**Luís Antoni Santaló** was a Spanish mathematician who worked on on convex sets and wrote some important Spanish text-books.

- On 1 December 1905 Silvestre Santaló became a teacher at the Escolar de Girona, which today is CEIP Joan Bruguera in the Gran Via de Jaume.
- Let us note at this point that Luís Antonio Santaló also gives his name as Lluis Antoni Santaló, and he uses this version of his first and second names on a couple of papers.
- It was at the primary school that was part of the Escolar de Girona that Luís began his education.
- At the secondary school he was taught mathematics by Lorenzo González Calzada, and Luís always appreciated his excellent teaching.
- Santaló completed his studies in Madrid in 1934, having undertaken in parallel his part-time military service, and was awarded a Degree in Mathematics.
- After graduating, Santaló took up a position as a mathematics teacher at the Lope de Vega Institute, a middle school in Madrid.
- However, he was advised by Rey Pastor to continue his studies in Germany, and Rey Pastor helped arrange a scholarship which enabled Santaló to go to Hamburg to work with Wilhelm Blaschke.
- The Nazis under Hitler were in power in Germany by this time and Santaló felt very uncomfortable in the atmosphere that they were creating.
- At the end of 1934 Luis Santaló found his now famous proofs of the isoperimetric inequality in the plane and Blaschke himself found the fundamental kinematic formula and started a series of papers under the general title of "integral geometry".
- Santaló returned to Madrid and submitted his thesis Nuevas aplicaciones al concepto de medida cinemática en el plano y en el espacio Ⓣ(New applications of the concept of kinematic measurement in the plane and in space) to the University of Madrid and was awarded a doctorate in 1936.
- Santaló left Madrid and returned to his home town of Girona where he joined the Republican air force.
- By early 1939 the Republicans were defeated and Santaló together with many of his fellow soldiers and civilian refugees, escaped from Barcelona to France.
- Santaló was now one of around 500,000 Spanish refugees in France but they were not welcomed there, especially the Republican soldiers.
- Santaló was sent to a concentration camp at Argeles sur Mer but managed to escape to Colliure from where he wrote to Rey Pastor and Blaschke asking for help.
- Santaló knew that many of his fellow Republicans had, after fleeing to France, been shipped to South America.
- On arrival he was met by another Spanish mathematician, Manuel Balanzat (1912-1994), who had arrived in Argentina after a similar experience to Santaló, having fled to France at the end of the Spanish Civil War and from there sailing to Argentina.
- Julio Rey Pastor had arranged for Balanzat to meet Santaló when his ship arrived in Buenos Aires.
- This began a friendship between Santaló and Balanzat which lasted throughout their lives.
- Once in Argentina, Santaló went to the city of Rosario in the Province of Santa Fe, on the banks of the Rio Paraná where Rey Pastor had arranged for him to be appointed to the National University of the Littoral.
- Santaló taught courses in the Faculty of Mathematical, Physical-Chemical and Natural Sciences Applied to Industry which was at that time about to set up a Mathematical Institute.
- Santaló was appointed as Principal Investigator and Deputy Director of the Institute, positions he held for ten years from 1939 to 1949.
- Hence Levi was there for ten years after Santaló left but the two would continue to collaborate.
- At Chicago he met Saunders Mac Lane, André Weil, Hassler Whitney, Antoni Zygmund and other leading mathematicians.
- Back in Argentina, Santaló was appointed as a Professor of Higher Mathematics at the National University of La Plata in the city of La Plata, in the Province of Buenos Aires.
- La Plata is only about 50 km from Buenos Aires and Santaló was often at the University of Buenos Aires, supervising the theses of his first two doctoral students, Leticia Varela (who received a Ph.D. in 1952) and of Alberto Ayub (who received a Ph.D. in 1955).
- By 1957 Santaló already had almost 100 publications and, as one of the foremost mathematicians in Argentina, it is not surprising that in that year he became a full professor in the Faculty of Exact and Natural Sciences at the University of Buenos Aires.
- Santaló wrote several books, some in English and some in Spanish: Introduction to Integral Geometry (1953); Geometrias no Euclidianas Ⓣ(Non-Euclidean geometry) (1961); Geometria proyectiva Ⓣ(Projective geometry) (1966); Integral Geometry and Geometric Probability (1976); Vectores y tensores con sus aplicaciones Ⓣ(Vectors and tensors with their applications) (1977).
- Although the mathematical work of Santaló was basic research, some of his findings were of decisive importance for other applied disciplines, particularly in operative research, biology and stereology.
- A key aspect of Santaló's work was his profound contribution to social progress and his constant efforts to modernize the teaching of mathematics in Spanish-speaking countries.
- The University of Girona created the Santaló Chair on July 27, 2000.
- As to his character and interests outside mathematics, Santaló said he had a total ineptitude for manual tasks and little interest in so-called cultured music; liking folk songs and, above all, tangos.
- This is the beginning of Integral Geometry, to which Luis Santaló contributed so much.

Born 9 October 1911, Girona, Spain. Died 22 November 2001, Buenos Aires, Argentina.

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Origin Spain

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive