Contact

01Wolfbone

Mathematical thought, across media.

A research project for exploring and constructing mathematics through connected representations. Follow an idea, inspect its relationships, and build something you can reason about.

StatusIn development

Talk to the team
One object, three ways to see itAn object f at the left is joined by hairlines to three forms of itself: an arrow diagram that maps 1 to a, 2 to b and 3 to a; a two-column table of x and f(x) with the same three rows; and the equation f(1) = a.f123abxf(x)1a2b3af(1) = aobjectdiagramtableequation
One object, three ways to see it.

What changes when you can work with an idea in more than one form?

A diagram can reveal a relationship. A table can make every case explicit. An equation can express a pattern compactly. Wolfbone asks how these ways of thinking can stay connected as you explore and construct mathematics.

The function f from A to BCollection A holds 1, 2 and 3. Collection B holds a and b. Arrows map 1 to a, 2 to b and 3 to a. Every input has exactly one output.123abAB
Illustrative example. Both views describe the same finite mapping.

What the workspace does.

  • Explore the connections.

    Move through a library of mathematical ideas with original explanations, named relationships, and source references. A searchable index of mathlib declarations connects the library to formal mathematical literature.

  • Construct something precise.

    Create labelled finite collections, define a function by assigning each input an output, and compose compatible functions. Start with objects small enough to inspect in full.

  • Inspect what holds.

    Compare finite functions input by input. When they differ, inspect a particular disagreement. Move between table and diagram, and keep your work through browser storage and file export.

A first medium for a larger question.

The current local workspace brings the mathematics library and editable finite constructions together.

Status
In development
Repository
Private
Public release
MIT-licensed release in preparation
Checks
Finite mappings, evaluated directly
Formal proof checking
Future work
Translation between systems
Future work
mathlib
A source index, not a connected proof engine

Help shape a medium for mathematics.

We would like to hear from mathematicians, educators, researchers, and people who think through making. Tell us which ideas you want to explore, and what your current tools make difficult.

Start a conversation