TBA

A network of roads and a cavity in a material are all features of shape. How can we turn such features into quantities that a computer can recognise, and then use those quantities to design something new?

This talk introduces topology as a language for describing and shaping data. We begin with electrical circuits, where counting connected components and independent loops leads naturally to the linear algebra of homology.

We then introduce persistent homology, which follows these features across scales, helping us explore structure without committing to a single threshold. Examples from materials, images, and networks show what this viewpoint can reveal.

The final part reverses the question: instead of asking what shape the data have, we ask what shape we would like them to have. Topological information can guide optimisation, encouraging connected structures or loops. 

This talk explores the two-way relationship between mathematics and AI through two case studies. The first examines how mathematical ideas, particularly those from topology, can guide AI learning in visual tasks that require determining whether two points are connected by a path. The second presents an AI-assisted approach to collecting and analyzing publicly available EBS Math data, focusing on the distribution of resources across grades, topics, and formats, as well as patterns in view counts. Together, these cases illustrate how mathematics can inform AI learning and how AI can support the analysis of mathematics education resources. 

The need for mathematics education has traditionally been explained not only in terms of academic achievement in school, but also in terms of the ability to use mathematics in occupational performance and everyday life. Nevertheless, the primary focus of mathematics education and opportunities for learning have remained concentrated on the school-age population. Even after leaving school, individuals are required to interpret and judge mathematical information in a wide range of real-life contexts, including health, finance, consumption, public statistics, and digital information. In particular, as population aging and digital transformation accelerate, there is a growing need to expand the scope of mathematics education from school-age students to lifelong learners.

Mathematical thinking is not limited to performing calculations or applying formulas. It involves understanding the structure of problems, identifying rules and relationships, exploring multiple solution strategies, and logically evaluating one’s own judgments. In this sense, learning mathematics may function as a form of “mental exercise,” providing opportunities for continuous intellectual activity throughout life. In an era in which artificial intelligence is replacing a substantial part of calculation and problem solving, it has become increasingly important for individuals to continue thinking consciously, reasoning, and making critical judgments. Therefore, future lifelong mathematics education should move beyond an instrumental view of mathematics and be reoriented toward education that supports the sustained development of reasoning abilities cultivated through mathematical activity.

In Korea, since Ko (2007) proposed the potential of mathematics education for older adults, subsequent studies have addressed the development and field application of practical mathematics materials (Ko, 2010), the design of senior mathematics applications and user-centered approaches (Ko, 2016; Ko & Lee, 2016), numeracy education based on the experiences of older learners (Lee & Ko, 2018), cognitive activities using smart applications (Lee et al., 2019), and the development of senior numeracy education programs (Kim, 2024). These studies have demonstrated the experiences and characteristics of out-of-school learners as well as the potential of mathematics learning. Internationally, the importance of adult numeracy has also been emphasized (Gal et al., 2020), while empirical research on actual teaching and learning remains insufficient (Gal, 2024).

Against this background, this presentation examines the conceptual and educational value of lifelong mathematics education, reviews the achievements and limitations of practical mathematics and adult mathematics education research in Korea, and proposes directions for lifelong mathematics education in the age of artificial intelligence. In particular, it discusses the possibility of developing mathematics learning as an intellectual activity that supports sustained reasoning ability throughout life. It also addresses future curriculum and instructional directions, the expansion of mathematical culture, research methods for evaluating educational effectiveness, and related academic challenges.