GIUSEPPE PEANO

Giuseppe Peano was born in 1858 in a hamlet of Cuneo. It is said that, as a boy, he had to walk many kilometers every day to go to school, as is still typical today in many parts of the world. He then continued his studies in Turin thanks to his maternal uncle who recognized his talent. He graduated in mathematics from the University of Turin in 1880, where he then taught for many years.
He worked on logic, language, and various branches of mathematics.

Peano is credited with introducing various logical symbols now commonly used: ∃ for the existential quantifier, ∪ for the union of two sets, and ∩ for the intersection. We should also mention his attempt to create a universal language, namely Latin sine flexione, that is, a simplified Latin without the typical endings of classical Latin.

Today, Peano's axioms for arithmetic are spoken of all over the world, because Peano was made one of the first attempts to arrive at an axiomatic definition of natural numbers. In a completely different field, the Peano curve is famous, which has properties clearly contrary to intuition: although it is a continuous curve, it is so "dense" that it passes through all the points of a square.

It should be added that Peano was appreciated by the international community during his lifetime. For example, after an international conference in Paris, Bertrand Russell was to say that “in all discussions Peano and his followers possessed a precision that the others did not have”.

In his honor, an asteroid today bears his name.

AUOQUAMEL

Abū Kāmil Shujāʿ ibn Aslam, also known as al-Ḥāsib al-Miṣrī ("The Egyptian Calculator") and in the West as Auoquamel, was an Egyptian mathematician who lived around the years 850-930, during the Islamic Golden Age. The Islamic Golden Age is a period of 4-5 centuries in which the Islamic world became an intellectual center for science (mathematics, study of nature, but also alchemy and astrology), medicine, and philosophy. Great importance was attributed to knowledge, and therefore to education and the translation into Arabic of earlier works. This period saw various scientific and engineering discoveries, including profound discoveries in optics, with the first attempts to build cameras; in surgery; in trigonometry; in physics, with the first attempts at flight.

Auoquamel contributed various studies and results, for example, general methods for solving linear equations; but the most significant fact is that Auoquamel was the first mathematician to systematically use irrational numbers. Irrational numbers (square roots, cube roots, ...) were accepted by him as solutions to equations and also as coefficients. The mathematical techniques described in his works were later taken up by Leonardo Pisano, known as Fibonacci, and thus contributed to the subsequent development of algebra in Europe.

JEAN-LOUIS KRIVINE

Jean-Louis Krivine is a French scholar, born in 1939, who has worked in mathematical logic, set theory, and theoretical computer science. He was a student at the École Normale Supérieure in Paris and then taught for many years at the University “Paris Cité” (also known as Paris VII). Among the people who studied under his supervision is Jean-Yves Girard.

In 1969, he wrote one of the first books on axiomatic set theory, which was widely disseminated. In the field of computing, he devised an abstract computing machine, known as the Krivine machine, which allows for the calculation of particular logical functions.

In 2007, together with Yves Legrandgérard, he published the article Valid Formulas, Games and Network Protocols, in which the UVA game was introduced, of which Luì (so named in honor of Krivine) is an evolution. The idea of using the UVA game in a educational context is by Emmanuel Beffara, who studied under the supervision of Vincent Danos, who in turn was supervised by Girard.

Among his students, some phrases he said in class have become popular, such as “Vous pouvez avoir une démonstration triviale qui fait 2 kilomètres de long” (you can have a trivial demonstration that is 2 km long). The meaning is that a long proof is not necessarily difficult to understand and learn, while conversely, a short proof can capture a brilliant and non-spontaneous idea.