by SCOTT TAYLOR
Like most mathematicians, I hear confessions from complete strangers: the inevitable “I was always bad at math.” I suppress the response, “You are forgiven, my child.”
Why does it feel like a sin to struggle in math? Why are so many traumatized by their mathematics education? Is learning math worthwhile?
Sometimes agreeing and sometimes disagreeing, André and Simone Weil were the sort of siblings who would argue about such questions. André achieved renown as a mathematician; Simone was a formidable philosopher and mystic. André focused on applying algebra and geometry to deep questions about the structures of whole numbers, while Simone was concerned with how the world can be soul-crushing.
Both wrestled with the best way to teach math. Their insights and contradictions point to the fundamental role that mathematics and mathematics education play in human life and culture.
André Weil’s rigorous mathematics
Unlike the prominent French mathematicians of previous generations, André, who was born in 1906 and died in 1998, spent little time philosophizing. For him, mathematics was a living subject endowed with a long and substantial history, but as he remarked, he saw “no need to defend (it).”
In his interactions with people, André was an unsparing critic. Although admired by some colleagues, he was feared by and at times disdainful of his students. He co-founded the Bourbaki mathematics collective that used abstraction and logical rigor to restructure mathematics from the ground up.
Nicolas Bourbaki’s commitment to proceeding from first principles, however, did not completely encapsulate his conception of what constituted worthwhile mathematics. André was attuned to how math should be taught differently to different audiences.
Tempering the Bourbaki spirit, he defined rigor as “(not) proving everything, but … endeavoring to assume as little as possible at every stage.”
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