Euler's Quartic Conjecture/Historical Note

Historical Note on Euler's Quartic Conjecture
put forward this conjecture in $1772$.

Nobody made any progress on proving it one way or another until discovered the counterexample $20 \, 615 \, 673$ in $1987$, and proved that there exists an infinite number of such solutions.

Soon after that, found the smaller counterexample $422 \, 481$, and demonstrated that there were none smaller.

Both counterexamples were published in the cited article in by  in $1988$.

This discovery was subsequently reported in the New York Times.

found the solution $638 \, 523 \, 249$ in $1997$.