A practical, foundational question drives our work:

How much of modern mathematics—the kind that appears in today’s journals and powers breakthroughs in science and industry—can be fully generated by a computer program?

Put more humanly: how close are we to software that approaches a solvable mathematical conjecture the way a skilled researcher does—frames it, works through it, and produces a proof, counterexample, or independence result—then explains the reasoning clearly?

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Our Thesis

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1. Model the maker, not just the math.
   AMI aims to meta-model the intellectual process a human mathematician follows when receiving a concrete, solvable conjecture: understand, formalize, search, prove (or refute), and write a human-style explanation.

2. Build on the best of cognitive science.
   The most successful theories of mind are computational at their core. This offers strong heuristic support for formal, computational meta-models of mathematical reasoning—not just crunching numbers, but constructing concepts and proofs.

3. Stand on solid foundations.
   Contemporary mathematics is framed by ZFC set theory, proof theory, recursion, and model theory. If a conjecture has a solution within ZFC, then—at least in principle—its proof can be found by a process that a program can simulate with mechanical, logical deduction.
   AMI starts here: decidable, human-solvable problems where a proof or counterexample exists in ZFC (i.e., where most mathematical practice—and most applications—live). With traction, we extend to independence and undecidability patterns.

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What AMI Will Do

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• Generate human-style solutions to essentially every human-solvable conjecture faster than an average professional mathematician, including formal proofs/counterexamples and readable explanations.

• Translate mathematical insight into impact across domains—where many “interdisciplinary” problems are, in reality, mathematical bottlenecks awaiting the right formalization.

• Progressively handle independence results, offering human-style meta-reasoning for conjectures that lie beyond ZFC (a later-stage focus).

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Evidence So Far

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We’re not starting from zero. Our research has already co-discovered new structures and refined existing theories with the help of programs that simulate analogy-making and conceptual blending:

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• Number Theory & Algebra: Refactorable Numbers; Multiplicative (Containment–Division) Rings; (quasi-)integers and (quasi-)complex numbers; prime ideals over Dedekind domains.

• Field & Galois Theory: Artificial generation of core notions—fields, field extensions, automorphism groups, and meta-Galois groups.

• Axiomatizations: Partial axiomatizations for the integers; for commutative rings with unity under compatible divisibility; and for Goldbach rings.

• Cognitive Engines: Software prototypes that simulate analogy and conceptual blending in early-stage theories—core capabilities AMI will industrialize.

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For technical details and publications, see: www.DAJ-GomezRamirez.com

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Why This Really Matters—Humanly and Economically

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Mathematics sits at the heart of drug discovery, energy systems, finance, logistics, climate modeling, and secure infrastructure. Yet the world’s hardest problems still rely on small teams and long timelines. AMI is a path to:

• Compress Research&Development cycles by orders of magnitude.

• Expand the frontier of solvable problems—not by replacing researchers, but by amplifying them.

• Make advanced reasoning explainable, so decisions are trusted, auditable, and aligned with ethical standards.

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Our Ethos

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This project is ultimately about human capability. We believe in transparent, explainable reasoning, rigorous evaluation, and ethical governance that aligns scientific progress with real societal benefit. AMI isn’t just about faster proofs—it’s about turning deep understanding into better choices for people, institutions, and the planet.