Summary of Considerations on Approaches and Metrics in Automated Theorem Generation/finding in Geometry, by Pedro Quaresma (university Of Coimbra) et al.
Considerations on Approaches and Metrics in Automated Theorem Generation/Finding in Geometry
by Pedro Quaresma, Pierluigi Graziani, Stefano M. Nicoletti
First submitted to arxiv on: 22 Jan 2024
Categories
- Main: Artificial Intelligence (cs.AI)
- Secondary: Logic in Computer Science (cs.LO)
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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 research paper explores the properties required for automated reasoning programs to generate new and interesting theorems in geometry, a significant goal in itself. The authors address the challenge of separating trivial facts from valuable insights by discussing different approaches and metrics for discovering geometric theorems. A key finding is that determining whether an algorithmic procedure can produce interesting theorems is undecidable, rendering it a non-deterministic task. To overcome this hurdle, human experts must survey existing work on theorem provers and metrics for evaluating interest in geometric theorems. The paper concludes by outlining the structure of two surveys and suggesting future research directions. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The researchers are trying to make computers better at finding new math problems that are important and interesting. They want to create a computer program that can find these problems on its own, but it’s hard because there might be many unimportant problems mixed in with the good ones. The paper talks about different ways that scientists have tried to solve this problem, including using special metrics to measure how interesting a math problem is. One important finding is that it’s impossible for a computer program to perfectly decide whether a math problem is interesting or not. So, instead of relying on computers alone, the researchers think that human experts should be involved in evaluating the importance of these problems. |
