**Interpretation #1**: [P vs. NP][1]

There are many hard-to-solve problems with easily verified solutions.  It can be a real talent to present a proof which is especially easy for humans to verify.  In like manner, a good counterexample can be very enlightening.  Those who have searched for counterexamples can testify to the fact that these can be very hard to find in the first place.

*Do not confuse the ease of verifying a solution with the difficulty of finding that solution.*

**Interpretation #2**: [Kolmogorov complexity][2]

There are many proofs in the literature that are gigantic case checks, one of the most famous being the [four color theorem][3].  Another is Helfgott's proof of [Goldbach's weak conjecture][4].  Some proofs require an extraordinary amount of data, which simply cannot be compressed into a smaller space.  However, we don't usually celebrate the fact that a computer actually checked all those cases (even though that really does need to be done).  Rather, we delight in the fact that we understand how to turn it into a finite task, doable in a small time-frame.  The important parts of the proof are the key ideas, which sometimes are quite small in comparison to the rest of the work.

*Do not confuse length with importance.*

**Interpretation #3**: [Obfuscation][5]

Good mathematical writing makes things *clearer*.  One should "eschew obfuscation, espouse elucidation".  My greatest joy in my research is discovering something new and then explaining it to others, in a way that makes it clear and *easy* to them as well.  In my experience, a large amount of time should go into writing the solution well.

*Do not confuse lack of clarity with brilliance.*

  [1]: https://en.wikipedia.org/wiki/P_versus_NP_problem
  [2]: https://en.wikipedia.org/wiki/Kolmogorov_complexity
  [3]: https://en.wikipedia.org/wiki/Four_color_theorem
  [4]: https://en.wikipedia.org/wiki/Goldbach%27s_weak_conjecture
  [5]: https://en.wikipedia.org/wiki/Obfuscation