The software field is in a knot-twist about AI; but the people who are doing some of the best thinking about the impacts of AI are mathematicians.
(Note: I’m going to use AI here because it’s the parlance of the times. I continue to be very frustrated by the terminology flattening caused by continuous use of the term AI -- the difference between LLM, agent systems, generative video and image systems, audio processing, transcription, virtual manipulation and ink detection, and more is enormous, but we flatten everything into a single pair of characters: AI. This lack of nuance makes us weaker as a society, but for the purposes of this post, I’ll take the battle as lost.)
The famous mathematician and talented communicator Terence Tao has been leading the charge, or so it seems, on thinking through some of this. He has invited mathematicians to write guest posts on his blog, a good number of which I have read. I quite enjoyed “What should we tell our students”, especially the metaphor of the "polytope-of-ideas". Math is moving fast, but watching experts in the field have serious conversations about the field has been fascinating.
Yesterday Dr. Tao posted slides to a lecture Math 2.0. He highlights the change from a history of math where proofs were scarce to one where proofs were abundant, the challenges of recognizing the boundaries of the field and how AI helps and how it doesn’t.
The thing that I want to note more than anything is his model of problem solving: The ability to produce a verified artifact in pure mathematics without involving humans bypasses human understanding, and reduces ultimately the ability of humans to produce good results in the world of applications.
Human endeavour is ultimately just that: Human. I suspect the inhumanity is why people react so poorly to AI art and why art seemingly has to show it is human now. The challenge faced by so many fields now is going to be redrawing the lines: Where augmentation is legitimately helpful and where it starts to sap the human endeavour. Different fields will draw these lines differently: It seems likely to me that painters probably won’t land on the side of ‘lots of augmentation’ -- but other fields are going to have to walk this line.
Even the humanities will need to walk these lines. A recurring theme many fields are discovering is: “ChatBot: Solve My Problem” is rarely the thing -- instead, many fields are discovering that these tools are augmentations for those with expertise, and horrible preemptive amputations for those who do not yet have expertise.
The bottleneck will soon become not research findings themselves, but the attention of experts in niche topics.
At the end of the day, each field needs to figure out: what exactly is the endeavour? Math is discovering (or reminding itself) that it’s not proofs. For other fields, the answers here will be diverse -- and so too will be level of augmentation.
In my own field, the answers will be incredibly diverse! For some programmers the endeavour is the programming, the code is the art, and for them no level of AI augmentation will be acceptable. For others, sometimes the code isn’t art -- it’s a means to an end, a disposable artifact to serve some other need. For those programmers, AI can be a helpful augmentation, reducing tedium and allowing one to focus on the actual task at hand.
In 2023 I wrote about Crossing an AI Rubicon. The world has only gotten stranger in every possible dimension since then. On the AI front, we’re all having to grapple with what it means for these strange tools to exist.
I just hope that more fields can find their Terence, and navigate this time with care and compassion.