pi-Base: A usable map of the forest

Talk notes for South's ACM & Math Clubs

Posted by Steven Clontz on September 12, 2017

Here are my notes for today’s talk on pi-Base for the University of South Alabama’s ACM and Math Clubs.


  • Notes/links from this talk are available on my website.

Relationship of Math and Comp Sci

  • Math folks: knowing computer science/engineering can help you get a job.
    • Don’t have to take classes; just pick up a fun sideproject!
  • CS folks: knowing math can help you get a job.
    • Having a math background makes people think you’re (a) smart, (b) a problem-solver (in general).
  • I hope to see future collaborations between ACM and Math Club, and I encourage members of both groups to be involved with the other and leadership to work together to support their memberships.

What is Topology?

  • Topology is the a of mathematical structure that generalizes geometry and calculus.
  • One goal of topology is to identify the properties of topological spaces that characterize them.
    • Compactness: \([0,1]\) is compact, but \(\mathbb{R}\) is not.
    • Hausdorff: \([0,1]\) is Hausdorff, but an indiscrete space is not.
    • Normal: \([0,1]\) must be normal, because it is compact & Hausdorff.

What is pi-Base?

Where is pi-Base going?

  • Currently I have a small grant to convert pi-Base into a modern tool for mathematical researchers.
    • Major flaw in current version: lack of citations and peer-review.
    • ACM officer Cody Martin worked for me last summer to add citations from pi-Base to Counterexamples.
    • Once this audit is complete, all contributions will require references to a peer-reviewed manuscript to be marked as verified.
  • pi-Base will become a treasure trove for undergraduate research.
    • There are still many unknowns in topology.
    • pi-Base can automatically catalog space/property pairs that are missing.
    • Three possibilities:
      • The question has been answered in literature not in pi-Base.
      • The question hasn’t been answered because it’s hard.
      • The question hasn’t been answered because no one’s tried: perfect for undergrads!