Gemini Deep Think: Redefining the Future of Scientific Research

This post details the application of Gemini Deep Think mode, powered by an agent named Aletheia, to solve professional research problems in mathematics, physics, and computer science. It introduces a math research agent with a natural language verifier and Google Search integration for iterative solution generation and revision. The agent has achieved autonomous solutions to four open questions on Bloom's Erdős Conjectures database and contributed intermediate propositions to further papers. In physics and computer science, the 'Advisor' model with 'Vibe-Proving' cycles and 'balanced prompting' techniques are detailed. Specific breakthroughs include solving 'Max-Cut' and 'Steiner Tree' problems by applying concepts from continuous mathematics, refuting a decade-old conjecture in online submodular optimization with a combinatorial counterexample, explaining an adaptive penalty in ML optimization, extending a 'Revelation Principle' for auctioning AI generation tokens to continuous real numbers using topology and order theory, and finding a novel solution to gravitational radiation integrals from cosmic strings using Gegenbauer polynomials. The post also discusses a taxonomy for classifying AI-assisted mathematics research and highlights the value of AI as a high-level scientific collaborator.