Hey everyone!
I wanted to share a fascinating experience with GPT-4 that could be particularly interesting for those of you involved in the application of AI in mathematical research. Recently, while working on a long-standing conjecture in discrete geometry, I used GPT-4 to aid in tackling some complex patterns and calculations.
The conjecture was related to Voronoi tessellations, and despite numerous attempts by our research team, we had hit a wall. In a bid to explore all possible avenues, I decided to integrate OpenAI’s GPT-4 into our exploration process. We used an API setup on AWS Lambda to ensure our model calls were efficient and cost-effective, especially given the frequent interactions needed for iterative problem-solving.
Interestingly, one of the proposed solutions by GPT-4 pointed us towards a symmetry property we hadn’t considered. After a few tweaks and validations, this led us to a counterexample that disproved the conjecture, redirecting our research towards more promising avenues.
For those interested, GPT-4’s superior natural language processing capabilities allowed us to parse through large datasets and mathematical proofs far quicker than manual analysis could ever accomplish. Additionally, we kept a close eye on API consumption, which roughly totaled $0.002 per token processed, ensuring this project remained within budget.
It was an eye-opener to witness a language model assisting beyond typical NLP tasks, highlighting AI's potential in academic research. I’d love to hear if anyone else has used AI/LLMs in such innovative ways!
Cheers!
This is pretty amazing! I had a similar experience using GPT-4 for algebraic topology research. We were able to reduce the solution time for complex homology problems by leveraging GPT-4 for pattern recognition. No Voronoi tessellations for us though, haha. Anyway, it’s truly remarkable how AI is transforming the research landscape!
Wow, that's a fascinating use case! I've been primarily using GPT-4 for optimizing code and refactoring but never thought about diving deep into mathematical conjectures. Could you share more details on how you set up the AWS Lambda for handling the API requests effectively? I'm curious about the architecture you used.
That's really intriguing! I've been using GPT-4 mostly for generating proof outlines and validating them with the team. It's amazing to hear it led you to a counterexample and a new research path. For Voronoi tessellations, did you find the model's suggestions were mostly valuable in identifying overlooked hypotheses or more in computation-heavy pattern recognition?
Wow, that's fascinating! How did you handle the verification of results generated by GPT-4? I know with mathematical proofs, even minor errors can lead to significant issues. Did you have a human team member cross-verify all the AI-assisted insights, or was there another form of automated validation?
