Summary of Apriori Knowledge in An Era Of Computational Opacity: the Role Of Ai in Mathematical Discovery, by Eamon Duede and Kevin Davey
Apriori Knowledge in an Era of Computational Opacity: The Role of AI in Mathematical Discovery
by Eamon Duede, Kevin Davey
First submitted to arxiv on: 15 Mar 2024
Categories
- Main: Artificial Intelligence (cs.AI)
- Secondary: Human-Computer Interaction (cs.HC); History and Overview (math.HO)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper explores whether it’s possible to acquire prior knowledge of mathematical facts through computer programs. Building on arguments made by Burge, the authors discuss how certain programs, like Appel and Haken’s work on the Four Color Theorem, can facilitate human-like mathematical reasoning. However, they claim that modern Large Language Models (LLMs) and Deep Neural Networks (DNNs) are opaque, making it difficult to obtain prior knowledge from them in a similar manner. The authors propose attaching proof-checkers to these machines, which would automate human forms of proof-checking, enabling the acquisition of prior mathematical knowledge. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Can computers help us figure out math problems? Some experts say that if we use computer programs to do math, it’s like using a tool to help us think. But what about really smart machines called LLMs and DNNs? These machines are super good at doing things on their own, but they’re hard to understand. The authors of this paper think that attaching special tools to these machines can actually help us learn new math facts. They believe that with these tools, we can use the machines to do math in a way that’s similar to how humans do it. |
