**Manuel Valdivia** was a Spanish mathematician who worked in topology and analysis.

- While studying at the college in his home town, Valdivia read Charles Hermite's proof that e, the base of natural logarithms, is transcendental.
- Since his passions were mathematics and poetry, it is not hard to understand that the law course went badly for Valdivia.
- Valdivia met Dario Maravall Casesnoves (1923-2016) who had been awarded a doctorate in mathematical sciences from the Complutense University of Madrid in 1956 and a doctorate in agronomist engineering from the School of Agronomist Engineers at the Polytechnic University of Madrid in 1958.
- Dario Maravall helped Valdivia continue his move towards pure mathematics by introducing him to Ricardo San Juan Llosá who had studied for his doctorate under Julio Rey Pastor.
- Ricardo San Juan became his thesis advisor and quickly realised that Valdivia had extraordinary talents for mathematics.
- Valdivia was awarded his doctorate in 1963 for his thesis Sucesiones de aplicaciones continuas, absolutamente continuas y sumables con diversos tipos de convergencia Ⓣ(Sequences of continuous functions, absolutely continuous and summable for various types of convergence).
- Following the award of his mathematics doctorate, Valdivia was awarded a fellowship by the "Juan March" Foundation for Research in Mathematics in 1963.
- In 1969 Valdivia was appointed to the Chair of Algebra and Infinitesimal Calculus at the Escuela Técnica Superior de Ingenieros Agrónomos of the Polytechnic University of Valencia.
- The pioneering aspect of Valdivia's mathematical research must also be emphasized, since when he began research in the early sixties mathematical research in Spain was practically nonexistent, at least according to international standards, which he immediately attained with multiple functional analysis results.
- Investigations by Valdivia have focused on a surprising variety of topics: analysis and topology, geometry of Banach spaces, Fréchet spaces and locally convex spaces, compact spaces, real analytic functions, Schwartz distributions, polynomials, multilinear forms, ...
- We highlight, also as an illustration, his interest in weak compactness in Banach spaces, the study of which led him to define the notion of compact space that has been fertile for many researchers and is now known as the compact space of Valdivia.
- Three problems posed by Alexander Grothendieck were solved by Valdivia in the papers Solution of a problem of Grothendieck (1979), On quasi-normable echelon spaces (1981) and A characterization of totally reflexive Fréchet spaces (1989).
- These words can be applied to Professor Valdivia.
- He has directed more than thirty doctoral theses and there are many articles with thank-you notes to Professor Valdivia.
- Valdivia was also awarded an honorary doctorate by Alicante University on 2 May 2000.
- In 1982 Valdivia published the 510-page monograph Topics in locally convex spaces.
- We have already mentioned some honorary degrees that Valdivia was awarded.
- This International Functional Analysis Meeting in Valencia, held to celebrate the 70th Birthday of Manuel Valdivia, was a Satellite Conference to the Third European Congress of Mathematics held in Barcelona.
- The great success of mathematical research and functional analysis in Spain would be inconceivable without the pioneering work of Manuel Valdivia.

Born 12 November 1928, Martos, Jaén, Spain. Died 29 April 2014, Valencia, Spain.

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Origin Spain

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