&gt; Isn&#x27;t proving a major conjecture enough?<p>Not necessarily. And not because of a lack of tangible rewards, but because of a lack of mathematical ones.<p>Mathematicians are not just after true statements, or proof, but understanding, and new theories that open up new areas of study. For that reason, a new proof of an old theorem is often quite interesting.<p>I seem to recall reading that Wiles&#x27; proof of Fermat&#x27;s last theorem was sensational, but ultimately less exciting than it could be--the proof did not create a new way of viewing or systematizing things so much as apply very specialized machinery to a specific problem. Take that with a grain of salt--I don&#x27;t have a hundredth of the mathematical background to judge it myself.