Post #2920381

2026-05-13 12:33 UTC

@wikiemol@mathstodon.xyz Problem solving and theory building are in fact highly synergistic. I can continue the food analogy with this quote from Erdos, often regarded as a quintessential "problem solver": "A well-chosen problem can isolate an essential difficulty in a particular area, serving as a benchmark against which progress in this area can be measured. It might be like a 'marshmallow', serving as a tasty tidbit supplying a few moments of fleeting enjoyment. Or it might be like an 'acorn', requiring deep and subtle new insights from which a mighty oak can develop." To continue the analogy further, current levels of AI technology are like blenders that can now produce significant amounts of paste consisting of both ground up marshmallows and ground up acorns, which can score well on such benchmark metrics as edibility, nutrient value, and digestibility, yet remain distinctly unappetizing. As the technology improves, the flavor and acorn content of this paste may get better, but - as you say - this is still insufficient to generate oaks. Nevertheless, I do not believe that the solution to this issue is to ban blenders and food processors, or decry them as evil, but to view them as highly situational tools for cooking - very useful in certain scenarios, when used responsibly, but wholly inappropriate for use in others. Furthermore, the culture of racing to be the first to produce an edible substance will need to be de-emphasized in favor of a more holistic approach to the broader objectives of sustainable food production, preparation, and cultivation.

Replies (1)

@wikiemol@mathstodon.xyz 2026-05-13 14:38

@tao@mathstodon.xyz Thank you for the articulate response. I wholly agree, but want to emphasize this point > very useful in certain scenarios, when used responsibly, but wholly inappropriate for use in others I think the main issue that I see is that there is a huge gap in the average person's knowledge about which uses of AI are inappropriate. I think this is a combination of two things: 1. Positive use cases are easier for media to pick up than negative cases. (This is a point you've made many times in the past) 2. There does not seem to be sustained focus from prominent researchers in mathematics on ironing out the limitations of AI on a theoretical level. It is this second point that I most lament, because I think it is the area where mathematicians can be most beneficial for AI development, in the same way that Godel effected the computer revolution. And it seems there are a lot of 'low hanging fruit' in this area based on classical logic and classical information theory alone. Let alone utilizing more modern ideas. Here is a short 'heuristic' example of the kind of thing I am talking about: when one examines AI's behavior with respect to an inquisitive form of the Liar's paradox. "Are you going to give a negative answer to this question?" An AI will correctly answer that this is a paradoxical question, but if you further ask it what the true answer was, it will hallucinate. A human, on the other hand, will be able to know what the true answer to the question will be before they even answer, let alone after the fact. To me it seems that making this formal lies just outside of 'standard' logical theories, and requires non-standard ideas like Inquisitive semantics and non-well founded logic.

Open ##2920382