16/09/2020

Weierstrass introduced mathematical analysis into basic education.

Reproduction of Marcelo Viana's column in Folha de S.Paulo.

Early in my career as a mathematician, I spent some time at the Mittag-Leffler Institute in Djursholm, a chic suburb of Stockholm. Housed in the institute's comfortable residence, happily engaged in research on Swedish food (and drink…), I had a spacious office in the former residence of the Swedish mathematician Gösta Mittag-Leffler, bathed in the generous light of the Scandinavian summer.

The only problem was the painting on the wall opposite my desk: an oil painting by the German Karl Weierstrass (1815–1897), teacher and hero of Mittag-Leffler. Believe me, dear reader, it is very difficult to do mathematics (and maintain a healthy ego) under the stern gaze of one of the greatest masters of the 19th century, the creator of mathematical analysis as we understand it today.

The field of analysis, probably the most developed in mathematics, with countless applications and connections throughout science, dates back to the discovery of calculus by Isaac Newton and Gottfried Leibniz in the 17th century, and has received important contributions from successive generations of mathematicians. Following the important work of the Frenchman Augustin-Louis Cauchy, it fell to Weierstrass to establish the ideas of the pioneers on solid foundations, with precisely defined concepts and rigorously presented proofs.

And yet, young Karl's early years were not promising. The son of a Prussian government dignitary, Weierstrass was groomed to follow in his father's footsteps. Unfortunately for the family's plans, in high school he developed an incurable love for mathematics. Sent to study law, economics, and finance at the University of Bonn, at his family's expense, Karl paid little attention to his classes and continued to dedicate himself to his secret passion.

As a result, time ran out before Weierstrass obtained his diploma. His father, worried about his son's future, had no choice but to secure him a place at the teacher training college, where at least he graduated.

It was as a primary school teacher, starting in 1843, isolated and far from the centers of influence of the university world, that Weierstrass carried out much of his best mathematical work. While teaching mathematics, physics, botany, and even physical education, he published important articles that earned him a solid reputation.

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