A coin flip by any other name (2023)

If this appears to be nothing more than an interesting toy problem, I wouldn't underestimate the value of that.

An athletics program helps to prepare people for jobs that need physical skills and teamwork. It's not that you need to play soccer to do the jobs, but that play develops skills for general use.

Mathematics trains a lot of skills that are generally applicable in engineering. Decomposing complex problems into non-trivial sequences of manageable steps, being able to prove that the design works, spotting appropriate invariants to build type hierarchies/abstractions around, communicating it all in an intentional and comprehensible way where each of the next steps follows from some of the previous, etc., etc.

These problems seem to have the flavor of interview questions I heard for quant positions.

It depends a bit on exactly what you mean.

But eg if you want to write a new hash table (with a new hash function), you'd want to do pretty similar-ish analysis to figure out whether it's a good idea.

I used some neat math in my time to justify much simpler algorithms than what we were using before. (But not hash table related.)

https://www.keithschwarz.com/darts-dice-coins/ is also a joy to read. (As mentioned in the discussion on https://news.ycombinator.com/item?id=8006336 )

Have a look at eg https://www.eecs.harvard.edu/~michaelm/postscripts/handbook2... for some more in this flavour.

Lots of problems in finance benefit from understanding combinatorics, probability and graph theory. So there are lots of roles as say a quant dé√eloper where knowing some of this stuff is very beneficial.

That said, I would strongly encourage people to pursue knowledge because things are interesting and understanding stuff is cool. Don’t worry about whether a specific role exists where a specific piece of knowledge is beneficial. Just learn things you find interesting and get good at learning in general.

The advantage of doing it this way is you are learning things you find fun for the sake of learning so your motivation stays high and in my experience roles will materialize that benefit from the knowledge you have acquired but in much more interesting and less direct ways than you could have predicted ahead of time.

Large scale DBA and Ops. For them typical daily solving tasks like "what is more reliable - two RAID-0 in stripe or two stripes in one RAID-0" - mathematics thinking gives exact answer.