**Gomes Teixeira**'s parents were Manuel Gomes Teixeira Pinto, a merchant, and his wife Maria Magdalena Machado. Gomes had two brothers, Pedro who became a military engineer, and Sebastiao who became a trader in Sao Cosmado. He also had a sister Victoria Carolina. Gomes was baptised on 6 February in the church of his home town. His godparents were his cousin Dr Francisco Gomes de Carvalho and Maria Jose Teixeira.

Gomes began his education in his home town of São Cosmado, which is about 80 km east of Porto. This small town had around 600 inhabitants when Gomes was born there and his initial education, where he was taught reading and writing, was at a primary school which, in July 1924, was renamed "School EB 2/3 Gomes Teixeira." For his secondary education, however, he had to move to the larger town of Lamego, about 12 km north west of São Cosmado. There he lived in the house of his cousin Francisco Carvalho, who was a doctor in the town, and attended the Padre Roseira College. This college had been founded in 1859 and, at the time that Teixeira studied there, the director was the founder of the College, António Joaquim Lopes Roseira. As Teixeira's education progressed he was drawn in two different directions. His father was keen that he should study theology or law and wanted him to train in both these areas. The cousin, who he was staying with, saw that Teixeira was a talented scientist and suggested that he should study mathematics and physics at university. Many years later, talking about his time at school, he said [1]:-

His father asked young Teixeira which of these options he would prefer and, perhaps surprisingly, he said he was happy to follow either the theology or the science option. His father then told him to let luck decide and, after tossing a coin, luck chose the science option. It turned out to be a lucky toss of the coin but, as we see from the quote above, at this stage Teixeira was more attracted to physics than to mathematics.The subject that most attracted my attention was Physics, since it explained phenomena I saw every day. I had no affection or aversion to mathematics, I studied it, and well, just to do my schoolwork.

There was a problem, however, since the College in Lamego did not train their pupils for the examinations which would give university entry. He therefore went, in 1868, to Coimbra where he studied at the S Bento College preparing to take the examinations. In 1869 Teixeira enrolled in the Mathematics Faculty of the University of Coimbra and he lived in the house of Filipe Quental (1824-1892). Quantal, after studying mathematics and philosophy, had gone on to study medicine and was a professor in the medical school at Coimbra. Things did not go well at first for Teixeira, mainly because his health was poor. After attending the first few mathematics lectures, he returned to Sao Cosmado with the idea that he should change to a different faculty and study a different topic. However, after returning to the university, Teixeira was taught by Tôrres Coelho who strongly influenced him to become a mathematician. He explained in an interview later in his life how Coelho encouraged him (see [1]):-

In his first year of study, 1869-70, Teixeira took courses on Higher Algebra, Inorganic Chemistry and Technical Drawing. He won a prize for his performance in algebra. In his second year of study, 1870-71, he took the course on Differential and Integral Calculus, for which he was awarded a prize, and courses on Organic Chemistry, Analytic Chemistry and Physics. His performance had been outstanding and in 1871, while still an undergraduate, he wrote... I went to the University of Coimbra, with the plan that, if I could succeed in the mathematics course, then I would proceed to follow military engineering. One of my teachers, Dr Torres Coelho, after encouraging me twice to his lectures, went to tell Dr Filipe Quental, in whose house I was living, that he considered me to be the best student on the course. Knowing this, I felt stimulated. This fact has decided on my final predilections. Since then I have devoted myself exclusively to mathematics ....

*Desenvolvimento das funçoes em fracçao continua*Ⓣ which showed how to develop functions as continued fractions and applied these techniques to approximate roots of equations using rapidly converging series. One of Teixeira's lecturers at the University of Coimbra was Daniel Augusto da Silva (16 May 1814 - 6 October 1878). He had been a naval officer before becoming a lecturer at Coimbra and had been elected a full member of the Royal Academy of Sciences of Lisbon in 1859. He was impressed with Teixeira's paper and encouraged him to submit some of his work to the Royal Academy of Sciences and, in 1872, da Silva presented Teixeira's paper

*Aplicaçao das fracçoes continuas à determinaçao das raizes das equaçoes*Ⓣ to the Royal Academy of Sciences of Lisbon and it was published in volume 4 (1872-73) of their

*Journal*.

