{"id":73862,"date":"2024-08-21T00:03:06","date_gmt":"2024-08-21T04:03:06","guid":{"rendered":"https:\/\/world.edu\/?p=73862"},"modified":"2024-08-21T00:03:06","modified_gmt":"2024-08-21T04:03:06","slug":"the-mystic-and-the-mathematician-what-the-towering-20th-century-thinkers-simone-and-andre-weil-can-teach-todays-math-educators","status":"publish","type":"post","link":"https:\/\/world.edu\/the-mystic-and-the-mathematician-what-the-towering-20th-century-thinkers-simone-and-andre-weil-can-teach-todays-math-educators\/","title":{"rendered":"The mystic and the mathematician: What the towering 20th-century thinkers Simone and Andr\u00e9 Weil can teach today\u2019s math educators"},"content":{"rendered":"

\"\"<\/a><\/p>\n

Like most mathematicians<\/a>, I hear confessions from complete strangers: the inevitable \u201cI was always bad at math.\u201d I suppress the response, \u201cYou are forgiven, my child.\u201d<\/p>\n

Why does it feel like a sin to struggle in math? Why are so many traumatized by their mathematics education? Is learning math worthwhile?<\/p>\n

Sometimes agreeing and sometimes disagreeing,\u00a0Andr\u00e9<\/a>\u00a0and\u00a0Simone Weil<\/a>\u00a0were the sort of siblings who would argue about such questions. Andr\u00e9 achieved renown as a mathematician; Simone was a formidable philosopher and mystic. Andr\u00e9 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.<\/p>\n

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.<\/p>\n

Andr\u00e9 Weil\u2019s rigorous mathematics<\/strong><\/h4>\n

Unlike the prominent French mathematicians of previous generations, Andr\u00e9, 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 \u201cno need to defend<\/a>\u00a0(it).\u201d<\/p>\n

In his interactions with people, Andr\u00e9 was an unsparing critic.\u00a0Although admired<\/a>\u00a0by some colleagues, he was\u00a0feared by<\/a>\u00a0and at times\u00a0disdainful of<\/a>\u00a0his students. He co-founded the\u00a0Bourbaki mathematics collective<\/a>\u00a0that used abstraction and logical rigor to\u00a0restructure mathematics<\/a>\u00a0from the ground up.<\/p>\n

Nicolas Bourbaki\u2019s commitment to proceeding from first principles, however, did not completely encapsulate his conception of what constituted worthwhile mathematics. Andr\u00e9\u00a0was attuned<\/a>\u00a0to how math should be taught differently to different audiences.<\/p>\n

Tempering the Bourbaki spirit, he defined rigor as \u201c(not) proving everything, but \u2026 endeavoring to assume as little as possible at every stage.\u201d<\/p>\n

In other words, absolute rigor has its place, but teachers must be willing to take their audience into account. He believed that teachers must motivate students by providing them meaningful problems and provocative examples. Excitement for advanced students comes in encountering the unknown; for beginning students, it emerges from solving questions of, as he put it, \u201ctheoretical or practical importance.\u201d He insisted that math \u201cmust be a source of intellectual excitement.\u201d<\/p>\n

Andr\u00e9\u2019s own sense of intellectual excitement came from applying insights from one part of mathematics to other parts. In a\u00a0letter to his sister<\/a>, Andr\u00e9 described his work as seeking a metaphorical \u201cRosetta stone<\/a>\u201d of analogies between advanced versions of three basic mathematical objects: numbers, polynomials and geometric spaces.<\/p>\n

Andr\u00e9\u00a0described mathematics in romantic terms<\/a>. Initially, the relationship between the different parts of mathematics is that of passionate lovers, exchanging \u201cfurtive caresses\u201d and having \u201cinexplicable quarrels.\u201d But as the analogies eventually give way to a single unified theory, the affair grows cold: \u201cGone is the analogy: gone are the two theories, their conflicts and their delicious reciprocal reflections \u2026 alas, all is just one theory, whose majestic beauty can no longer excite us.\u201d<\/p>\n

Despite being passionless, this theory that unifies numbers, polynomials and geometry gets to the heart of mathematics; Andr\u00e9 pursued it intensely. In the words of a colleague, Andr\u00e9 sought the \u201creal meaning<\/a>\u00a0of every basic mathematical phenomenon.\u201d For him, unlike his sister, this real meaning was found in the careful definitions, precisely articulated theorems and rigorous proofs of the most advanced mathematics of his time. Romantic language simply described the emotions of the mathematician encountering the mathematics; it did not point to any deeper significance.<\/p>\n

Simone Weil and the philosophy of mathematics<\/strong><\/h4>\n

On the other hand, Simone, who was born three years after Andr\u00e9 and died 55 years before him, used philosophy and religion to investigate the value of mathematics for nongeniuses, in addition to her work on politics, war, science and suffering.<\/p>\n

All of her writing \u2013 indeed, her life \u2013 has a maddening quality to it. In her polished essays, as well as her private letters and journals, she will often make an extreme assertion or enigmatic comment. Such assertions might concern the motivations of scientists, the psychological state of a sufferer, the nature of labor, an analysis of labor unions or an interpretation of Greek philosophers and mathematicians. She is not a systematic thinker but rather circles around and around clusters of ideas and themes. When I read her writing, I am often taken aback. I start to argue with her, bringing up counterexamples and qualifications, but I eventually end up granting the essence of her point. Simone was known for the single-minded pursuit of her ideals.<\/p>\n

