The thesis of María Wonenburger reappears, the pioneering Spanish mathematician who remained forgotten for decades

Image of the thesis of María Josefa Wonenburger Planells.Otto Rutwig Campoamor-Stursberg

María Josefa Wonanburger Planells (1927-2014), a native of Oleiros (La Coruña), was one of the most prominent Spanish figures in mathematical research.

However, as her influence and importance grew and she was widely recognized in the United States and Canada, the Spanish scientific community did not learn of her existence until near the end of her days.

Her thesis, lost for decades among piles of papers, has recently been recovered and underlines the relevance of her work.

Wonenburger had defended his thesis in 1957 at Yale University, where he had attended with a Fullbright scholarship, in its first edition.

The work, entitled

and directed by the prestigious algebraist Nathan Jacobson, had a substantial impact on the American mathematical community.

However, when he tried to validate it in Spain, he was unable to do so, since at that time the degrees obtained abroad were not recognized by the Ministry of Education.

The only solution to become a doctor in Spain was to present a new work at the end of 1959 at the Central University, under the title

.

Shortly after his defense, the thesis fell into oblivion in our country.

Upon completion of the Spanish doctorate, with the support of Jacobson and Israel Halperin, Wonenburger returned to North America, where he developed a research career of great relevance in various institutions.

In 2006, 23 years after her unnoticed return to Spain and already far from the academic world, the Galician mathematician was finally recognized in the country, thanks to an interview by María José Souto Salorio and Ana Dorotea Tarrío Tobar, professors at the University of Corunna.

However, despite Wonenburger's undoubted international prestige —even Spanish specialists knew and cited her work, but without knowing that she was a Galician woman— rumors appeared within the national scientific community that doubted the very existence of her thesis.

Furthermore, although its defense and publication are now well established, the relevance of this memoir has been repeatedly stubbornly denied.

Until, in 2022, this writing was discovered by chance by the authors of the article, among old unclassified files.

In this unpublished file, Wonenburger deals with an important problem of the so-called Lie group theory, or representation theory.

Lie groups are an algebraic structure that allows us to describe the symmetries of a system and that generalizes the transformations of classical geometry, such as rotations.

These groups are originally defined from symmetries of differential equations, which makes their study difficult.

For this reason, it is interesting to look for other ways of describing them, based on matrices, which are much easier to handle.

This is what is known as a Lie group representation.

The mathematician María Wonenburger Planells, in an image taken in A Coruña in 2007.

At that time, that field of algebra was in full development.

The researchers observed that certain algebraic structures that appeared in different contexts —such as the so-called Jordan algebras, motivated by quantum mechanics, the Clifford algebras, or the so-called

proposed by Elie Cartan, in theoretical physics— showed similarities and relationships.

Wonanburger focused on the study of one of these algebraic structures: the so-called spinor representation of

.

In this way, he solved a difficult problem on structural properties—the determination of irreducible components—and extended the result to other cases.

These advances allowed him, in turn, to make an elegant description of certain types of geometric transformations of great importance, the so-called representations of the projective group of unitary similarities in the orthogonal group.

The report, divided into three chapters, impresses with the depth of its results and the clarity of its presentation, which highlights the characteristic conciseness of Wonanburger's scientific production.

Despite the length and complexity of the calculations, the author manages to synthesize them brilliantly, turning memory reading into a pleasant (although very demanding) and enriching experience.

The contents of the thesis were published in various articles in the

in 1960. Jean Dieudonné, at that time one of the most renowned specialists in group theory in Europe, was the reviewer of these texts and, as such, highlighted the difficulty of the problem posed and the brevity and precision of the solution.

The appearance of an original copy of the thesis has also made it possible to clarify a question that had been discussed for some time regarding its direction: Germán Ancochea Quevedo, then professor of Descriptive Geometry at the Central University, was its director exclusively, and not together with Tomás Rodríguez Bachiller, professor of Mathematical Analysis at the same university, as was thought.

This thesis constitutes a historical document that deserves to be made public.

Although several decades late, it contributes to mitigate the social and administrative injustice that was committed with the work of a brilliant and exemplary scientist.

The complete text can be consulted on the website of the Department of Algebra, Geometry and Topology of the Complutense University of Madrid.

Otto Rutwig Campoamor-Stursberg

Ágata Timón García-Longoria

Coffee and Theorems

Edition and coordination:

You can follow