Towards a comprehensive graph of mathematical domains and topics.
Math.mx (mathematics) is a zoomable tree map of hierarchical mathematical topics (a navigatable taxonomy of math). It's goal is to give one a holistic mechanism for exploring all of math, to learn what they don't know, to discover and see how fields are related, and to contribute/associate resources to help others better undestand each topic. Its data set is the American Mathematics Society (AMS) MSC2010 taxonomy classifications.
python -m SimpleHTTPServer 8000 index.html
- Here's my 1st announcement of math.mx on facebook + goals
- Here's an idea + complimentary initiatives you may want to explore
- Wiki Data Support: Resolve every math topic to a wikidata ID
- Entity Resolve w/ Wikipedia: Extend the math.mx DAG (which is from the AMS MSC2010 taxonomy -- query it here) with https://en.wikipedia.org/wiki/Category:Fields_of_mathematics (iterate over wikipedia math categories)
- Allow Users to Edit: CRUD (create, read, update, delete) (i.e. back with a database, like s3)
- Allow each box/cell to be annotated with users' resources (academic papers, videos)
- Allow users to add children or neighbors to a specific cell
- Improve Granularity: Make root nodes in the graph not be "domains", but be so granular they resolve to specific formula.
- Curricula Generation: From any given box/cell, allow the user to click a link which generates a (shortest path, ordered) list of dependencies (walks the graph) to learn/understand the selected formula or topic
- User accounts:
- Visualize your comprehension: imagine if each cell in math.mx was colored with a shade of red showing users w/ accounts how well they comprehend a cell (and all its dependencies).
Links as reference
- http://www.aaamath.com/grade6.htm#topic1 - elementary
Insofar as interesting data sets go, you may also be interested in https://michaelkarpeles.com/curations/the-foundation (which I hope becomes like the future math.mx described above)
The objective of this repository is to outline a comprehensive graph (currently a tree) of mathematics and mathematical subtopics, to keep track of which domains or principles I have converage (understanding), and to attach/associate resources with, in order to evaluate and effectively improve my holistic understanding.
Imagine if we could map each rectangle to a color who saturation intensity represents our degree of mastery of the underlying topics/skills.
This experiment could be extended such that, each box at the most zoomed setting directly maps to a wikipedia article containing e.g. equations. If/once one "checks" or asserts their understanding of the concepts of this article, the box becomes checked / colored. As you zoom out, the color of the box becomes the average saturation intensity of its children.
At the top-most level, a map of our ignorance.