Despite the discomfort her viewpoints provoke, they are worth engaging. Although\u00a0her childhood was largely happy<\/a>, her whole life she\u00a0felt stupid in comparison<\/a>\u00a0with her brother. She channeled her feelings of inadequacy into an exploration of how to experience a meaningful existence in the face of oppression and affliction. Over her life, she developed an\u00a0interpretation of beauty and suffering<\/a>\u00a0intertwined with geometry.<\/p>\n

Along with her lifelong mathematical discussions with Andr\u00e9, her views were influenced by one of her\u00a0first jobs as a teacher<\/a>. In a letter to a colleague, she described her pupils as struggling because they \u201cregarded the various sciences as compilations of cut-and-dried knowledge.\u201d Like Andr\u00e9, Simone saw the ability to motivate students as the key to good teaching. She taught mathematics as a subject embedded in culture, emphasizing overarching historical themes. Even those students who were \u201cmost ignorant in science\u201d followed her lectures with \u201cpassionate interest.\u201d<\/p>\n

For Simone, however, the primary purpose of mathematics education was to develop the virtue of attention. Mathematics confronts us with our mistakes, and the\u00a0contemplation of these inadequacies<\/a>\u00a0brings the ability to concentrate on one thing, at the exclusion of all else, to the fore. As a math teacher, I frequently see students grit their teeth and furrow their brow, developing only a headache and resentment. According to Simone, however, true attention arises from joy and desire. We hold our knowledge lightly and wait with detached thought for light to arrive.<\/p>\n

For Simone, the \u201cfirst duty\u201d of teachers is to help students develop, through their studies, the ability to apprehend God, which she conceptualized as a blending of Plato\u2019s description of the\u00a0ultimate Good<\/a>\u00a0with Christian conceptions of the self-abnegating God. A true understanding of God results in love for the afflicted.<\/p>\n

Simone might even locate the lingering anxiety and frustration of many former math students in the absence of attention paid to them by their teachers.<\/p>\n

Authors grapple with the Weil legacy<\/strong><\/h4>\n

Recently, others have wrestled with the Weil legacy.<\/p>\n

Sylvie Weil, Andr\u00e9\u2019s daughter, was born shortly before Simone\u2019s death. Her\u00a0family experience<\/a>\u00a0was that of being mistaken for her aunt, ignored or demeaned by her father and not being acknowledged and appreciated by those in her orbit.<\/p>\n

Similarly, author\u00a0Karen Olsson<\/a>\u00a0uses Simone and Andr\u00e9 to explore her own conflicted relationship with mathematics. Her forlorn quest to understand Andr\u00e9\u2019s mathematics eerily reflects Simone\u2019s desire to understand Andr\u00e9\u2019s work and Sylvie\u2019s desire to be seen as her own person, to not be in Simone\u2019s shadow. Olsson studied with exceptional math teachers and students, all the while feeling out of place, overwhelmed and intimidated by her fellow students. Most painfully, in the process of writing her book on the Weil siblings, Olsson asks a mathematician, who had been a student with her, for help in understanding some aspect of Andr\u00e9\u2019s mathematics. She was ignored. Both Sylvie Weil and Karen Olsson are living witnesses to Simone\u2019s observation that each of us cries out to be seen.<\/p>\n

Christopher Jackson, on the other hand, gives testimony to how mathematics can live up to Simone\u2019s vision. Jackson is incarcerated in a federal prison but found a new life through mathematics. His correspondence with mathematician Francis Su is the backbone of Su\u2019s 2020 book \u201cMathematics for Human Flourishing<\/a>,\u201d which uses Simone\u2019s observation that \u201cevery being cries out silently to be read differently\u201d as a leitmotif. Su identifies aspects of mathematics that promote human flourishing, such as beauty, truth, freedom and love. In their own ways, both Simone and Andr\u00e9 would likely agree.<\/p>\n

Author Bio:<\/strong> Scott Taylor is Professor of Mathematics at Colby College<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"

Like most mathematicians, I hear confessions from complete strangers: the inevitable \u201cI was always bad at math.\u201d I suppress the response, \u201cYou are forgiven, my child.\u201d 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,\u00a0Andr\u00e9\u00a0and\u00a0Simone […]\n… learn more→<\/a><\/p>","protected":false},"author":33,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[15645],"tags":[435063],"coauthors":[11733],"class_list":["post-73862","post","type-post","status-publish","format-standard","hentry","category-education","tag-mathematics-education"],"acf":[],"yoast_head":"\nThe mystic and the mathematician: What the towering 20th-century thinkers Simone and Andr\u00e9 Weil can teach today\u2019s math educators - World leading higher education information and services<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/world.edu\/the-mystic-and-the-mathematician-what-the-towering-20th-century-thinkers-simone-and-andre-weil-can-teach-todays-math-educators\/\" class=\"yoast-seo-meta-tag\" \/>\n<meta property=\"og:locale\" content=\"en_US\" class=\"yoast-seo-meta-tag\" \/>\n<meta property=\"og:type\" content=\"article\" class=\"yoast-seo-meta-tag\" \/>\n<meta property=\"og:title\" content=\"The mystic and the mathematician: What the towering 20th-century thinkers Simone and Andr\u00e9 Weil can teach today\u2019s math educators - World leading higher education information and services\" class=\"yoast-seo-meta-tag\" \/>\n<meta property=\"og:description\" content=\"Like most mathematicians, I hear confessions from complete strangers: the inevitable \u201cI was always bad at math.\u201d I suppress the response, \u201cYou are forgiven, my child.\u201d Why does it feel like a sin to struggle in math? 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