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.