Died: 21 January 1931 in Turin, Italy

Cesare Burali-Forti attended the University of Pisa, graduating in 1884. Immediately after graduating he taught in a school but he moved to Turin in 1887 where he was appointed to the Military Academy. Burali-Forti taught analytic projective geometry at the Military Academy where he continued to teach for the rest of his life.

A university teaching position would have been more to Burali-Forti's liking but in this he had difficulties. He was a great believer in vector methods but, at this time, these were not in favour. It is hard to believe from our present view of mathematics that vector methods would ever be less than welcomed. However, at this time many mathematicians opposed vector methods and unfortunately these views prevailed on the committee that considered Burali-Forti's submission for a doctorate. He was failed on these grounds, never tried again, and as a consequence was never able to teach in a university, although he did give informal lecture courses there.

In 1893-94 Burali-Forti gave an informal series of lectures on mathematical logic at the University of Turin. After the course the lectures were written up as a book and Burali-Forti presented a copy of the book to the Academy of Sciences of Turin in June 1894.

At the start of the 1894-95 academic session, Burali-Forti became Peano's assistant at the University of Turin. He was to hold this position until 1896.

The first International Congress of Mathematicians was held in Zurich from 9 to 11 August 1897. Burali-Forti attended the Congress and presented a paper The postulates for the geometry of Euclid and of Lobachevsky to the Geometry section of the Congress.

Burali-Forti is famed as the first discoverer of a set theory paradox in 1897 which was framed in technical terms but in essence reduces to a 'set of all sets' paradox. Cantor was to discover a similar paradox two years later.

As well as set theory and vector analysis, Burali-Forti also worked on linear transformations and their applications to differential geometry.

Not only was Burali-Forti a prolific writer, with over 200 publications, he was also very interested in how to teach mathematics. The "Mathesis" Italian Society of Mathematicians, aimed at school teachers of mathematics, was founded in 1895. Burali-Forti joined Mathesis in academic year 1897-98. He played a major role in the first congress of the Society which was held in Turin in September 1898.

Burali-Forti was a close friend of Peano's but his closest friend and mathematical collaborator was Roberto Marcolongo. Burali-Forti and Marcolongo were called the "vectorial binomial" by their friends. However this collaboration ended when they differed in their views on relativity. Burali-Forti never understood the theory of relativity and, together with Boggio, he wrote a book which claimed to prove that the theory of relativity was impossible.

Kennedy writes in [2]:-

1. H C Kennedy, Biography in Dictionary of Scientific Biography (New York 1970-1990). 
   http://www.encyclopedia.com/doc/1G2-2830900710.html

Books:

1. H C Kennedy, Peano : Life and Works of Giuseppe Peano (Dordrecht, 1980).

Articles:

1. R Feys, Peano et Burali-Forti, précurseurs de la logique combinatoire, Actes du XIème Congrès International de Philosophie, Bruxelles V (Louvain, 1953), 70-72.
2. P Freguglia, Cesare Burali-Forti and studies on geometric calculus (Italian), Italian mathematics between the two world wars (Bologna, 1987), 173-180.
3. R Marcolongo, Cesare Burali-Forti, Bollettino dell'Unione matematica italiana 10 (1931), 182-185.
4. G H Moore and A Garciadiego, Burali-Forti's paradox: a reappraisal of its origins, Historia Mathematica 8 (3) (1981), 319-350.

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