfezione nei numeri
Problemi classici
Numeri amici
Numeri primi e numeri perfetti
V. Le figure degli Indi
L'«Epistola» di Fredegiso di Tours
Un simbolo per il nulla
La Casa della saggezza
I numeri di Fibonacci
Abacisti e mercanti
L'immagine della Creazione
Un'idea semplice e ingegnosa
VI. Numeri immaginari
La «grande arte»
Numeri «falsi» e quantità «sofistiche»
«Più di meno» e «meno di meno»
Anfibi tra l'Essere e il nulla
Più grandi dell'infinito
La formula più bella
I numeri nel piano
Coppie e quaternioni
Numeri ipercomplessi
VII. Numeri reali
L'uomo aritmetizza
Numeri algebrici e trascendenti
Numeri transfiniti
Insiemi transfiniti e ipotesi del continuo
Numeri iperreali e numeri surreali
VIII. Cosa sono i numeri?
Estensioni di concetti
Creazioni del pensiero
Tra Hilbert e Brouwer
Per concludere... o ricominciare
Indice dei nomi
series "Intersezioni"
"Raccontare la matematica"
pp. 208, 978-88-15-25414-6
publication year 2015