Mathematics is hard for mathematicians to understand too | Science
At a recent conference focused on the evolving landscape of mathematics in the era of automated proofs, renowned mathematician and Fields Medalist Akshay Venkatesh delivered a thought-provoking talk titled “How do we talk to our students about AI?” Venkatesh began by sharing a poignant email from a young student who expressed concerns about the relevance of mathematics in a world where machines can provide answers to complex problems. This inquiry prompted Venkatesh to address a critical issue: the widening gap between the practice of mathematics and the core values that underpin the discipline. He emphasized that the essence of mathematics lies not merely in numbers or algorithms, but in fostering a deep understanding of concepts, a sentiment echoed by fellow mathematician William Thurston.
Venkatesh’s reflections highlight a broader concern within the mathematical community regarding the current state of research and education. He lamented that much of the work presented in academic papers and talks remains incomprehensible to the average mathematician, creating a barrier that undermines the true purpose of the field. This disconnect raises vital questions about the future role of mathematicians in an age increasingly dominated by artificial intelligence. As AI systems become more capable of solving mathematical problems, Venkatesh argues that it is crucial for educators and researchers to re-evaluate how they communicate the significance of mathematics to students. By prioritizing understanding over mere computation, mathematicians can better equip the next generation to navigate a world where AI plays an integral role, ensuring that the discipline remains relevant and valued.
In this context, Venkatesh advocates for a renewed focus on the philosophical and conceptual foundations of mathematics. He believes that by bridging the gap between technical expertise and fundamental understanding, educators can inspire students to appreciate the beauty and complexity of mathematics, rather than viewing it solely as a tool for problem-solving. This shift in perspective is essential not only for the enrichment of students’ educational experiences but also for the evolution of mathematics as a discipline in the age of AI. Ultimately, Venkatesh’s insights serve as a call to action for mathematicians to engage with their students more meaningfully, fostering a culture that values understanding and curiosity in an increasingly automated world.
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.
