Interpretation #1: P vs. NP

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

There are many proofs in the literature that are gigantic case checks, one of the most famous being the four color theorem. Another is Helfgott's proof of Goldbach's weak conjecture. 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

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.

Interpretation #1: P vs. NP

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

There are many proofs in the literature that are gigantic case checks, or extremely complicated analytic arguments handling many cases at once. One of the most famous is the four color theorem. Another is Helfgott's proof of Goldbach's weak conjecture. 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

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.

Interpretation #1: P vs. NP

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 compexity

There are many proofs in the literature that are gigantic case checks, one of the most famous being the four color theorem. Another is Helfgott's proof of Goldbach's weak conjecture. 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

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.

Interpretation #1: P vs. NP

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

There are many proofs in the literature that are gigantic case checks, one of the most famous being the four color theorem. Another is Helfgott's proof of Goldbach's weak conjecture. 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

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.