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Creator of Logic
Paraconsistent donates his personal archive to Unicamp

Newton da Costa, or
mathematics with art

LUIZ SUGIMOTO

O Professor Newton Carneiro Affonso da Costa, an affable and conversational gentleman whose vivacity hides his 73 years of age, is one of the most cited mathematicians internationally. “They did a survey of the citations and I must be in third or fourth,” he says, without a hint of presumption. He is the mentor of "Paraconsistent Logic", a theory published exactly thirty years ago and at the time considered abstract research, perhaps with applications in philosophy, but which today is disseminated throughout the technological area, from computing and robotics to production engineering, extrapolating to medicine.

Newton da Costa's CV does not deserve saving space. A civil engineer and mathematician graduated from the Federal University of Paraná, where he taught for 14 years, he came to the Institute of Mathematics, Statistics and Scientific Computing (Imecc) during the time of Zeferino Vaz (1968-69). He participated in its creation and to this day is a regular member of the Center for Logic, Epistemology and History of Science (CLE). He calls the masters and doctors he trained to integrate the cream of this area of ​​knowledge his children. At USP he was a professor at the Institute of Mathematics and Statistics from 1970 to 1985, and at the Faculty of Philosophy, Letters and Human Sciences from 1985 until his retirement. He currently teaches philosophy at the Federal University of Santa Catarina.

Da Costa estimates that his stays abroad total at least a decade, working as a lecturer and professor in renowned institutions in the United States, France, Italy, Spain, Australia, Mexico and Argentina, among others. Among numerous awards, he holds the Jabuti in Exact Sciences, the Medal of the Order of the Pine from the government of Paraná, the Moinho Santista and the Nicolau Copernicus Medal from the University of Torun, in Poland.

Asked to talk about his life, Newton da Costa immediately dispels the apprehension regarding the abuse of erudition and mathematical concepts that are incomprehensible to us mortals. "For me, mathematics is a subject that requires a certain type of talent, like painting, sculpture or even football", he says, simplifying the interview. "I like mathematics that doesn't use calculations. The tendency of modern mathematics is to replace calculations with ideas. It is fundamentally a game of ideas", he continues.

Therefore, the professor confirms a recent statement that almost every problem can be solved with reasoning and, therefore, he usually walks from one side to another, scribbling, until the light comes to light. "Studying is a fraction of the mathematician's intellectual work. He needs to think; if he doesn't think, he will never accomplish anything again," he adds. The image of his wanderings around the room, however, should not be associated with the stereotype that is made of mathematicians, physicists and other scholars who seem alien to earthly life: "As in every profession, there are those who live in the world of the moon and those who have their feet on the ground. German, Danish, French and Portuguese blood runs through my veins, which gave me European habits, such as sticking to schedules and what is promised. This is typical of those who have their feet on the ground."

Looking around - If the statements seem more like a thinker and less like a mathematician, it is because Newton da Costa never left the human sciences, since the time he attended the classes of his uncle Milton Carneiro, professor of history of philosophy at Federal do Paraná, and with him he read the great philosophers. "I've always been especially interested in philosophy of science. I'm not just interested in doing mathematics, I'm interested in understanding what it means to do mathematics", he philosophizes. And, to those who see antagonism between the two areas of knowledge, the professor predicts that certain aspects of finite mathematics, mainly logic, will certainly become fundamental in the human sciences. "Lacan, who everyone quotes and many criticize, said that logic is essential for psychoanalysis, which basically makes a logical analysis of the patient's language", he exemplifies.

On the other hand, in order to offer examples of mathematics in practical life, the teacher simply looks around. "This hotel was built with mathematics, construction stability calculations that engineers use all the time. Faraday studied electricity and magnetism, motivating Maxwell to use very interesting and original mathematics for the mid-19th century, developing equations that deal with of the electromagnetic field. Shortly afterwards, Hertz would prove the existence of the electromagnetic wave. From these discoveries they created the radio, the wireless telegraph, television, etc.", he teaches.

