Does a mathematical claim hold? Check proof gaps and counterexamples
Supply a statement, definitions and assumptions to draft proof steps, counterexample searches and unresolved gaps for expert checking.
Execution environment and usage
AI / software
Gemini
Where to operate
The Gemini web-chat input; this version requests a text draft.
Getting started
- Open an eligible account at gemini.google.com and start a chat without connecting external accounts.
- Prepare a precise statement, definitions, allowed results and a person able to check derivations.
- Request the draft/check and compare it with the original material. Suggestions are not evidence of execution.
Setup and plan requirements
Task inputs: Prepare a precise statement, definitions, allowed results and a person able to check derivations. Use an eligible tool that can read the supplied format; verify parsing, context limits and access before relying on it.
Prompt portability limits
The written request can be adapted to a chatbot that accepts the same input. It does not transfer the original agent, plugins or computer permissions.
Usage limitations
Provide precise definitions, allowed results and a qualified reviewer; finite tests and incomplete derivations are not proofs.This independent pass reviewed local case records, without revalidating original sources or hands-on testing.
Environment sources
適用情境 / When to use
Supply a statement, definitions and assumptions to draft proof steps, counterexample searches and unresolved gaps for expert checking. Provide precise definitions, allowed results and a qualified reviewer; finite tests and incomplete derivations are not proofs. Original case: DeepMind describes Aletheia using generation, verification and revision for mathematical research problems.
步驟 / Steps
- Prepare a precise statement, definitions, allowed results and a person able to check derivations.
- Develop proof ideas and counterexample searches separately, identifying the basis for each step.
- Verify citations and special cases manually; label incomplete work as partial or unresolved.
提示詞 / Prompt
Examine [statement, definitions and assumptions] by exploring both proof and counterexamples. Mark established results and unresolved steps, with verifiable citations, within [time/resource bounds]. Clearly label incompletion; never present finite tests, conjectures or self-assessment as proof.
留意事項 / Cautions
- Successful numerical tests are not general proofs.
- Model self-assessment does not replace expert or formal checking.
來源限制 / Evidence limits
This vendor report concerns a specialized research system, not equivalent capability in an ordinary chat interface or guaranteed solutions.
流程說明 / Workflow note
These steps and prompts are original, untested exercises by this site, not the author’s verbatim workflow. Reported results do not guarantee exercise outcomes.
原始工具組合 / Original tool stack
Aletheia research agent; Gemini Deep Think; natural-language verifier; Google Search
Source publication date: 2026-02-11
Source checked: 2026-10-19
Accelerating Mathematical and Scientific Discovery with Gemini Deep Think