# What should we tell our students? > Will AI replace mathematicians? A professor answers. - Title: What should we tell our students? · What's new | Shortify - Summary: Will AI replace mathematicians? A professor answers. Students should pursue math PhDs despite AI advances as passion and human understanding remain crucial. - Keywords: mathematics, phd, student, terence tao, alvaro lozano-robledo, convex hull, research, technology, startups, tell, students, What's new - Source: What's new — https://terrytao.wordpress.com/2026/10/08/what-should-we-tell-our-students - Published: 2026-10-08T14:43:35+00:00 - Read time: 2 min - Topics: ai, mathematics, phd, student, terence tao, alvaro lozano-robledo, convex hull, research, technology, startups ## Student worries about math careers A pure math undergraduate writes to Prof. Tao asking if math academia will remain accessible for passionate students despite AI advances. > Hey Prof, I’ve been watching your videos for a while now as a pure math undergraduate who once wanted to pursue a career in math academia. ## AI's impact on math research LLMs are disrupting academic research and education in mathematics, with some companies claiming to solve complex problems autonomously. > The advances in LLMs are disrupting almost all aspects of academic research and education in mathematics ## Student concerns about AI Students worry if AI will surpass human mathematical research ability within 5-10 years and if math PhDs are still worthwhile. > Will AI surpass the mathematical research ability of any human? ## The convex hull model Mathematicians propose that LLMs work within the convex hull of existing mathematical ideas, limiting their ability to create entirely new concepts. > The idea for the proof seems ingenious at first sight because it cleverly mixes strategies from two fields of math at the vertices of the polytope ## AI's limitations LLMs require significant resources to solve problems and may face ethical constraints on their use in mathematical research. > We would like to know if there is life on Mars, but in order to do so as soon as possible, we would need an absurd amount of funding and risk the lives of a human crew in the process. ## Mathematicians remain essential Human mathematicians are needed to interpret, understand, and communicate mathematical results, even with AI assistance. > Even in the most dystopian of scenarios where AI becomes super human in all research tasks, what good would a proof be if there are no human mathematicians to digest it and understand it? ## PhD advice for students Students should pursue math PhDs if passionate about mathematics, as LLMs can aid learning but not replace the need for human understanding. > The most important reason (and perhaps the only reason) to do a PhD in math should be that the candidate is passionate about mathematics and wants to become an expert in a particular topic within our field. ## OpenAI's recent release OpenAI released significant mathematical results, including solutions to several open problems, but mathematicians remain essential for understanding. > OpenAI released a huge treasure trove of results in mathematics: the resolution of the so-called quasi Riemann Hypothesis, Goldfeld’s conjecture, the Hodge Conjecture in the case of CM abelian varieties ## The future of math education LLMs can help students learn faster but do not replace the need for human mentors and the passion for mathematics. > Students can be involved in research earlier than ever before too because the LLMs can help them learn material faster (and deeper!) ## Why math PhDs matter Pursuing a math PhD provides unique opportunities for understanding, collaboration, and contribution to the field despite AI advancements. > I wanted to hear mathematicians talk about math, and rejoice in the small little details and miracles that make proofs work. ## The convex hull of ideas Mathematicians argue that LLMs will fill gaps between existing ideas but require human innovation to create new concepts. > The convex hull of ideas is a stellated high-dimensional polytope where the state-of-the-art ideas are placed at outer vertices ## AI's role in research LLMs can assist in research but do not replace the need for human intuition and creativity in mathematical discovery. > The LLMs are more than tools: they can be research collaborators but, as in any collaboration, the experience and the results are greatly improved when all parties contribute to the discussion. ## The future of math Mathematics will continue to be a vital field with human mathematicians playing a crucial role in understanding and communicating results. > There will always be areas of mathematics that are under-explored and where even beginners can break new ground. ## Key takeaway Students should pursue math PhDs despite AI advances as passion and human understanding remain crucial.