Comment by Tainnor
6 days ago
It's "not interesting" because no novel insight has to be used in order to solve this. It's immediately obvious how to solve it, just follow the textbook procedure.
This is distinct both from other typical IMO problems that I've seen and from research mathematics which usually do require some amount of creativity.
> exp(i\pi)+1=0
If your definition of "exp(i*theta)" is literally "rotation of the number 1 by theta degrees counterclockwise", then indeed what you quoted is a triviality and contains no nugget of insight (how could it?).
It becomes nontrivial when your definition of "exp" is any of the following:
- The everywhere absolutely convergent power series sum_{i=0}^\infty z^n/n!
- The unique function solving the IVP y'=y, y(0)=1
- The unique holomorphic extension of the real-valued exponential function to the complex numbers
Going from any of these definitions to "exp(i*\pi)+1=0" from scratch requires quite a bit of clever mathematics (such as proving convergence of the various series, comparing terms, deriving the values of sin and cos at pi from their power series representation, etc.). That's definitely not something that a motivated high schooler would be able to derive from scratch.
Those definitions of exp are all immediately obvious and nearly the definition of textbook, every university calculus course covers them. That is the issue with defining interesting as novel - nothing generally known is novel any more. And they don't require any special maths - sum_{i=0}^\infty z^n/n! is literally just multiplication and addition.
The long and short of it is it just isn't possible to tell someone that their problem isn't interesting. Interest isn't an inherent property of an equation, it is the state of mind of the person looking at the equation. And in this case the x+y/xy is a classic interesting puzzle despite (really because of) how well known the solution is.
> those definitions of exp are all immediately obvious
no