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Open problems in number theory and calculus, AI math breakthrough guides, calculus milestones, and honest explore prompts. # AI Math Kit — Open problems. Explore honestly. **Short description** Number-theory open problems + AI math breakthrough guides + honest explore prompts—in one Chrome popup. **Detailed description** Curious about Goldbach, Collatz, twin primes—but papers feel unreachable? Want to follow recent AI / formalization breakthroughs without knowing where to start? AI Math Kit packs open puzzles and frontier guides into a single Chrome popup. No new tabs, no folder diving—click the toolbar and explore. The problem bank has 217 plain-language entries: number-theory open problems (A–F, after R. K. Guy’s *Unsolved Problems in Number Theory*), classic calculus puzzles (G), obscure number theory (H), and cross-field open mysteries (I, from Riemann to P vs NP). The AI Breaks tab offers plain-language intros with formalization scope notes and paper hints. Explore gives prompt templates plus an honesty charter—AI is great at metaphors; it should not casually “prove” open conjectures. **Why AI Math Kit** • Three jobs, one popup: Problems · AI Breaks · Explore • 217 plain-language math problems (NT A–F, calculus G, obscure NT H, mysteries I), filterable by chapter • 242 AI / formalization breakthrough guides (scope notes + paper hints) • EN · ZH · JA UI; breakthrough copy ships in three languages • Payment status cached locally (15 days if paid / 7 if unpaid) to cut ExtPay API pulls • Privacy-minded: prefs and payment cache stay on-device **Problems (search · chapters · copy prompts)** Six chapters of classic open questions: Primes · Divisibility · Additive number theory · Diophantine equations · Integer sequences · Miscellaneous Each item has a one-liner, plain expansion, tiny example, and “why hard.” Pro unlocks full depth and per-problem AI prompts. **AI Breaks (frontier · plain · checkable scope)** Guides around recent formalization / AI-assisted math: quasi-Riemann-style statements, convex geometry, embeddings & energies, cones… Lists are browsable; deep detail, precise scope, and paper hints unlock with Pro. Guides orient you—papers and formal texts remain the source of truth. **Explore (prompts · method · honesty)** • Flow: pick a problem → copy prompt → demand examples first → honesty check • Templates: explain plainly · mini experiment · check my idea · compare known progress • Starters: Collatz, Goldbach, twin primes, and more • Charter: don’t treat AI drafts as theorems; don’t announce fake proofs **Free vs Pro (one line)** Free: install and browse chapters plus a starter set. Pro: full problem depth, breakthrough details, and prompt templates. **How to use** 1. Click the toolbar icon 2. **Problems** — filter by chapter or search; Pro copies tailored prompts 3. **AI Breaks** — skim guides; upgrade for scope notes and full write-ups 4. **Explore** — copy templates into your usual AI, explore honestly 5. Settings — language, upgrade Pro, or force-refresh payment status **Who it’s for** Anyone curious about open math · people who want AI as a tutor, not a fake prover · readers following formalization / AI-math progress · anyone tired of opening ten tabs for one explainer **Languages** English · 中文 · 日本語 **Notes** Popular guides for exploration—not a substitute for the book or papers, and not a claim that AI proved an open conjecture. Settings and payment cache stay local. Pro is an optional in-app purchase (ExtPay).