**Vera W de Spinadel** was the first woman to be awarded a mathematics Ph.D. by the University of Buenos Aires. She was an Argentine mathematician whose main contributions were to mathematics in architecture, art, and design. She introduced the "metallic means family" which generalises the Golden Ratio.

- Vera attended both primary and secondary school in Buenos Aires before entering the Faculty of Exact and Natural Sciences of the University of Buenos Aires in 1947.
- When Vera began her studies of mathematics at the University of Buenos Aires, Julio Rey Pastor was head of mathematics and Alberto González Domínguez (1904-1982) was a full professor.
- Vera was taught by González Domínguez who had strong links to a broad range of leading mathematicians throughout the world.
- Vera's mathematical interests were broad and she studied applications of mathematics to architecture, economics and engineering.
- In July 1952 Vera graduated with the degree of Bachelor of Physical-Mathematical Sciences.
- After the award of her Bachelor's degree, Vera was appointed as a Special Mathematics Teaching Assistant in the Faculty of Economic Sciences at the University of Buenos Aires.
- Two people now played a large part in her life, Erico Spinadel (1929-2020) and Emilio Oscar Roxin.
- Erico Spinadel (1929-2020) was an Austrian, born in Vienna on 6 May 1929.
- He then entered the University of Buenos Aires and was in the same classes as Vera for some of the mathematics courses he took as part of his engineering degree.
- Both Vera and Erico graduated in 1952 and Erico then worked from 1952 to 1955 for a firm that manufactured centrifugal and deep well pumps.
- Vera Spinadel attended a course on Nuclear Reactors at the Comisión Nacional de Energía Atómica in San Carlos de Bariloche in 1955 and for the following few years undertook research on nuclear reactors advised by Fidel Alsina Fuertes.
- The Argentine Atomic Energy Commission was planning for the start of construction of the RA-1 reactor, the first reactor to start up in all of Latin America and the southern hemisphere, and, in 1956, Spinadel worked on the calculation of the critical mass of the RA-1 Reactor.
- Beginning in 1956 Spinadel participated in a seminar on Non-Linear Differential Equations, directed by Emilio Roxin.
- In May 1958 Spinadel submitted her thesis Teoría de las Zonas Alcanzables en Sistemas Bidimensionales Ⓣ(Theory of reachable areas in two-dimensional systems) and was awarded the degree of Ph.D. in September of that year.
- Several references give Spinadel's thesis advisor as Emilio Roxin but this seems to be an error.
- In her thesis Spinadel does not acknowledge help from any thesis advisor but she does reference her joint paper with Emilio Roxin, namely Sobre un Problema de Sistemas de Ecuaciones Diferenciales Lineales Ⓣ(On a problem of systems of linear differential equations), as "to appear".
- Emilio Roxin submitted his thesis Puntos y zonas alcanzables en sistemas autónomos perturbados en forma arbitraria Ⓣ(Reachable points and areas in arbitrarily perturbed autonomous systems) to the University of Buenos Aires in April 1958, one month before Spinadel submitted her thesis.
- In it he expresses his thanks to Vera Spinadel and to Alberto González Domínguez and also references his joint paper with Spinadel as "to appear".
- Spinadel discussed the content of these new courses with her students and realised that since there was only a very basic mathematical content, students were exposed to no in-depth mathematical studies.
- Spinadel began publishing work on "Metallic Numbers" in 1997.
- Spinadel was an organiser of the First International Conference on Mathematics and Design held in 1995 and of the Second International Conference on Mathematics and Design held in San Sebastian, Spain in June 1998.
- Spinadel attended the Congress having been invited to organise the Study Group on Art and Mathematics Education.
- In April 2005, Spinadel founded the Mathematics and Design Laboratory of the University of Buenos Aires.
- In 2010 Spinadel retired and, in September of that year, was made Professor Emeritus in the Faculty of Architecture, Design and Urbanism.
- In 2018 the Vera W de Spinadel Award was set up.
- It invites students from any part of the world to discover and interpret new applications to the design of the proportions of Spinadel's Family of Metallic Numbers.

Born 22 August 1929, Buenos Aires, Argentina. Died 26 January 2017, Buenos Aires, Argentina.

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Origin Argentina, Women

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