ESHS/HSS Annual Meeting

“A Fragile and Precious Heritage”: Mathematics Research in the Age of Machines

• In Event: CTRL ALT SHIFT. Expériences, Knowledge, Activism, Methods - 2

English Abstract

The use of AI in contemporary mathematical research is currently the subject of exuberant claims, and of significant external investment on a scale dwarfing more traditional government funding. Some extraordinary results are being achieved, especially with the use of mathematically enhanced LLMs, and many see tremendous potential for further impact. Some practitioners are convinced AI will be transformative; some are sceptical; and many are apparently unaware of the debate.
We frame the present moment by looking at how computation emerged very early as a tool for research in pure mathematics, making major and indispensable contributions to the twentieth century mathematical challenge of classifying finite simple groups.
Some of the first non-numeric computations on early machines, such as the work of Max Newman, involved studying groups which could be represented as binary strings. Initially researcher access was limited to scarce government funded machines, with terse papers stating results but giving little hint of how they were obtained. Later, some leaders in the field advocated for the importance of mathematicians’ hands-on involvement in developing and maintaining algorithms and code, to ensure transparency, reproducibility and sustainability of the software effort. These teams pioneered the development of what we would now call open source software, early recognising the need for models of governance, reward and recognition for those so engaged. While some were opposed to this democratisation, this model of infrastructure has become increasingly important in mathematics research with systems such as GAP and Sage released under the GNU public license and widely used around the globe.
With the advent of opaque black-box modern AI systems questions of transparency, reproducibility, sustainability have a new salience, yet it is unclear if the mathematical community would have the capacity to sustain production and governance of an open-source alternative.

Author

• Ursula Martin, University of Oxford