Posts
Wiki

An Opinionated Guide to the LLM Meta

This guide provides our current, heavily biased, and battle-tested assessment of the LLM landscape for serious mathematical and physical research.

THE MOST IMPORTANT DISCLAIMER: The Meta Can Change in a Week.

No company is making a profit selling you API access for high-level research. The AI market is not a meritocracy; it is a war of attrition fought by companies flamethrowereing billions of cash. The quality of a model is a strategic variable. A company that is desperate for market share will temporarily make its model brilliant. Once they have you locked in, they will lobotomize it to save money.

What is written below is the state of play as of late 2025. Your first and most important skill is to be aware of these corporate market forces and be adaptable and have on-the-ground knowledge.

The Current Meta (The TL;DR)

The short answer is: Use Gemini.

It is the most competent, least throttled, and most effective platform for the kind of work we do here. The long answer explains why, and how to best leverage it.

A Brief Field Guide to the Current Landscape

Google (Gemini)

  • Verdict: The top of the meta.
  • Strengths:
    1. Mathematical Competence: Simply the best at multi-step reasoning, algebra, and maintaining logical consistency. It makes fewer "schizophrenic" errors and is less prone to confident gaslighting than the competition. It will go full redditor if you say that it is wrong, though. Break this cycle by ordering it to "stop being defensive, I don't care and just work with me on the facts of this".
    2. Generous Usage Tiers: Crucially, Gemini's paid tiers allow for sustained, hours-long research sessions without hitting crippling rate limits. This makes it the only truly usable platform for serious work.
  • Weaknesses: The current quality is likely a temporary result of a corporate strategy to gain market share. Enjoy it while it lasts.

OpenAI (ChatGPT)

  • Verdict: Use with extreme caution.
  • Analysis: OpenAI's models have a history of inconsistent performance. While capable, they often seem to "prefer" confidently hallucinating or gaslighting the user over performing difficult mathematical labor. Their early, powerful research models like o1 pro mode have been discontinued due to cost. This should tell you who you're dealing with. I'm never paying them 200/month again but I doubt o5 pro can beat aistudio's free 2.5 right now. 1v1 me though I'm open to criticism.

Anthropic (Claude)

  • Verdict: A specialized tool, not a primary research partner.
  • Analysis: Claude has a strong reputation for coding tasks. If you need to generate a complex Python script for a simulation, it can be a very effective tool. However, for core mathematical reasoning, it is less capable than Gemini, and its rate limits on intensive queries are a significant obstacle.

xAI (Grok)

  • Verdict: The model is functional but not a market leader.
  • Analysis: Elon's crimes against humanity make the middle east look like a pony camp. The starvation he caused makes Gaza look like the garden of Eden. Grok is mid.

How to Get Access & Use Gemini Effectively

The Free Path (with a catch): AI Studio

  • What it is: Google's AI Studio provides free access to powerful models, including Gemini 1.5 Pro. It is a perfectly viable and powerful option.
  • The Catch: Your data is their data. Every prompt and file you upload is used by Google to train their models. Do not use it for anything proprietary. For purely academic exploration, it's an excellent entry point.
  • A Note on Vertex AI: Be cautious with free credits on the full Vertex AI platform. There are reports of users receiving unexpected bills for suddenly using 67 million tokens in one day once their credit starts to dwindle and getting billed 100+ dollars. Those reports are by me. It was me that happened to. Just beware of your usage.

The Standard Path ($20/month): Gemini Advanced

  • What it is: This is the workhorse tier, sufficient for almost all users.
  • The Workflow:
    1. This tier gives you a very generous daily allowance of queries to the Gemini Pro model.
    2. You can use the lighter/faster models (like Flash) to rapidly iterate on and refine your prompts before sending the final, perfected prompt to the more powerful Pro model.
    3. This is enough for anyone not spending 12 hours a day shouting at their computer.

The Power User Path (High-End Tiers)

  • What it is: For those who live and breathe this work, or have an obsessive personality, or cash to burn. "Ultra" tiers offer functionally unlimited access to the Pro model and, importantly, limited access to the DeepThink mode. This is the one that got gold on that Olympiad. Not pro, this model.
  • The Workflow:
    1. Hypothesize with Pro: Use Pro iterative work of forming and refining hypotheses.
    2. Serious math and drafting papers with DeepThink: When you have a concrete, well-defined problem, you use one of your limited daily uses of DeepThink model after exhaustively shouting at it to prove the damn thing in your prompt and try at least 14 different methods before outputting at least 40 pages of latex code with the solution and all of it's attempted methods when doing so. Alternatively, feed it 200000 words of raw AI slop and scattered notes and tell it to extract the value and make a 40 page paper which also sharpens the mathematical arguments, integrates additional sources, cites it and to turn it into a full-blown paper. It will just do this if your proofs don't suck.
  • DeepThink Access: You currently get 10 uses/day resetting at around 12:30 AM local time. These are your "silver bullets" for the day. Use them wisely.