Manfredo do Carmo, a Brazilian math enthusiast

Professor Manfredo do Carmo
(photo credit: La Janela/APG IMPA)
Manfredo do Carmo is one of the most distinguished Brazilian mathematicians. He obtained his doctoral degree from University of California, Berkeley, under the supervision of S. S. Chern, in 1963. His books on Differential Geometry, originally written in Portuguese or English, have been translated into several languages including Spanish, German, Russian, Greek, and Chinese. At 86 years of age, he continues to make important contributions to Geometry, thus, confirming again and again the words of Blaine Lawson, written a quarter of century ago, in the preface of the book Differential Geometry – A symposium in honour of Manfredo do Carmo: "(…) his intellectual leadership and tireless devotion have brought into being in Brazil one of the finest and mostactive schools of Differential Geometry in the world." 

Do Carmo gave the following interview to Hilário Alencar, professor at the Federal University of Alagoas and member of the Brazilian Academy of Sciences: 

Alencar: The International Mathematical Union (IMU) is going to have one of its Congresses, held each four years, in Brazil. What do you think of that?

Do Carmo: I think it is a natural response to the extraordinary development of Mathematics in Brazil in the last six decades. If we ask when this started, we can probably date it from 1957 with the first Brazilian Colloquium of Mathematics. Before that, we had only a handful of people doing mathematical research in Brazil. A few years after that, in 1962, we had about fourteen doctoral students abroad, and in 1965, the Annals of Mathematics had published, at least, four papers from Brazilian mathematicians. After 1957, the Colloquia were held each two years, and had a strong influence on the way mathematics was looked upon in Brazil. Courses were offered for students from all over the country which now could look forward to be professional mathematicians. Along these six decades, we improved our classification in the IMU from I in 1957 to IV in 2005. The top classification is V, which is reserved for countries like France, Germany, USA, Russia, and a few others. So, as I said, the 2018 Meeting of IMU is a natural consequence of our progress in mathematical research.

Today, we have a visible mathematical community in Brazil. How did it come about?

In 1969, IMPA with the support of BNDES (a national bank for social development), inaugurated a Doctor´s Program whose goals were to spread mathematical research of high quality throughout Brazil and to stimulate the creation of an advanced mathematical literature in the country. Once started, the process accelerated rapidly. Doctor’s programs were created and amplified in the main universities of Brazil (S. Paulo, Brasilia, Recife, Rio, etc). Young doctors, formed in these programs, would come back to their original universities and would press for better conditions of work, namely, full-time positions and a strong association of university teaching andresearch.

What made you dedicate yourself completely to Mathematics?

A stay at IMPA, from the beginning of 1959 to the middle of 1960, invited by my childhood friend, Elon Lima. Elon had just received a Ph.D. of Mathematics from the University of Chicago. By this time, Mauricio Peixoto had published his seminal paper on Dynamical Systems. In the beginning of 1960, Steve Smale, invited by Peixoto, came to visit IMPA (This was the time when he found the proof of Poincaré Conjecture for dimensions greater than or equal than five).

Before 1959, I had studied some books suggested by Elon, like Chevalley’s Lie Group’s, Nomizu’s Lie Groups and Differential Geometry, and others. It was a solitary study, very slow, and full of unsolved problems. Through conversations with Elon, the questions disappeared, and I began to feel more confident in my studies.

Peixoto and Lima would often get together to discuss questions they were interested in. When I happened to be presen in such occasions, I just kept quiet, witnessing bewitched the creation of new mathematics. This was a crucial point in my experience, and I decided that, if possible, I would like to be a mathematician. I never repented that decision.