[Computers are] solving mathematical problems that have resisted some of the world's greatest mathematicians for decades. Why are mathematicians concerned instead of celebrating? The answer reveals a fundamental misunderstanding of what makes mathematics valuable. From Euler's seven bridges of Königsberg to the race to the Moon, I explain why solving a problem is not necessarily the same as advancing science, and why the real value of mathematical research often lies in the discoveries made along the way. More importantly, I explore a potentially devastating consequence of [computers'] growing capabilities: what happens when the next generation of talented students no longer sees a reason to become mathematicians? The implications could extend far beyond mathematics and affect the future of scientific progress itself.