世話人：阿部 拓郎（立教大学）
安田 雅哉（立教大学）
第二回：
Speaker ：Bruno Buchberger (Johannes Kepler University)
Time/date ：11:00--12:15, 8 September 2025
Venue ：MB01(B1), McKim Hall(Building No. 15)
Title:The Future of Mathematics, Computer Science, and Artificial Intelligence:Some Personal Views
Abstract:
I will begin with some episodes and remembrances about the time when I invented
the Gröbner Bases theory and algorithmic methodology in 1965 under the guidance
of my Ph.D. advisor, Professor Wolfgang Gröbner (1899–1980). I will then
summarize the main applications and extensions of the theory over the years,
including some recent advances.
Considering the development of Gröbner bases theory from a bird’s-eye view, I will
analyze how the invention of mathematical knowledge and methods proceeds and
how this process could be automated – by mathematical means – i.e., how
mathematics advances and trivializes itself on higher and higher (meta-)levels.
Automated (semi-automated) mathematical knowledge invention and verification
(including algorithm invention and verification) can be attacked in two fundamentally
different ways: By “symbolic computation” and by “machine learning”. For the first
approach, my “lazy thinking” method is an example (by which, in 2002, I managed to
mimic the invention process of my Gröbner bases algorithm). For the second
approach, the recent popular “Large Language Models” technology is a prominent
example.
I consider the application of ML methods to symbolic computation and the
application of SC methods to ML as the next important step forward in the
development of mathematics, computer science, and artificial intelligence, which
together I view as just one unified “thinking technology” (or simply “mathematics”).
From this perspective, I will also draw some conclusions on the education of the next
generation of “thinking technologists” and the future of society.
第一回：
講演者：鍛冶 静雄（九州大学/京都大学）
日時 ：2025年5月22日 17時15分--18時45分
場所 ：立教大学池袋キャンパス4号館4342室
タイトル：工学に現れる超平面配置
アブストラクト：ユークリッド空間内における有限個の超平面からなる「超平面配置」は，社会科学や工学分野への応用を持つことが知られている．応用上重要な配置は，しばしば最適化問題の解，すなわちあるエネルギー関数の極小点・平衡点として自然に現れる．本講演では，このような視点から，機械学習および形状設計における超平面配置の具体例を取り上げ，関係する数学的な問いを紹介する．