**Joaquim Gomes de Souza** was the first Brazilian to be awarded a doctorate in mathematics. He had great difficulty in getting his memoirs published since leading mathematicians of the time failed to report on them.

- He was the grandson of José Antônio Gomes de Souza.
- He had a military career becoming a lieutenant colonel and was also an alderman of the Chamber of São Luís.
- It was an important city partly because of the Catholic Seminary there, which was built at the time of the Portuguese colonisation, and also for the Faculty of Law of Olinda which is now part of the Federal University of Pernambuco.
- This College dates back to 1792, and was modelled on the Military Academy in Lisbon.
- It became the Royal Military Academy in 1811, then the Imperial Military Academy in 1822 when Brazil gained its independence.
- It became the Academia Militar da Corte in 1832 and, in 1840, it was renamed the Escola Militar.
- At the Escola Militar, Souzinha excelled academically in the engineering course, showing outstanding abilities in mathematics.
- In 1845 he took examinations in Latin and Philosophy and gained entry to the Faculty of Medicine in Rio de Janeiro.
- The Faculty of Medicine had been founded in 1808 and today is part of the Federal University of Rio de Janeiro.
- His passion for mathematics was such that after two years studying medicine he decided to give up his medical studies and concentrate on mathematics.
- Although he had never registered for a degree in Mathematical and Physical Sciences at the Escola Militar, the request he made in 1847 to be allowed to take the examinations for that course was granted.
- He took a series of examinations and was awarded a bachelor's degree in Mathematical and Physical Sciences on 10 June 1848.
- Souzinha believed that he had taken his studies of mathematics to the level of a doctorate since he had been undertaking research for several years so he now requested the Escola Militar to be allowed to undertake a public defence of a doctoral thesis.
- This was allowed and, on 14 October 1848, he defended his 55-page thesis Dissertação Sobre o Modo de Indagar Novos Astros Sem o Auxílio das Observações Diretas Ⓣ(Dissertation on how to Investigate new stars without the aid of direct observations).
- Souzinha's thesis had been motivated by the work of John Couch Adams and Urbain Le Verrier who had used the way that Uranus deviated from its expected orbit to predict the position of a previously unknown planet to account for the deviations.
- Their predictions were made known in September 1845 and June 1846 respectively and led to the discovery of Neptune on 23 September 1846 by Galle at the Berlin Observatory.
- To what degree of approximation should we bring our formulas so that the mistake disappears?
- We will deal first with the movement of the centre of gravity of the stars, then with their figures and with their movement around the same centre.
- It is also important for it is the first mathematics doctorate to be awarded by Brazil and it marks the beginning of mathematical research in Brazil.
- He continued to undertake research in mathematics and he published a paper Resolution of numerical equations in number 5 of Guanabara, a monthly artistic, scientific and literary magazine.
- He described existing methods, in particular those given by Euler, Laplace, Liouville, Fourier and Jacobi.
- It is clear that these three papers constitute around half of what Souzinha intended to publish in this series.
- Souzinha believed that he had produced some important mathematical results but with no colleagues undertaking mathematical research in Brazil, he was very limited both in undertaking research and in making his results known.
- His request was granted and he was asked to undertake two missions, first to study the penitentiary system of European countries with the aim of improving the system in use in the Rio de Janeiro prison, the Casa de Correção da Corte, and secondly to obtain information about European astronomical observatories.
- If the first of these missions seems a strange one to give Souzinha in fact it was not since he was the secretary of the Casa de Correção da Corte.
- He spent 1855 and 1856 partly in London and partly in Paris at the Sorbonne where he attended courses.
- He presented papers to the French Academy of Sciences and enrolled at the Faculty of Medicine in Paris, obtaining the degree of Doctor of Medicine in 1856.
- A committee consisting of Liouville, Lamé and Bienaymé was set up by the French Academy of Sciences to report on the memoirs Souzinha had submitted to the Academy and later Cauchy was asked to join the committee.
- The anthology contains poems in seventeen languages, each poem in its original language, German, English, French, Italian, Portuguese, Spanish, Russian, Polish, Serbian, Bohemian, Hungarian, Dutch, Danish, Swedish, Modern Greek, Latin, and Ancient Greek.
- Why would anyone buy such a book consisting of poems most of which were in languages they could not understand?
- How many times has man truly fond of literary art felt, in moments of solitude, when their mind needs a diversion after very serious reflections, and a quiet occupation, the desire to have in hand a meeting of the most perfect literatures all nations possess, in order to let their thoughts wander and find feelings that correspond to the dispositions of their spirit?
- Back in Brazil, Souzinha was sworn in as Deputy on 19 May 1857 and made his first speech on 25 June 1857.
- Souzinha's own health was also deteriorating and, suffering from the lung disease hemoptysis, he had returned to Maranhao for health reasons in 1862.
- He wanted to continue his duties despite his health problems and returned to Rio de Janeiro taking up residence on the Santa Teresa hill.
- Hoping for good medical treatment in England, he made the trip in March 1864, but he died two months later.
- (3) On the determination of the constants, which, in the problems of mathematical physics, enter into the integrals of the partial differential equations, according to the initial state of the system.
- (4) Proof of some general theorems for the comparison of new transcendental functions.
- (6) Memoir on the determination of the unknown functions which enter under the sign of definite integration.
- His reasoning is this one - the speed of sound is proportional to the square root of the quotient of the elasticity and density of air, in the case where forces are not considered; now, in the case of the latter, he says, this relationship does not change; so the speed of sound is constant.
- But whence did he deduce the above law of the propagation of sound?
- Geometricians who have dealt with the theory of sound, in order to simplify the formulas, assume that all vibrations of air molecules are very small.
- Poisson was the only one who considered motion in the case of variable temperature, as it exists in nature, but he deals only with motion in a straight tube.
- Do you want to know the propagation of motion inside bodies?
- the figure of the planets which deviate significantly from a spherical shape?
- the law of variation of their densities, etc.
- When you see all these theories depending on this calculation and this calculation itself reduced to a single problem, there is something that pushes you, which pulls you along almost in spite of yourself.
- Souzinha was hailed as a genius by most Brazilians following his death.
- This paper is concerned with the relations between Gomes de Souza's mathematical works and the controversy about the legitimate use of divergent series in the nineteenth century.
- It brings a brief introduction of Gomes de Souza.
- Then, it succinctly describes the characteristics of the polemic about the use of divergent series.
- Finally, it reveals the critical considerations of these authors concerning Gomes de Souza's Works.

Born 15 February 1829, Itapecuru-Mirim, Maranhao, Brazil. Died 1 June 1864, London, England.

View full biography at MacTutor

Origin Brazil

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