The community's anxiety

We knowsuspect that applied category theory is powerful stuff, capable of immense good as well as immense harm. Also, as Grothendieck's spirit permeates the field, it has attacted people who are aware of the ethical imperatives of survival and the promotion of a stable and humane order on our planet (Jackson, p. 1202). How do we reconcile our love of mathematics with our deep ethical sense?

Lawvere's prophecy is an older (1992) answer to this question: do math which clarifies dialectical philosophy, which will in turn inform efforts to build a better society.

Jade Master made waves in the ACT community in 2020 with her public refusal to take military money, an echo of Grothendieck's protest against the IHÉS. There have been many debates in the community after this about the possibility of ACT being used for harm.

John Baez has great thoughts on this question in his fundamental 2021 talk Mathematics in the 21st century (slides). He says mathematicians should:

Baez has done all three of these things in his own life. He hesitates to fly to conferences, didn't have children, ran the Azimuth Project, which compiled information about the climate crisis, and now is working on agent-based models, with application to epidemiology and public health.

A secret society?

Given the potential power of applied category theory, it wouldmight seem reasonable to restrict access to a secret society, where we vet people for moral character before allowing them to learn category theory. After a lifetime of extreme openness and clarity, Grothendieck attempted to restrict access in an extreme way in 2010 through his Déclaration d'intention de non-publication. This was not very effective, as his work was already foundational for so much mathematics.

Today, applied category theorists again practice extreme openness, writing great expository texts like Seven Sketches in Compositionality which will aid anyone who puts in the effort in learning category theory, to good purpose or ill. Why?

The general mentality is that we are in a global crisis, and the benefit of getting category theory out quicker to those who will use it for good is worth the cost of also getting it out quicker to those who will use it for ill.

It is important that we use it for good quicker than others can use it for ill.

What are the main barriers to that?

According to Lawvere's prophecy, to apply category theory to X requires that category theorists learn X and experts in X learn category theory. However, learning category theory requires years of study, and it is the rare institutional structure that will fund an established expert to learn an entirely new field from the ground up. Similarly, to learn X on a deep enough level to apply category theory to it requires a lot of time, and it is hard to justify to institutions.

Another important danger is that as the ACT community grows, it will accrue people who are not attuned to the guiding philosophy, instead merely working on existing abstractions, the same way that one could work on existing abstractions in any mathematical subfield. In this way ACT will become institutionalized, losing its specialspecific philosophical, ethical, and spiritual character.

Finally, it is difficult to get funding for ACT as it is meant to be practiced. Funders generally want to see immediate relevance, and are not interested in the kind of long-term study necessary for ACT to thrive. The ultimate solution to this is to become independent from large sums of money, by living simply in a mathematical monastery similar to the Nesin Maths Village. Math requires little else but pencil and paper, so it is ideally suited to an inexpensive monastic lifestyle. This was the original impetus behind the Let Me Think project (theorizing, first trial). There is also a trial run of a mathemematical monastic environment called Learning Being (no public announcement) being conducted this year (2024).