Folha: “Was modern mathematics a success or a failure?”
Reprint of Marcelo Viana’s column in Folha de S.Paulo.
In the 1950s and 1960s, the Modern Mathematics movement—which began in the United States and soon spread to many other countries, including Brazil—sought to modernize the teaching of mathematics while bringing it closer to the research being conducted at universities and research centers.
Among its primary motivations at the outset was a sense of urgency to make up for the perceived lag behind the Soviet Union, which had just launched the first artificial satellite (Sputnik), a development that had taken the American institutions by storm. But the movement had even deeper roots.
At the turn of the 20th century, the German Felix Klein—one of the greats of his generation and founder of the International Commission on Mathematical Instruction— the international body for mathematics education, had already criticized the disconnect between school and university mathematics, arguing that school curricula needed to incorporate the spectacular advances achieved in the previous century.
Intellectually influenced by Nicolas Bourbaki—the group of prominent French mathematicians who were rebuilding the foundations of the discipline—the Modern Mathematics movement embraced abstraction, proposing to teach all of mathematics based on set theory. The result was not universally accepted: the high level of abstract reasoning—which the teachers themselves were not prepared to teach—and the apparent disconnect from concrete reality were misunderstood and quickly became a source of ridicule.
Morris Kline, one of its harshest critics, argued in the book *Why Johnny Can’t Add* that modern mathematics prioritized abstraction at the expense of understanding concepts and basic proficiency in essential tasks. Discredited, the movement gradually lost momentum throughout the 1970s. When I was in elementary school, high school seniors still had “modern math” classes, but by the time I reached that stage, that option had already been eliminated.
What, then, remains of that experiment? In fact, much more than most people realize. The fundamental concepts of set theory—such as union, intersection, and inclusion—are so deeply ingrained that we no longer even realize they were once controversial innovations. But the legacy of modern mathematics goes much further. In particular, it deserves credit for finally bringing into school curricula ideas that were very dear to Klein and that we now consider indispensable—such as the concept of a function, which forms the basis of countless modern mathematical tools.
Education also began to adopt a more precise language, with a greater focus on reasoning—including the concept of proof—and less on the mechanical execution of routine calculations, which had prevailed in classrooms until then.