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#mathematics

66 innlegg47 deltakere7 innlegg i dag

A neat little trig relationship arose in class today.

In answering a question some students "panicked" and chucked it into "solve" in their TI Nspire graphics calculator (let's not get distracted by my hatred of such tech) and as part of the solution got:

π/2 - arctan(1/10)

Whereas if one did it (very simply) by hand, this term was:

arctan(10)

One hopes anyone marking this would understand they're the same, but it baffled the students... queue learning moment. 1/n

"In the hopes that these systems are someday released to outside review, here are some questions that we hope some day will be answered.

- How do these systems work and how were they trained? What allows them to do so much better than earlier systems? Do they come with a cost in solving other sorts of problems? In the case of OpenAI-IMO, do the "new techniques" employed at all explain the stylistic weirdness?

- What is the scope of these systems? Do they generalize to other kinds of mathematical problems, to scientific problems, to more general classes of problems? Or can they be extended to deal with these? Or would they be a useful component in a larger system that dealt with these?

- What was the cost per problem, both for inference time (clearly high) and any domain-specific expertise required for training/augmentation etc and what would the economics of using these models be when it is released?

- Are these system compatible with tools such as computational tools, coding, and web search?

- What did the two systems do with problem 6, the one they couldn’t correctly answer? Did they give up, did they produce a partial answer that was in the right direction, or did they hallucinate a nonsensical answer?

Overall, the new work certainly might be exciting. Until outside scientists get to dig for a serious review we won’t really know for sure what it all means."

garymarcus.substack.com/p/deep

Marcus on AI · DeepMind and OpenAI achieve IMO Gold. What does it all mean?Av Ernest Davis