Theorem graphs

Theorem graphs are as useful as text in conveying information on the mathematical or theoretical subject being studied.

There are several types of graphs or graph categories and an application is needed to let users manipulate those graph category to cover a particular theorem , theory or field of study.

Such an application should enable users to select what types of graphs they want to view or update (edit)

as well as to view more types of graphs at the same time

The ability to zoom in and out navigate edit and update the graph

Zooming should be implemented both
a) visually (the familiar zoom in out scaling)
b) and structurally by the ability to "collapse" a group of nodes or subgraph (if the subgraph is collapsible) into a single node and to expand a node to a collection of nodes or subgraph , if the node happens to be "expandable".

This enables the user's navigation across layers of abstraction or layers of detail, and lower level of the theoretic body.

The graphs should cover a wide range of fine-ness , from the most general, broad label, type graphs ,

to the very fine structure of the elements that go into a definition or a theorem.

In the limit, a theorem graph should be able to "graphize" even the elements of a proof of a theorem, through a combination of logic and object graphs.

The Types of graphs:

object graphs: where
nodes tend to represent
- entities , such as sets and sequences
- operations, such as binary relations or maps (eg, functions)
- properties, such as linearity, commutativity
edges to to represent a relation of the type "this goes into this, or makes up this"
more formally, the child "has" the parent property or relation or set

logic graphs
where emphasis is on meanings of edges, which include:
parent proves child
the edges represent a sequence of steps in a proof, with the ultimate node being
an enunciation of the theorem
There is still some ambiguity on the choice of what nodes are to represent.
They can represent steps in a single proof , in sequence ,
where each step is node


historical graphs
nodes include
writings
persons
experiments
date node: plaintext nodes with "year" labels connected by invisible edges to make a timeline, as seen in the old unix
history dot graph.

Nodes also include
definitions
theorems
hypotheses , conjectures, etc.
theories : more general than theorem, and generally correspond to a distinct field of study as well as part of a theoretic framework

Edges in historical graphs often denote "contributes to" as well "leads to"

Because there are different categories of graphs, the user should be able to switch graph categories on and off according to their convenience.

In a historical graph, a user should be able to click on a node for a given theorem, and thus expands a subgraph which in fuller detail, shows the user depending on his choice, either the object or logic makeup of the theorem or definition.

Examples with static graphs and more notes can be found at math_graphs.