Thinking Hard Above AI
The author argues that large language models are cultural and social technologies that allow mathematicians to interact with accumulated knowledge through a new interface. By treating AI-generated proofs as a baseline rather than a final conclusion, researchers can engage in 'mathematics above AI' to seek deeper understanding and simpler explanations. This approach helps avoid the accumulation of mathematical technical debt while leveraging AI to accelerate the discovery of elegant arguments.
- ▪Large language models are described as interactive games that let users play with voices from the accumulated cultural conversation rather than acting as truly intelligent agents.
- ▪The author defines 'mathematics above AI' as the process of using AI-generated answers as a starting point to search for more canonical or obvious proofs.
- ▪AI tools have recently demonstrated the ability to solve complex mathematical problems, including a seventy-year-old conjecture in topology and set theory.
- ▪Treating AI outputs as a second step in literature review helps researchers avoid flooding the mathematical community with undigested or poorly written content.
- ▪The goal of this new mathematical activity is to find the simplest explanation and the right level of abstraction for a phenomenon, going beyond what the AI initially provides.
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Story provenance
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Record
| Original publisher | Merlin's Notebook |
| Canonical URL | https://bmbumpus.com/2026/09/16/thinking-hard-above-ai/ |
| Publication time | Thu, 17 Sep 2026 06:34:32 +0000 |
| Retrieval time | 2026-09-17T06:43:41.603Z |
| Last seen | 2026-09-17T06:43:41.603Z |
| Headline source | Publisher (no WeSearch rewrite) |
| Excerpt source | publisher body |
| Excerpt method | First ~120 words (~800 chars) of extracted publisher body, fair-use limited. |
| Summary | WeSearch · cerebras-chat (WeSearch summarizer) |
| Summary source text | contentText |
| Citation coverage | Summary is a WeSearch-generated derivative; primary citation is the original publisher URL. |
| Cluster | EPLLBCot_BaD · 1 stories |
| Cluster logic | Grouped by semantic title/content similarity across sources within a rolling window. Same-publisher template collisions are excluded from coverage comparison. |
| Ranking reason | Story pages are not engagement-ranked. Hub feeds use recency, with optional source-diversified chronological ordering (cap consecutive stories per source). No personalized ranking. |
| Publisher visit | Yes — open original |
| Substitutes article? | No — link-out required for full text |
Rights status (four layers)
WeSearch handling by dimension
| Indexing | May the item be indexed (stored, ranked, made findable)? | Allowed |
| Snippet | May a short excerpt of the publisher's text be shown? | Allowed |
| AI summary | May WeSearch generate its own short summary of the article? | Limited |
| Retrieval / RAG | May the content be exposed for third-party retrieval-augmented generation? | Not asserted |
| Model training | May the content be used to train AI models? | Not asserted |
| Commercial reuse | May the content be reused commercially? | Not permitted |
Basis: Derived from the published RSS/Atom feed. Contact: [email protected]. Reviewed: 2026-07-24.
Opening excerpt (first ~120 words) tap to expand
Thinking Hard Above AI September 16th, 2026 It’s interesting to ask mathematicians about why they do mathematics. Some tell me that it’s a pursuit of truth. Others seek understanding. Occasionally there’s an admission of the pursuit of glory. My personal claim is that I’ve always wished to have a voice and to contribute to The Great Conversation, the sharing of thoughts, insights and perspectives with all those around me and who came before me. The question now is: “What’s this have to do with AI?”. Well, recently I read an article by Henry Farrell, Alison Gopnik, Cosma Shalizi and James Evans that awoke me to an obvious fact — one I think deliberately obscured by AI companies — about what LLMs actually are. They are not “..intelligent agents but ..
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Excerpt limited to ~120 words for fair-use compliance. The full article is at Merlin's Notebook.
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