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Federigo Enriques's family moved from Livorno to Pisa where Federigo was educated. He entered the University of Pisa, also studying at the Scuola Normale in Pisa and he was awarded his degree in 1891. He was fortunate to have been taught by Betti in Pisa. In 1892 Enriques asked Castelnuovo, who was in Rome, for advice on which direction his research should take. He took Castelnuovo's advice and worked on algebraic surfaces, sometimes collaborating with Castelnuovo.
After his degree, Enriques continued to study at Pisa for a year before moving to Rome to work with Castelnuovo. Again he spent a year studying before moving again, this time to Turin where he worked with Corrado Segre. As well as Betti and Corrado Segre, Enriques had been taught by Dini, Bianchi and Volterra.
Enriques was appointed to the University of Bologna where he taught projective geometry and descriptive geometry. Appointed a professor at Bologna in 1896 he remained there until 1923 when he accepted the chair of higher geometry at the University of Rome.
While the Fascist regime was in power Enriques felt that he could not work with them and he retired from teaching from 1938 until 1944.
Enriques made important contributions to geometry and to the history and philosophy of mathematics. He produced a series of papers over a period of 20 years which, together with Castelnuovo, finally produced a classification of algebraic surfaces. His work on algebraic surfaces gained worldwide recognition when it was highlighted by H F Baker in his presidential address to the International Congress in Cambridge in 1912.
Another topic which Enriques worked on was differential geometry. In this area he also won fame with the joint award of the Bordin prize to him and Severi in 1907 for work on hyperelliptic surfaces.
The foundations of mathematics had always interested Enriques, and, at Klein's request, he wrote an article on the foundations of geometry. His interest also extended to psychology when he asked questions such as:
What leads a mathematician to make a conjecture?His book Problemi della scienza written in 1906, stressed the unifying aspect of scientific theories, the association of ideas and of scientific representation. He writes:
It is plainly seen that scientific questions include something essential, apart from the special way in which they are conceived in a particular epoch by the scholars who study such problems. ... In the formulation of concepts, we shall see not only economy of thought ... but also a somewhat determinate mental process ... .In addition to his research work, Enriques also wrote textbooks for schools. He was president of the Italian Philosophical Society from 1907 until 1913 and during that time he organised the fourth international congress of philosophy in Bologna in 1911.
Enriques was awarded an honorary degree by the University of St Andrews.
References (32 books/articles)