## 1 + 1 = 2… Usually

### A Mathematics Lesson

1 + 1 = 2. Could anything possibly be simpler? This is the first equation we all learn at school, but also the first paradox of the mind. How much is a pear plus an apple? What is it equal to? In this whimsical overview – encompassing early humanity’s efforts to use fingers to count, ancient number systems, the logic of computer science, Cantor’s transfinite arithmetic, and Gödel's incompleteness theorems – John Barrow offers his readers an extraordinary mathematics lesson. He raises many questions and supplies many answers, without ever losing sight of the deceptive, unreasonable effectiveness of this basic equation. Is “1 + 1 = 2” a discovery or an invention? Seemingly simple models, such as arithmetic, are so rich and powerful that they reveal the structure of the universe. A structure that, ultimately, relies on “1 + 1 = 2”.

John Barrow, a major world expert of modern cosmological research, taught Mathematical Science at the University of Cambridge and headed its Millennium Mathematics Project. John Barrow's previous books include The Book of Nothing, The Constants of Nature, The Infinite Book, Cosmic Imagery, the bestselling 100 Essential Things You Didn't Know You Didn't Know, The Book of Universes, 100 Essential Things You Didn't Know You Didn't Know About Sport, and, most recently 100 Essential Things You Didn't Know You Didn't Know About Maths and the Arts.

World translation rights controlled by Il Mulino.

Prefazione
I. 1 + 1: è veramente così difficile?
II. Mani e piedi. All’origine del contare
III. Cambiando le basi: i bit e l’aritmetica binaria
IV. La definizione dei numeri
V. Sommando insiemi e altre cose
VI. 1 + 1 = 2. La dimostrazione di Whitehead e Russell
VII. L’aritmetica transfinita
VIII. L’incompletezza di Gödel
IX. Perché gli uno e i due sono così comuni
X. Che cos’è la matematica?