What is pop math?
as popularly understood,
Graspable by lay person,
w/o introducing much machinery.
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EG of cut-off is
Noyes Chapman's 15 puzzle
(claimed, falsely, by Sam Loyd)
Can't solve if switch the 14 and 15.
The statement is graspable by any,
...but the solution is just a bit too technical:
sign of permutations (& proof is a bit tricky;
conceptually it's just sign of permutation).
[There are other elementary questions, esp. in combinatorics and number theory,
like twin primes or Fermat's Last Theorem,
but those are far, far more complicated.]