For most of recorded history, one of the scarcest things was access to knowledge. If you wanted an explanation, a reference, a proof, or a worked solution, you had to find someone who knew it, or spend hours searching through books. The answer itself was the expensive part.
That is changing quickly. A capable model can now produce an explanation, a summary, an analysis, a piece of code, or a candidate answer in seconds, at a marginal cost close to zero. The change is real, and it is large. But it has a boundary worth stating plainly: these systems are capable, not infallible. They can be wrong, subtly or loudly, and they can be wrong in ways that look confident.
The bottleneck moves
If answers are becoming dramatically cheaper to obtain, the scarce resource shifts. Knowing what to ask is becoming as important as knowing the answer — and in many cases, more important. So the abilities truly worth cultivating begin to move upstream: discovering worthwhile problems, asking precise questions, identifying assumptions, reasoning from evidence, finding counterexamples, verifying results, and deciding which question should come next. Good questions require observation, abstraction, decomposition, and judgment. None of these skills disappear because a faster tool arrives; all of them become more valuable when answers are cheap.
Questioning is not prompting
It is tempting to call this "prompt engineering," but that misses the point. A person can ask a model hundreds of questions without asking one genuinely valuable question. Prompt technique is about phrasing a request clearly. Good questioning is about noticing what deserves to be asked. It usually begins before the typing: in the sense that something here seems strange, or in the unease behind "Why must this be true?"
Answers still have to be checked
Because the systems are not infallible, an answer is never the end of the work. It has to be questioned, reasoned about, and verified — against logic, against known cases, and against what would follow if it were wrong. In a world of cheap answers, the expensive part is judgment.
Where this is trained
Mathematics has one distinctive quality: it rarely lets us stop at "it sounds plausible." Why must this conclusion hold? Are the conditions sufficient? Is there a counterexample? If one condition changes, does the conclusion still hold? Mathematics keeps asking us to turn "I think so" into "I can show why."
This is precisely the discipline that mathematics education, at its best, develops. We learn mathematics not only to get answers, but to become better thinkers and better questioners: to define terms before using them, to check assumptions instead of inheriting them, to search deliberately for counterexamples, and to verify rather than assume. The stronger the answering tools become, the more important this training becomes — not less. Stronger AI should make us reconsider how mathematics is taught; it should not make us abandon it.
The point of hard problems
This is also where I think good Olympiad problems have their real value. Their value lies first not in difficulty, but in unfamiliarity. If seeing a problem's type tells you which formula to apply, then however complex the calculation, the thinking it trains is limited. A truly good problem does not put the path directly in front of you. It asks you to observe the conditions, try one method, find it does not work, and change perspective; to discover hidden structure, form a conjecture, and verify it; and finally to solve it and look back over the whole process.
The final answer may be only a number. What is truly valuable is how that answer was thought up.
If Olympiad mathematics becomes only acceleration, memorized techniques, or medals, it loses this central value.
So the fact that AI keeps getting better at answering questions is not a reason to reduce training in thinking.
Quite the opposite.
As getting answers becomes easier, we need all the more to help children learn to observe, to question, to reason, and to verify — and to find their own path through unfamiliar problems.
We learn mathematics not only to write down the correct answer on an exam paper. More importantly, we learn how to begin thinking when the answer is still unknown.
The answer is not the destination. Thinking is.