The Atlas

Interactive research maps spanning mathematics, empirical science, and the humanities. Open problems, established results, and reasoning connections — across 300 subfields.

300 Subfields

5,794 Open Problems

1,927 Papers Scored

8 Interactive Atlases

🌐 The Complete Map

Everything in one view.

The Unified Atlas

ALL 300 SUBFIELDS

Every open problem and established result from all three domains — mathematics, empirical science, and humanities — in a single interactive graph. The complete map of contemporary research frontiers.

📊 547 KB interactive page 🔍 Search across all domains 🔗 Cross-domain connections visible

❓ Open Problems

What we don't know yet — organized by domain.

Open Problems — Mathematics

100 subfields of mathematics with their unsolved problems. From algebraic geometry to combinatorics, number theory to topology. Each problem includes context, prior approaches, and potential pathways.

📐 100 subfields ❓ ~2,000 open problems

Open Problems — Empirical Sciences

100 subfields of empirical science with their open questions. Physics, biology, chemistry, neuroscience, climate, medicine, and more. Where the frontiers are and what's blocking progress.

🧪 100 subfields ❓ ~2,000 open problems

Open Problems — Humanities

100 subfields of humanities and interpretive disciplines with their unresolved debates. Philosophy, linguistics, history, political theory, aesthetics, ethics, and cognitive science.

🏛️ 100 subfields ❓ ~1,800 open questions

✅ Established Results

What we do know — the proven, verified, and consensus results.

Results — Mathematics

Landmark theorems, proofs, and established results across mathematical subfields. The proven foundations that open problems build upon.

📐 Mathematics ✓ Verified results

Results — Empirical Sciences

Established findings, replicated experiments, and scientific consensus across empirical disciplines. What we know with confidence.

🧪 Sciences ✓ Established findings

Results — Humanities

Scholarly consensus, landmark arguments, and established interpretive frameworks across humanities disciplines.

🏛️ Humanities ✓ Consensus positions

🧠 Reasoning Engine

How results connect — proof search across the whole corpus.

The Reduction Atlas

Proof search across the entire corpus. Maps logical dependencies, reductions, and inferential connections between results. Shows which problems reduce to which, which results enable which proofs, and where the critical dependencies lie.

🔗 Cross-domain connections 🧩 Reduction pathways 📊 166 KB interactive

The Reasoning Engine

The brain on top of the map. Three capabilities: counterfactual surgery (if we solved X, what else falls?), probability estimates with real sources, and self-audit (does the map contradict itself?). Cross-field bridge finder spots a proven tool in one domain sitting next to an unsolved problem in another.

⚡ 688 KB interactive 🔍 Bridge finder 🧮 Counterfactual surgery

Live recursive decomposition of human ignorance. 5,794 wishes across 3 levels, 90 shared walls blocking multiple problem areas, 619 hubs referenced across domains. Interactive visualization of the topology of what we don't know.