Brilliant only allows questions with a natural number as an answer. This is very understandable, because it allows for automatic checking of one's work. It turns out to work brilliantly.
However, what I think is more interesting about math than calculating an answer, is proving something. Brilliant was set up for olympiad mathematics originally, but olympiad math is usually not about giving the right answer, but about proving something.
There are many olympiad problems on the internet in which something has to be proved, and the solutions can usually be found as well. However, practicing with proofs is not very easy, currently: finding the right difficulty level is a challenge on its own, and if you don't know the solution, just looking at the solution does not make you a better problem solver.
I think Brilliant could fix this. Just like with the current topics, it knows at what difficulty level you are, and the grading could be done by the community: I would love to check some papers from other Brilliant users and give them feedback, and I'm sure many other Brilliant users think about it the same way.
Why this would be better than the current situation:
- The difficulty level would be just right.
- Feedback would be given rather than a full solution, hence you would still do a problem yourself, even if you didn't see it at first sight.
- Marking proofs by others would improve your ability to explain what is really going on, which is a very useful skill.
- For each problem, the best and most elegant proofs could be listed and perhaps voted on, providing the internet an awesome database of beautiful problems and proofs.
If this would all work, that would be amazing. I think it can be done by the Brilliant community, because we love maths and love helping others with it. Also, if I'm really proud of a proof I've done, I love sharing it with others. ;-)
I think many users visit this site in order to train for the olympiads, which will be a lot easier if proving things could be trained here as well, because that is essentially what olympiad mathematics is all about. Most math olympiads put their problems online, so those can be used already. And of course, users could come up with their own problems!
Hopefully this can become a thing, I think it would really be great.