Are maths a language?

Mathematician, committed politician and influential member of the French intelligensia, Émile Borel alone embodied the ideal of the "Republic of Professors". From Dreyfusism to the Resistance, via the Popular Front and the early days of European construction, he conducted scientific research and civic struggle side by side, convinced that the same rational rigor governs science and politics. His work on measure and chance — notions whose mathematical depth far exceeds intuition — laid lasting foundations, from Lebesgue's theory to normal numbers. The latter, whose strangeness the writer Jorge Luis Borges seemed to have foreseen in his fiction, still open up unexpected horizons today, from ergodic theory to computer science.

Language and mathematics have a complex relationship that neither philosophy nor neuroscience has managed to establish. Some thus imagine that mathematics is a language among others. It is from this perspective that Leibniz worked on a universal language modeled on algebra which would allow, in addition to mutual understanding for all, to establish, through a "calculation", the truth of stated propositions. Neuroscience, for its part, teaches us that at the cerebral level, mathematics constitutes, for the brain, a distinct semantic system, independent of natural language and rooted in universal numerical and spatial intuitions. The question of the relationship between mathematics and language remains, in the age of artificial intelligence, completely open.