**José Sebastião e Silva** was a Portuguese mathematician who worked in analytic functionals and the theory of distributions.

- He then entered the Faculty of Sciences in Lisbon where he studied Mathematical Sciences graduating in 1937.
- Being unable to continue to undertake research at this stage, Silva had to wait until 1940 before he received a grant from the Instituto de Alta Cultura to support his work.
- He published his first paper in Portugaliae Mathematica in 1940, this being On the numerical resolution of algebraic equations (Portuguese).
- In the following year he published Problems concerning rational functions of the roots of an algebraic equation (Portuguese) in the same journal.
- These two papers were major works, the first being around 30 pages long and the second being 15 pages.
- Max Zorn reviewed this second article.
- The coefficients of a normalized factor belong to a field generated by the symmetric functions of ppp of the nnn roots.
- In favorable cases, this field is generated by the sum or the product of these ppp roots.
- Determine the equation whose roots are all sums of ppp roots; if there is a factor in the field, then this equation has a root in the field.
- Assuming that it is possible to find all roots of an equation in a field, the preceding section furnishes a method of finding the coefficients of the factor, if it exists.
- Silva continued publish papers with two further papers appearing in Portugaliae Mathematica in 1941, namely Sur l'axiomatique des espaces de Hausdorff Ⓣ(On the axioms of Hausdorff spaces) in which he characterized Hausdorff spaces with the operations of frontier, orle and border, and Sur une méthode d'approximation semblable à celle de Gräffe Ⓣ(On a method of approximation similar to that of Graffe).
- A further research paper in 1942 was Les ensembles fermés et le problème de Wiener Ⓣ(Closed sets and the Wiener problem) in which he considered a problem on abstract spaces proposed by Wiener and described in Fréchet's book Les espaces abstraits Ⓣ(Abstract spaces) (1928).
- Silva reproved Wiener's results and proved a number of new related results.
- But Silva was not only publishing research articles, he was also publishing articles on mathematical education during these years such as Mathematical logic and education (in three parts all published in 1941), On the way to establish Taylor's formula (1942), The theory of the logarithms in school education (1942), and Reason?
- In 1942 the Instituto de Alta Cultura awarded Silva a grant which allowed him to go to Rome to further his research career.
- There he learnt from Enriques, Castelnuovo, Severi and Fantappie.
- Silva began working on a doctoral thesis in logic entitled Towards a general theory of homomorphisms.
- Enriques thought that the proposed thesis would not be understood at that time, and thus Silva produced a second thesis in functional analysis Analytic functions and functional analysis.
- was only published posthumously, forty years after being written, but is, in the recent opinion of scholars, a work of great originality, containing a wealth of ideas, which continue to be of interest today.
- He did, however, publish Sugli automorfismi di un sistema matematico qualunque in Italian in 1945.
- These conclusions not only systematize and clarify many things in all parts of mathematics, but can also be usefully applied to problems in functional analysis.
- The theorems which are announced here will shortly be demonstrated in another paper.
- He also published papers on functional analysis such as Sull'analisi funzionale lineare nel campo delle funzioni analitiche Ⓣ(Linear functional analysis in the field of analytic functions) (1946).
- The paper summarises the results Silva had obtained modifying the work of Fantappiè on the theory of analytic functionals of analytic functions.
- Silva's functional analysis thesis was submitted to the Faculty of Sciences in Lisbon in 1949 and Silva was awarded his doctorate; the thesis was published as a 130 page paper in Portugaliae Mathematica in 1950.
- A considerable portion of the paper is given over to the exposition of background material and known results.
- There is an eight-page summary in French.
- Silva was appointed as a professor in the Instituto Superior de Agronomia in 1951 and remained there for ten years before returning to the Faculty of Sciences in Lisbon to the chairs of Mechanics and Astronomy.
- For twenty years he was Director of the Centre for Mathematical Studies of Lisbon.
- In these papers Silva investigates analytic functionals, the theory of distributions, vector-valued distributions, ultradistributions, the operational calculus, and differential calculus in locally convex spaces.
- Silva died of cancer at the age of 57.
- He is considered by many to be the greatest Portuguese mathematician.
- Sebastiao e Silva was truly a great man.

Born 12 December 1914, Mértola, Alentejo, Portugal. Died 25 May 1972, Lisbon, Portugal.

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Astronomy, Origin Portugal

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