## Essentials

a mathematician and software engineer. plays with ideas and code.### Research Highlights

30+ publications in top-tier discrete mathematics and philosophy journals. A couple of favorites:D.W. Cranston and L. Rabern. Planar graphs are 9/2-colorable. Journal of Combinatorial Theory, 2017. This article is about coloring countries on a map so that adjacent countries receive distinct colors. It was conjectured in 1852 that any map could be colored thusly using only 4 colors. This was finally proved in 1976, but the proof is not human-checkable; it requires many hours of computer time to check thousands of cases. Finding a human-checkable proof is still an open problem. To prove that 5 colors suffice is relatively simple. We gave a human-checkable proof that 4.5 colors suffice; this means that we get to use 9 colors, but have to assign each country 2 colors.

- Settled a 20-year old conjecture on the existence of such a proof.
- Featured on Computational Complexity, a popular computer science blog by Lance Fortnow & Bill Gasarch.

B. Rabern and L. Rabern. A simple solution to the hardest logic puzzle ever. Analysis, 68(2), April 2008. Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are da and ja, in some order. You do not know which word means which.

- Showed how to trivialize the puzzle by asking questions that elicit meaningful answers from Random.
- Showed how to solve the puzzle in only two questions by using paradoxes to explode god-heads.
- This article led to the problem getting a lot of press and many follow-up papers have been written.

this interview with my phd advisor Hal Kierstead gives some idea of the type of math i tend to work on.