Speaker: Bruno Buchberger，RISC, Johannes Kepler University Linz

Inviter: 冯如勇

Title: The Mathematician’s Last Theorem? — Reflections on the Future of Our Field

Language: English

Time & Venue: 2026.10.28 16:00 PM Linz time Zoom 会议号： 959 8303 9207 （密码：326958）

Abstract: For nearly six decades—since 1965—the SIGSAM community has dedicated itself to inventing symbolic and algebraic algorithms. Now, shockingly, the very recent (post‑2023) breakthroughs in what many call “Artificial Intelligence” threaten to turn our hard‑won tools against us. Through successive rounds of “reflexion”—the self-application of these algorithms to automate the process of mathematical invention, including the invention of algorithms themselves – “machines” are beginning to do what we once thought required human genius.

In this talk, I will first examine the essence of the fields that converge in this new landscape: computer algebra, automated reasoning, symbolic computation, machine learning, natural language processing, automated programming, neuro-symbolics, and artificial intelligence. I will show how they relate to and amplify one another, driving the automation of mathematical theory creation. The synergy among them has, unexpectedly for most (though dreamt of and predicted by a few), exploded into systems like Aristotle, GitHub Copilot, and Leanstral - systems that may soon radically change how we invent, present, teach, and apply mathematics.

The heart of the talk is personal: I will offer my own answers to a cascade of urgent questions. Where does human creativity fit in this new era? Should we be afraid of a “math winter”? What should mathematical education become? What is the “White‑Box–Black‑Box” principle in the age of AI‑powered mathematics? What future awaits established software platforms such as Mathematica and Maple? How must mathematical journals—especially the Journal of Symbolic Computation and the Communications in Computer Algebra—re‑imagine their roles? How can we responsibly shape the next stages of automated mathematics and its role in automated science? And what does Gödel have to say to us today?

I will close with a brief look at how we are likely to revive our own early (1995–2002) efforts to automate mathematics in the THEOREMA Project, now in light of everything that has changed. In other words: Would Gröbner, today, still take Buchberger as a Ph.D. student?