The greatest creation - Paraconsistent logic deals with information systems where there are inconsistencies, explains Newton da Costa. "For example: when organizing a medical database, you interview many experts, gather thousands of data and put them in the database. Obviously contradictory information will appear, because for one doctor a certain symptom may represent a disease and, for a second doctor, another. And you have to manipulate this. If you use classical logic, which cannot deal with contradictory information in a comfortable way, the system explodes. Paraconsistent logic prevents you from being led to a trivialization of the system by manipulating contradictory information." .

Unip, in São Paulo, has already created a subject of paraconsistent logic in production engineering, and at the Polytechnic it is also taught to engineers. "An absolutely theoretical concept, from the upper stratosphere, that thirty years ago no one thought would have a future, is serving philosophy, mathematics, engineering, everywhere, especially in Brazil and Japan. I, who started all of this, have already I can keep up with world literature."

"Million Show" - Three years ago, the Clay Mathematics Institute announced a $1 million prize for each solution of seven important open-ended math problems. "P=NP?" is the enigma with which Newton da Costa and professor Francisco Doria are involved. "Clay is an American millionaire. To win the prize, a person needs to write an article and publish it in an international scientific journal, without it being challenged for a period of two years. I believe we have already made a good contribution to winning this challenge," he says.

Warning that he would need at least an hour to offer the layman a palatable statement for the question "P=NP?", the mathematician only informs that it relates to computing. But he comforts us by pointing out that these are incredibly complicated problems. "The 'Riemann hypothesis', another problem included in the challenge, has lasted more than a hundred years, without great mathematicians being able to solve it. Sooner or later they will. But so far no one has won the million."

In defense of the centers of thought

Professor Newton da Costa donated his personal archive to the Center for Logic, Epistemology and History of Science (CLE), last year. There are approximately 10 thousand items, including academic correspondence exchanged with Brazilian and foreign researchers, largely unpublished manuscripts, articles citing his work, newspaper clippings and reprints. The material is receiving archival treatment before being made available to the public. Da Costa was at Unicamp in the last week of May, as a mandatory presence at the celebrations of CLE's 25th anniversary, one of the best initiatives implemented in the country, in his opinion. "I'm just afraid that, like all good things, the Center is ephemeral. I'm even surprised that it's still here. If a good genetics researcher appears, his work receives support; when he retires, genetics at the institution ends. We need to planning for up to 50 years. I hope that Unicamp will support the CLE, already thinking about the researchers and employees who will replace the current ones. We passed and only the large institutions remain or should remain", he states. The mathematician insists that destroying thought centers is a stupid attitude. On the one hand, he recalls Nehru, Indian Prime Minister, for whom his country was so underdeveloped that it could not afford not to support basic research in all sectors. On the other hand, he recalls a time when he taught in Buenos Aires: One of those generals said: "we here in Argentina and Latin America are very smart, we let the northern hemisphere think and we apply it". Skeptical of those in power, the veteran professor hears as a fallacy the speech that it is necessary to take care of poverty before developing universities. "It is necessary to attack both problems simultaneously. If education is not systematically organized, Brazil will always be the country of the future. We turn on the light invented by Edson, brush our teeth with the American Tech toothbrush, drink Nestlé milk Swiss, watches Japanese Mitsubishi television, goes to work in a German Volkswagen. Could it be that Brazilians are incapable of inventing anything?", he asks. As for his skepticism, he justifies: "As a boy, I really liked Freud, who said: "I always thought the worst about everyone, including myself, and I was never wrong." But, it is not because he disbelieves the world or because he is tired, that Newton da Costa made Florianópolis his retreat. He just sees the city as a good option for old age: "I can't stand metropolises like São Paulo anymore, I'm old, and I think that now I can help a good, new and airy university like the Federal University of Santa Catarina. The beach is just a few blocks away. home and I can go football at night. Besides, my children live there. There comes a certain age when only the children can put up with you."

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