Gomes Teixeira (1851-1933)

Francisco Gomes Teixeira, the mathematician, was born on 28 January 1851 in the village of S. Cosmado, parish of Armamar, in the district of Viseu.

He completed his primary education in his hometown and then went on to study at the Colégio do Padre Roseira, in Lamego. He enrolled at the Faculty of Mathematics of the University of Coimbra in October 1869. While he was still doing the course, Gomes Teixeira wrote his first work, which he published in the University’s press in 1871. He completed the course in 1847, obtaining the maximum grade of “Very Good by Unanimous Vote”, with 20 values. In 1875, he did a post-graduate examination where he presented his thesis and immediately afterwards his PhD, in which he also obtained the maximum grade.

In 1876, he became a corresponding member of the Academia Real das Ciências de Lisboa and substitute lector at the Faculty of Mathematics. In 1878, he was nominated third astronomer of the Astronomical Observatory of Lisbon, but he only held this position for approximately four months, returning to the University of Coimbra.

In 1879, he was elected deputy by the Regenerating Party, having participated in Parliamentary sessions in that year and again in 1883 and 1884. In November 1879, he was entrusted with the subject of mathematical analysis, becoming full professor in February 1880. In 1884, Gomes Teixeira asked to be transferred to the Academia Politécnica do Porto, where he directed the subject of Differential and integral calculus. Shortly afterwards he became director of this Academy, a position he held until 1911, when he was nominated rector of the recently created University of Oporto.

He was on good terms with some mathematicians of world renown at the time and published works in the scientific periodicals of several countries. He travelled frequently to other countries where he contacted other mathematicians and participated in congresses. He was a member of several national and international scientific societies and science academies.

He died in Oporto on 8 February 1933.

Scientific Activity

While still a student, he wrote a work titled Desenvolvimento das funções em fracção contínua, where he presented formulas to develop functions in continuous fractions, which he then transformed into ordinary fractions, and applied the continuous fractions to integral calculus and to the determination of the roots of equations, thus obtaining more convergent results than using the methods of Netwon (1643-1727) and Lagrange (1736-1813). This work called attention to his capabilities, not only within the University of Coimbra but also outside of it, as was the case of Daniel da Silva, who, after this publication, supported and encouraged Gomes Teixeira’s research work.

In 1872, Daniel da Silva made a presentation to the Academia das Ciências of Gomes Teixeira’s Aplicação das fracções contínuas à determinação das raízes das equações, where he uses fractions to determine to the roots of equations. His post-graduation thesis was titled Integração das equações às derivadas parciais de segunda ordem. In this thesis he anticipated the results which Andrew Forsyth (1858-1942) only managed to obtain later. This thesis also won him the recognition of Edouard Gousat (1858-1936), the great mathematical writer of treaties of the time. In order to occupy the position of substitute lector at the Faculty of Mathematics, he wrote up the thesis Sobre o emprego dos eixos coordenados oblíquos na mecânica analítica.

In 1877, he founded the Jornal de sciencias matemáticas e astronómicas, which was published over a period of 28 years, until it was integrated in the Anais Scientificos da Academia Politécnica do Porto. This scientific periodical played a very important role in the dissemination of the progress of mathematical and astronomical sciences and also contributed to the dissemination of the work of Portuguese researchers.

In 1887, already at the Academia Politécnica do Porto, he published the Curso de análise infinitesimal, Cálculo Diferencial (one volume), where he updated the teaching of mathematics in Portugal. In 1889, he published the first volume of the Curso de Análise infinitesimal, Cálculo integral, and the second volume in 1892. In this work he sums up the progress made by the analysis and introduces a new level of rigour in the presentation of mathematics.

In 1895, he submitted his work Sobre o desenvolvimento das funções em série to an open competition, in 1893, by the Royal Academy of Sciences of Madrid. The Academy awarded him a prize, albeit outside the competition, for having presented the text in Portuguese. In 1897, he competed once again for the prize of the Royal Academy of Sciences of Madrid with the work Tratado de las curvas especiales notables, tanto planas como alabeadas (Tratado das curvas especiais notáveis, tanto planas como torsas, having won the prize ex-aequo with Gino Loria (1862-1954). It is considered a classical work of great scientific and historic quality of international impact, having been re-edited in New York in 1971 and in Paris in 1995.

He continued to produce and publish regularly scientific texts in national and international scientific magazines. After a first phase dedicated to Analysis, he started concentrating increasingly more on Geometry. In the last years of his studies, he dedicated himself to the History of Mathematics in Portugal, having elaborated a work that became a reference for science scholars in Portugal, the História das Matemáticas em Portugal.


Due to the vast number of texts published (almost three hundred) we only present the references to some of the works that marked the beginning of the scientific career of Gomes Teixeira and the Obras de Matemática, which bring together in several volumes many of the texts previously published. For an extensive list of the texts published, those interested should consult the work of Henrique Vilhena, O Professor Doutor Francisco Gomes Teixeira.

Desenvolvimento das funções em fracções contínuas. Coimbra, Imprensa da Universidade, 1871.

“Aplicação  das fracções contínuas à determinação das raízes das equações”, Jornal de Ciências matemáticas, físicas e naturais., Lisboa, IV, 1872-73.

Integração das equações à derivadas parciais de 2ª ordem, Coimbra, Imprensa da Universidade, 1875.

Jornal de Ciências matemáticas e astronómicas, Coimbra, Imprensa da Universidade, 1877. Jornal fundado por Gomes Teixeira, publicado até 1905, dedicado inicialmente às Matemáticas superiores e às Matemáticas elementares, mas que a partir de certa a altura se dedicou exclusivamente às Matemáticas superiores.

Anais Científicos da Academia Politécnica do Porto, Coimbra, Imprensa da Universidade, 1905-1906. Substitui, na parte referente às matemáticas, o Jornal de Ciências matemáticas e astronómicas.

Obras sobre Matemática, Coimbra, Imprensa da Universidade, vol. I, 1904; vol. II, 1906; vol. III, 1906; vol. IV, 1908; vol. V, 1909; vol. VI, 1912; vol. VII, 1915.

Panegíricos e conferências, Coimbra, Imprensa da Universidade, 1925.

História das matemáticas em Portugal, Lisboa, Academia das Ciências de Lisboa, 1934.

Fernando Reis


GUIMARÃES, Rodolfo, Biografia de Francisco Gomes Teixeira, Lisboa, Imprensa Nacional, 1914.

VILHENA, Henrique de, O Professor Doutor Francisco Gomes Teixeira (Elogio, Notas, Notas de Biografia, Bibliografia, Documentos), Lisboa, 1935.


História das Matemáticas em Portugal
Matemático por acaso

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