In 1871-72 he took courses on Rational Mechanics, Descriptive Geometry and Physics. In his fourth year, 1872-73, he studied Practical Astronomy, Geodesy and Botany. In his final year, 1873-74, he studied Celestial Mechanics, Mathematical Physics and Mineralogy. After graduating with his first degree on 21 July 1874 with the highest possible grade, Teixeira continued to undertake research at Coimbra and on 8 January 1875 submitted his thesis *Importância da observaçao do transito de Venus pelo disco do sol para a determinaçao da paralaxe solar. Apreciaçao dos diversos methodos de observaçao* Ⓣ. On 19 June he submitted his thesis *Nota sobre o numero das funçoes arbitrarias que entram no integral de uma equaçao ás derivadas parciaes* Ⓣ. On 30 June 1875 he defended his inaugural thesis *Integraçao das equaçoes à derivadas parciais de segunda ordem* Ⓣ and his second thesis* Theses de Mathematicas puras e applicadas* Ⓣ. Just over two weeks later, on 18 July, he graduated as a "Doctor of Mathematics" with the highest possible grade.

At the age of 25, in 1876, Teixeira was appointed as a Substitute Lecturer at the University of Coimbra. In the same year he was elected as a corresponding member of the Royal Academy of Sciences of Lisbon. At this time his work became better known internationally when he published *Sobre o emprego dos eixos coordenados obliquos na Mecanica analytica* Ⓣ (1876). Among the papers he published in the following few years we mention several in French, namely *Sur la décomposition des fractions rationnels* Ⓣ (1877), *Sur le nombre des fonctions arbitraires des intégrales des équations aux dérivées partielles* Ⓣ (1878), *Sur les dérivées d'ordre quelconque* Ⓣ (1880) and *Sur les principes du calcul infinitésimal* Ⓣ (1880).

In 1877 Teixeira founded the journal *Jornal de Ciências matemáticas e astronómicas* which was published by Coimbra University Press. This journal played an important role in encouraging research in mathematics and astronomy in Portugal and it was published for 28 years. After that it was integrated into the journal *Anais Scientificos da Academia Politécnica do Porto.* In the second volume of this journal, which appeared in 1880, Teixeira published a paper on the integration of second order linear partial differential equations and an obituary of Giusto Bellavitis.

A rather strange career move happened in 1878. Teixeira was named as third astronomer at the Astronomical Observatory of Lisbon in that year. Although this does not seem particularly strange, in fact he only remained in that position for four months and after that time he returned to the University of Coimbra. As well as his mathematical interests, Teixeira was involved in politics and in 1879 he joined the Regenerator Party and was elected to the Parliament. The Regenerator Party was a conservative, right wing party which had been formed in 1851 and was one of the two major political parties that held power in Portugal during the second half of the 19th century. At the time that Teixeira was elected, the leader of the party was Fontes Pereira de Melo who was Prime Minister of Portugal from January 1878 to May 1879 and again from November 1881 to February 1886. In addition to his academic duties, Teixeira participated in parliamentary sessions and on 19 May 1883 he became a member of a parliamentary committee:-

Although Teixeira does not seem to have played a major role in the Regenerator Party, it is clear from a number of letters that he received that he was very well respected by the other members.... whose powers were extended to inquire into the negotiations of the public administration in the overseas provinces.

In November 1879, Teixeira took charge of the teaching of mathematical analysis at Coimbra and, in February of the following year, he was named as Professor.

In 1881, Teixeira married Ana Arminda Cardoso who was 17 years old. Ana, the only daughter of a trader, had been born in Porto. Gomes and Ana Teixeira had a son who was stillborn, and three daughters. In 1883, for family reasons, Teixeira moved to Porto where he was appointed to the Polytechnic Academy. In Porto, the Teixeira family lived in Rua de Costa Cabral in the house where Ana's parents lived. At the Polytechnic Academy, Teixeira occupied the chair of differential and integral calculus. In 1886 he was named as Director of the Polytechnic Academy, a position he held until 1911. Although the family lived in Rua de Costa Cabral for most of the year, they owned a second house in Rua do Godinho in the centre of the town of Matosinhos, only a short distance north of Porto. The family spent holidays in this second home in Matosinhos.

