A Mathematical Picture Language Program

Teaching Programming for Mathematical Scientists

Over the past thirty years or so the authors have been teaching various programming for mathematics courses at our respective Universities, as well as incorporating computer algebra and numerical computation into traditional mathematics courses. These activities are, in some important ways, natural precursors to the use of Artificial Intelligence in Mathematics Education. This paper reflects on some of our course designs and experiences and is therefore a mix of theory and practice. Underlying both is a clear recognition of the value of computer programming for mathematics education. We use th…

在计算不透明时代中的先验知识：人工智能在数学发现中的作用

Apriori Knowledge in an Era of Computational Opacity: The Role of AI in Mathematical Discovery

本文探讨了在计算不透明时代，通过AI获取数学先验知识的挑战与可能方法，强调证明检查器在其中的关键作用。

Exploring mathematical objects from custom-tailored mathematical universes

Toposes can be pictured as mathematical universes. Besides the standard topos, in which most of mathematics unfolds, there is a colorful host of alternate toposes in which mathematics plays out slightly differently. For instance, there are toposes in which the axiom of choice and the intermediate value theorem from undergraduate calculus fail. The purpose of this contribution is to give a glimpse of the toposophic landscape, presenting several specific toposes and exploring their peculiar properties, and to explicate how toposes provide distinct lenses through which the usual mathematical obje…

印度数学科学中心（CMS）：A.M. Mathai教授75岁生日

Centre for Mathematical Sciences India (CMS): Professor A.M. Mathai's 75th Birthday

简要介绍了成立于1977年的印度数学科学中心及其教学和研究计划。

Mathematics Education in Russia and Mathematical Circles

This Master's Thesis analyzes thoroughly the topic of the Mathematics Education in Russia and Mathematical Circles. It deals with the historical context of the Mathematics Education in Russia in the XVIIIth, XIXth and XXth centuries; the programs of the Mathematics Education which were developed between 1930 and 1985 in the Soviet Union, including the Mathematical Circles for its particularly importance and influence on the rest of the Programs and on the way of understanding the Mathematics Education; the objectives and the organization of practical cases nowadays, legacy of the Russian Mathe…