Mathematics is hard for mathematicians to understand too | Science
At a recent conference focused on the evolving role of mathematics in the era of automated proofs, renowned mathematician and Fields Medalist Akshay Venkatesh sparked a thought-provoking dialogue with his presentation titled “How do we talk to our students about AI?” Venkatesh shared an insightful email from a young student who posed a challenging question: “Do you believe that mathematics is worth being studied in a world in which a machine can answer everything for you? What do you believe would be the ‘job’ of a mathematician in this world?” This inquiry highlights a growing concern among students and educators alike regarding the relevance of traditional mathematical study in an age increasingly dominated by artificial intelligence and machine learning.
Venkatesh seized this opportunity to address what he perceives as a significant disconnect between the practice of mathematics and the core values that underpin the discipline. He referenced the thoughts of fellow mathematician William Thurston, who articulated that mathematics transcends mere numbers and algorithms; it is fundamentally about understanding. This philosophical foundation raises critical questions about the current state of mathematical research, which Venkatesh critiques as lacking in accessibility and comprehension. He lamented that for the majority of academic papers and presentations, true understanding is often elusive, leaving many mathematicians and students grappling with complex ideas without a solid grasp of their implications or applications. This disconnect, as Venkatesh suggests, presents an opportunity for the mathematical community to reevaluate its priorities and methods, ensuring that the discipline remains both relevant and comprehensible in the face of rapid technological advancements.
By framing AI not as a threat but as a catalyst for change, Venkatesh encourages a reimagining of the mathematician’s role in society. He advocates for a shift towards fostering a deeper understanding of mathematical concepts, emphasizing the importance of teaching methodologies that prioritize clarity and insight over rote memorization and procedural knowledge. This perspective not only addresses the concerns raised by students about the future of mathematics but also aligns with the broader educational goal of nurturing critical thinking and problem-solving skills in an increasingly automated world. As the landscape of mathematics continues to evolve, Venkatesh’s insights serve as a crucial reminder of the discipline’s enduring value and the need for a renewed focus on understanding in both teaching and research.
https://www.youtube.com/watch?v=m6ltzaOpPl8
At a recent conference on mathematics in the age of automated proofs, mathematician and Fields Medalist Akshay Venkatesh presented “How do we talk to our students about AI?” He quoted an email he’d received from a young student who asked, “Do you believe that mathematics is worth being studied in a world in which a machine can answer everything for you? What do you believe would be the ‘job’ of a mathematician in this world?” Venkatesh framed AI as an opportunity to correct what he called an “essential gap that has opened between the practice of mathematics and our values.” Mathematician William Thurston has explained these values by writing, “mathematics is not about numbers, equations, computations, or algorithms: it is about understanding.” But Venkatesh argued that the record on this is terrible, lamenting that “for a typical paper or talk, very few of us understand it.” He is not alone in thinking that something is wrong with the current state of mathematics research.