In 1892 the Spanish Royal Academy of Sciences proposed a prize problem requiring:-

The problem was posed again in 1895 and, in 1899 Teixeira was awarded the prize for his entry which was published asAn orderly list of all the curves of every kind to which definite names have been assigned, accompanying each with a succinct exposition of its form, equations and general properties, and with a statement of the books in which, or the authors by whom, it was first made known.

*Tratado de las Curvas Especiales Notables*Ⓣ in 1905. For an extract from a review of this work by Charles H Sisam, see THIS LINK.

When Teixeira moved to Porto, the city had no university. The Polytechnic Academy, which had been founded in 1837, was one of a number of institutions which trained students. Others included the Nautical Class (established 1762), the Drawing Class (established 1779 and becoming the Porto School of Fine Arts in 1881), the Royal Academy of Maritime and Trade Affairs (established 1803), and the Royal School of Surgery (established 1825). Up to 1910, Portugal was a constitutional monarchy but, following the 5 October 1910 revolution, the Portuguese Republic was established. Soon after that, on 22 March 1911, the University of Porto was founded which incorporated some of the earlier educational institutions. Initially, the university had two faculties, Science and Medicine. Teixeira was appointed as the first president of the University of Porto and served in that role from 1911 to 1917. After his term as president ended, he was made honorary president. During these years as President and honorary President, he continued to teach mathematics in the Chair of Differential and Integral Calculus.

Teixeira had an amazing publication record and Henrique de Vilhena in [4] lists nearly 300 publications. As well as numerous papers, he also wrote books in Portuguese, Spanish and French. We give a selection of extracts from reviews of these books at THIS LINK.

To show the high regard for these works, we give a few sentences here from these reviews. James Pierpont reviewing Teixeira's Portuguese three volumes work *Course of Infinitesimal Analysis *(1892-96) writes [13]:-

[The anonymous reviewer [4] writes:-Teixeira], the distinguished director of the Academia Polytechnica at Porto, has been uniformly successful in the difficult task of selecting from the immense material available. The manner of presentation leaves nothing to be desired. The style is lucid and elegant, and the whole work bears in a refreshing manner the imprint of an original mind.

Raymond C Archibald, reviewing another of Teixeira's books, writes [8]:-Dr Teixeira has laid under tribute practically the whole of available mathematical literature. Vast as is his display of erudition, he has marshalled, modernised, and presented his material with great skill.

After he retired from teaching at the University of Porto, Teixeira embarked on his last major work, namely a history of mathematics in Portugal. This work,We heartily recommend Professor Gomes Teixeira's book for every mathematical library, as no other publication of the kind can take its place. The little book is characterized by marked individuality.

*História das matemáticas em Portugal*Ⓣ, only appeared in 1934, the year after he died. The book begins as follows:-

For an extract from this book, in which Teixeira writes about his teacher Daniel da Silva, see THIS LINK.The object of this book is the history of the culture of Mathematics in Portugal from the foundation of the Kingdom until the middle of the nineteenth century and the relations of this culture with the political evolution of the country. In order to appreciate the state of the studies of that history at the time this book appears, we briefly mention and analyse the works previously published on this subject; and in order to place the special subject which is the subject of this book within the framework of the general history of mathematical thought, we will give a detailed account of the evolution of this thought from antiquity to the emergence of the sciences in Portugal. These are the subjects that we are going to study in this Introduction. Pure mathematics is closely linked to Cosmology, which illuminates it, and Philosophy, which directs scientific thought; so to the history of those sciences we will join the history of Astronomy, a science that in Portugal played a great role in nautical studies, and, from time to time, some notions of the history of Physics and Philosophy.

Teixeira received many honours. He was awarded honorary doctorates by the University of Madrid and the University of Toulouse. He received the Binoux Prize for the History of Mathematics from the Academy of Sciences of Paris in 1917. There are streets and squares named for him in a number of towns: the Gomes Teixeira Square in Porto; the Rua Professor Doutor Francisco Gomes Teixeira, Porto; Rua Professor Doutor Francisco Gomes Teixeira in Carnaxide, Oeiras, Lisbon; and the Rua Francisco Gomes Teixeira in Setubal.

Following his death in 1933, Teixeira was buried in the cemetery of the Church of São Cosmado.

**Article by:** *J J O'Connor* and *E F Robertson*