I discussed with them several things raised by Halmos (placed in the context of CS
rather than just math):
Distinction between pure and applied “math”; how it is reflected even in fields like literature (manuals vs. Shakespeare) or music (military marches vs. Mozart).
The objective of pure “math”: generality, clean definitions, precision, elegance, logical analysis, non-trivial arguments
How doing “math” can be 'creative' and experimental
The necessity of commitment when it comes to research
Also classic Halmos teachings on how to lecture and how to write
I then gave two examples of work that I have done:
First work, on approximating independent sets in graphs
Later collaboration on packet admission policies in networks, and how that can also be viewed as an online and distributed version of the independent set problem.
I then asked them to suggest a problem to tackle. Freysteinn brought up solid-state memories,
that are arranged into banks, where writes take much longer time than reads. We discussed
for a while the possible problems and formulations involved, making limited progress but
energetic discussion.
EOF