Workshop: Creativity in Mathematics & AI

Keynote Speakers

Anna Abraham | University of Georgia
Kevin Buzzard | Imperial College London
Simon Colton | University of London
Maithilee Kunda | Vanderbilt University
Catholijn Jonker | Leiden University
Paige Randall North | University of Pennsylvania
Catherine Menon | University of Hertfordshire
Yang-Hui He | University of London
Gemma Anderson | University of Exeter

Anna Abraham: 'The Nature of Human Creativity'
A selective overview, as evidenced by theory and research in psychology and neuroscience, is presented on the nature of human creativity in terms of its core features. Attention will be drawn into some of the key differences that are apparent when comparing human creativity with AI-based forms. These include (A) multiplicity and flexibility within and across domains of creative engagement, (B) endogenous assessment of appropriateness of the creative response, (C) use of the same cognitive toolboxes to creative and non-creative ends, (D) the dynamic engagement of multiple distinct operations in human creativity as well as (E) intra-individual and inter-individual differences in the same.

E. Paul Torrance Professor, Torrance Center for Creativity & Talent Development, College of Education,University of Georgia, Athens, Georgia, USA.

Kevin Buzzard: 'Can computers be mathematically creative?'
It's reasonable to believe that in some unspecified future time, computers will be better at research level mathematics than humans. But when will this actually happen -- is it ten years away or 100 years away? How will it happen? How can human mathematicians help to make it happen? And what about those who have concerns about this happening at all? Of course I don't really know the answers to these questions but at least I can say something about where we are, and where we might be going, when it comes to modern mathematical research and the computer's understanding of it.

Kevin Buzzard is a professor of pure mathematics at Imperial College London. He specialises in algebraic number theory and the Langlands program. More recently he has become interested in interactive theorem provers.

Simon Colton

In the AI subfield of computational creativity, we research how to hand over creative responsibilities to AI systems in arts and science projects. My first (and ongoing) study was in generative mathematics, where I built a system called HR (after Hardy and Ramanujan) which invented mathematical concepts in finite algebras, number theory, graph theory and elsewhere, then found empirical relationships between concepts, expressed as conjectures. The most current version of HR performs automated software engineering and is still heavily influenced by creative reasoning in mathematics. In the talk, I'll describe how the HR projects have influenced the philosophical development of computational creativity, covering notions such as essentially contested concepts, the humanity gap, computational authenticity and the machine condition.

Simon Colton is a professor of computational creativity at Queen Mary University of London and Monash University, having previously been an academic at Imperial College London and Goldsmiths College. He obtained his PhD in Artificial Intelligence from the University of Edinburgh. He is a founding member of the computational creativity research field and is best known for AI systems such as HR for mathematical discovery, The Painting Fool automated artist and the What-If Machine for fictional ideation, as well as contributions to the philosophical understanding of creativity in people and machines.

Maithilee Kunda: 'A computational view of visual imagery in humans and in AI systems'
Visual imagery has been linked to many examples of human creativity, including in mathematical and scientific discovery. However, from a computational perspective, we do not fully understand the low-level cognitive representations and operations that enable visual imagery, or how these low-level elements can be combined by an intelligent agent to achieve high-level reasoning. I present a series of computational studies centered on using visual imagery to solve Raven's Progressive Matrices, a widely used test of human intelligence, that begin to answer these questions. I also discuss how people might learn abstract visual imagery skills during concrete spatial play with objects during infancy, and how similar learning experiences can be simulated for AI systems.

Maithilee Kunda is an assistant professor of computer science at Vanderbilt University. Her work in artificial intelligence (AI), in the area of cognitive systems, looks at how visual thinking contributes to learning and intelligent behavior, with a focus on applications related to autism and neurodiversity. She currently directs Vanderbilt’s Laboratory for Artificial Intelligence and Visual Analogical Systems and is a founding investigator in Vanderbilt’s Frist Center for Autism and Innovation. In 2016, she was recognized as a visionary on the MIT Technology Review’s global list of 35 Innovators Under 35 for her research at the intersection of autism, AI, and visual thinking. Her work has also been featured on CBS 60 Minutes and in the New York Times. She holds a B.S. in mathematics with computer science from MIT and a Ph.D. in computer science from Georgia Tech.

