Mathematics is hard for mathematicians to understand too | Science
At a recent conference focused on the evolving landscape of mathematics in the age of automated proofs, renowned mathematician and Fields Medalist Akshay Venkatesh tackled a pressing question posed by a student: “Do you believe that mathematics is worth being studied in a world in which a machine can answer everything for you?” Venkatesh’s response delved into the implications of artificial intelligence (AI) on the field of mathematics, suggesting that rather than diminishing the importance of mathematical study, AI presents a unique opportunity to bridge the widening gap between mathematical practice and the fundamental values that underpin the discipline. He emphasized that mathematics should be viewed not merely as a collection of numbers and algorithms but as a pursuit of understanding—a sentiment echoed by fellow mathematician William Thurston.
Venkatesh lamented the current state of mathematics research, suggesting that the communication and understanding of complex mathematical ideas have deteriorated. He argued that for many academic papers and presentations, comprehension among peers is alarmingly low, which raises questions about the accessibility and relevance of mathematical work in today’s world. By framing AI as a tool that can enhance understanding rather than replace it, Venkatesh called for a reevaluation of how mathematics is taught and discussed. He envisions a future where AI acts as a collaborator, helping mathematicians to focus on deeper understanding and theoretical exploration, rather than getting bogged down in tedious computations. This shift could redefine the role of mathematicians, positioning them as guides who help others navigate the complexities of mathematical thought in an increasingly automated landscape.
This dialogue around AI and mathematics is particularly timely, as technology continues to reshape educational paradigms and professional landscapes. Venkatesh’s insights challenge educators and researchers to rethink their approaches, emphasizing the need for clarity and engagement in mathematical discourse. As AI systems become more capable of performing calculations and solving problems, the emphasis must shift towards fostering critical thinking and a deeper appreciation for the beauty and intricacies of mathematics itself. By addressing these challenges, the mathematical community can ensure that the discipline remains vibrant and relevant, inspiring future generations to explore the profound questions that mathematics seeks to answer.
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.
