Semioscape.org is a "concept cartographer" -- an app that maps out concepts and their associations -- except you don't make the concept associations -- they're done with AI, more specifically using the Claude (Anthropic) API.
To give it a whirl, I punched in... (oh, you all know what's coming... yes I did...) "mathematical proofs".
It came back with: Axioms, Deductive Reasoning, Logical Connectives, Counterexamples, Theorems, Lemmas, Induction, Contradiction, Formal Logic, and Rigor.
For each of these, it gives me 3 options to generate more associations: "General", "Concrete", and "Abstract".
I clicked "General" and it gave me: Postulates, Logical Inference, Consistency, Independence, Completeness, Abstraction, Deductive Reasoning, Foundational, Intuition, and Formal Systems.
I clicked "Concrete" and it gave me: Postulates (again), Logical Inference (again), Deductive Reasoning (again), Geometric Constructions, Foundational Assumptions (again), Self-Evident Truths, Logical Consistency, Formal Systems (again), Logical Symbols, and Abstraction (again).
I clicked "Abstract" and it gave me: Logical Consistency (again), Deductive Reasoning (again), Abstraction (again), Completeness (again), Independence (again), Minimalism, Formal Systems (again), Intuition (again), Rigor (again), and Foundations (again).
Hmm. Maybe "mathematical proofs" wasn't the best topic to start with as it doesn't lend itself to general/concrete/abstract distinctions.
I went to "Deductive Reasoning" and clicked "General". It gave me: Axioms, Logical Inference, Syllogism, Modus Ponens, Contrapositive, Proof by Contradiction, Transitive Property, Logical Connectives, Quantifiers, and Formal Logic.
I went on to click a whole lot more -- the whole first layer -- but I'll stop here describing it to you all. Hitting the "save" button gave me a JSON download, so I can get that to you if you want it.
Overall, I'd say this tool works as advertised. I picked a starting point ("mathematical proofs") and it gave me a map of related terms and short descriptions of what they mean. Well, after expanding out the first layer. A great way of getting a map of all the concepts related to mathematical proofs. Nice.
