GABRIELE LOLLI

Mathematics as Narration

Poetry says more with fewer words. So does mathematics. Dating back to early cosmological myths, humanity has always attempted to narrate its destiny. Events are given meaning by stories, without which they would be lifeless. The same is true for mathematics, which needs a story to narrate its meaning. In the “programmes” pursued by great mathematicians – such as Hilbert, Klein and Langlands – the key concepts are characters in a fable combining novel ideas in familiar patterns, according to techniques stemming from ancient Greek rhetoric and poetry. Any mathematical proof thus turns into an account of a voyage to an unfamiliar land, a quest for new roads and connections. Whether these journeys be brief, lengthy or rough, mathematicians always prefer roads that lead them to mountaintops and provide spacious views.

Gabriele Lolli formerly taught Mathematical Logic at the University of Turin and Philosophy of Mathematics at the Scuola Normale Superiore in Pisa.

Premessa
I. Grandi racconti
Il mulino di Amleto
L'universo degli insiemi
Gruppi e geometrie
Hilbert e l'infinito
Il programma di Langlands
II. Il senso delle dimostrazioni
Una sporta di dimostrazioni
Metafore e immagini
Il senso delle storie
Dimostrazioni e storie
III. Tre indizi
Etimologie
Dimostrazioni dinamiche
La natura degli enti matematici
IV. La tradizione
Platone e Aristotele
Eredi moderni
V. Il linguaggio matematico
Simboli e significati
Le regole del gioco di formule
VI. Le origini dell'argomentazione
Da Omero alla retorica
Il chiasmo
VII. Poesia e logica in Euclide
Gli Elementi
I Dati
Conclusioni
Appendice: Notazioni e terminologia
Riferimenti bibliografici
Indice dei nomi
series "Intersezioni"
"Raccontare la matematica"
pp. 224, 978-88-15-27422-9
publication year 2018