All people, regardless of intelligence, converge to a level of stupidity that causes them unbearable anxiety.
The reason this happens is that thinking itself causes anxiety via energy expenditure. People don’t realize how much energy we burn just by using our brains for simple calculations- a Putnam problem may be comparable to running a mile. Therefore, we tend to conserve energy when we aren’t sure that spending it will result in a decent payoff. But if we are driven by some greater anxiety, this can cause us to think. For instance, anxiety about winter impending will cause a man to plan ahead and store up food.
The convergence occurs by definition because 1) if the anxiety is bearable, then by definition we will bear it and 2) if the anxiety is unbearable, then by definition we will take action to reduce it.