Boston Colloquium for Philosophy of Science

Mathematics with a Human Face
Presented by the Boston Center for the Philosophy and History of Science
Co-Sponsored by the University of Bergen’s Norwegian Research Council Grant

Abstract
How important are creativity and the human element to mathematics? In an age of AI and progress in automating proofs, these questions arise. To ask philosophically, we need to include a characterization of actual mathematical practice, and not exclude the cultural, linguistic, pedagogical, computational and conceptual development of mathematics within wider historical and social contexts. The question of the human as mathematician is emblematic for our time, when larger philosophical and cultural questions about the automation of human labor become increasingly central. Is human bias something to be celebrated or eradicated? What is the relation of mathematics to cultural concerns and values? Can we learn from confronting its history in terms of the present?

In 1947, in his Lecture to the London Mathematical Society, Alan Turing raised the question explicitly:

The Masters [i.e., mathematicians] are liable to get replaced because as soon as any technique becomes at all stereotyped it becomes possible to devise a system of instruction tables which will enable the electronic computer to do it for itself. It may happen however that the masters will refuse to do this. They may be unwilling to let their jobs be stolen from them in this way. In that case they would surround the whole of their work with mystery and make excuses, couched in well-chosen gibberish, whenever any dangerous suggestions were made. I think that a reaction of this kind is a very real danger.

There are many philosophical questions embedded in Turing’s remark, which was not simply a throwaway, but a prescient observation about what he elsewhere called “The Cultural Search”, which he believed would become increasingly important over time, and include “the human community as a whole” (1948, “Intelligent Machinery”). In this one-day event philosophers, mathematicians, logicians, historians and computer scientists will take stock of the issues.

Schedule
Monday, April 22
All events to take place at Barristers Hall, BU Law School
765 Commonwealth Ave, Boston, MA 02215

9:30am-10:00am Breakfast

Part I: Mathematics: Concepts, Languages, Arts and Cultures

10:00am-10:55am
“Innate Arithmetical Knowledge: A Look at the Empirical Evidence,” Sorin Bangu (University of Bergen)

11:00am-11:50am
“Max Dehn and Mathematical Late Modernism,” Philip Ording (Sarah Lawrence College)

12:00pm-1:00pm Lunch

1:00pm-1:55pm
“Mathematical Hygiene,” Andy Arana (Université de Lorraine, Archives Henri-Poincaré)

2:00pm-2:55pm
“The Technological Sublime,” Juliette Kennedy (University of Helsinki)

3:00pm-3:15pm Tea break

Part II: Automating Mathematics
Moderator: Assaf Kfoury (Boston University)

3:15pm-4:00pm
“Will AI’s Ever ‘Do Math’?”
David Mumford (Brown University & Harvard University)

4:00pm-4:45pm
Comments: Michael Harris (Columbia University)

4:45pm-5:15pm
Closing discussion