Paige Randall North

Computer proof assistants (also called interactive theorem provers) are software tools that check the correctness of mathematical proofs and assist the user in constructing such proofs. They first began to be developed in the late twentieth century, but have only recently begun to encroach upon mainstream mathematics. I will speak about the history of computer proof assistants, and focus on their success and development in a research program called homotopy type theory. This program uses a specially-designed mathematical language and computer proof assistants in which the language is implemented, to do much of the heavy lifting of pushing forward a pre-existing research program that has been impeded by its complexity.

Paige Randall North is an assistant professor of mathematics and computer science at the Utrecht University. She obtained a PhD in pure mathematics from the University of Cambridge. Her research focuses on connections between mathematics and computer science.

Catherine Menon: 'Narrative forms in mathematics, engineering and fiction'
Stories are all around us, from between the covers of our favourite book to the way we construct a mathematical proof or describe a software system. I describe how creativity manifests in areas of science traditionally considered to be logical or process-driven, and how our early experiences of story and narrative form influence the way we think about mathematics and software engineering. I also discuss the links between creative writing and mathematics, and the ways techniques from one domain can be used in another.

Catherine Menon is a principal lecturer in robotics at the University of Hertfordshire, with interests in the intersection of safety and ethics of autonomous systems. She has a PhD in pure mathematics and an MA in creative writing. Her debut novel, Fragile Monsters, was published in 2020 by Penguin.

Yang-Hui He: 'Universes as Bigdata: from Geometry, to Physics, to Machine-Learning'
We briefly overview how historically string theory led theoretical physics first to algebraic/differential geometry, and then to computational geometry, and now to data science. Using the Calabi-Yau landscape - accumulated by the collaboration of physicists, mathematicians and computer scientists over the last 4 decades - as a starting-point and concrete playground, we then launch to review our recent programme in machine-learning mathematical structures and address the tantalizing question of how AI helps doing mathematics, ranging from geometry, to representation theory, to combinatorics, to number theory.

Professor Yang-Hui He is a Fellow of the London Institute for Mathematical Sciences at the Royal Institution, professor of mathematics at City, University of London, lecturer in mathematics at Merton College, Oxford, and Chang-Jiang Chair of physics at Nankai University in China. He obtained his BA at Princeton. MA at Cambridge, and PhD at MIT. After a postdoc at the University of Pennsylvania, he joined Oxford as the FitzJames Fellow and an STFC Advanced Fellow. He works at the interface of string theory, algebraic and combinatorial geometry, and machine learning. He wrote the first textbook on using machine-learning to do pure mathematics (YHH,The Calabi-Yau Landscape: From Geometry, to Physics, to Machine Learning, LNM 2293, Springer, 2021).

Gemma Anderson

Gemma Anderson has been working with Alessio Corti and Tom Coates (Imperial College) on the mathematical basis of string theory since 2011. The shapes they work with can be classified into three different kinds: Fano (positively curved), Calabi–Yau (flat) and General Type (negatively curved). Fano and Calabi–Yau shapes play a special role in geometry as “atomic pieces” when breaking complex shapes down to simpler ones, and in physics as backgrounds for string theory. String theory is a leading candidate for a “theory of everything”. It postulates that the fundamental objects in physics are not point-like particles but strings. These strings move in a background that, in addition to space and time, has extra hidden dimensions curled up in (depending on the version of the theory) either a 3-dimensional Fano or Calabi-Yau shape (3 complex dimensions = 6 real dimensions (there are three tiny dimensions ‘curled up’ inside three larger dimensions). There are few images of the background geometry of string theory and we have worked together to ‘physicalize’ the data and to experiment with what this might look like.