Now, persuading a group of mathematicians to believe a claim is a high bar, and they are very good at finding logical holes, gaps, and mistakes. As Nietzsche points out in Beyond Good and Evil, it is quite possible that humans as a species have all sorts of blind spots in our reasoning abilities, and that such blind spots are essential for life itself.

In fact, we know of many of these blind spots, or failures of human reason. One great example is the Monty Hall problem. Others are the lottery, gambling, stock market events, advertising (the effects of), and all sorts of experiments that economists do these days.

So before you get concerned about the Pentium IV's accuracy, and 'mathematically proving' it is correct, consider that your brain is a very imperfect reason engine, and there is no reason to suspect that our intuition is accurate except in (and still imperfectly in) those situations where those intuitions improved the reproductive chances of our ancestors.

>...our intuition is accurate except in (and still imperfectly in) those situations where those intuitions improved the reproductive chances of our ancestors

That actually contradicts my point. Our intuition and reasoning powers did not evolve toward accuracy or better understanding the world, it evolved purely toward whatever kept our monkey ancestors out of lion mouths. Sometimes that could have caused our primitive ancestors to believe that they could only safely cross the plains while holding magic rubaduba fruit. This would of course be reinforced, since perhaps the rubaduba fruit only is on trees in the one month a year that lions are far away looking for water. The proto-humans who believed the rubaduba bullshit survived because they were able to pick up on a correlation, but they only acted on it because they believed in causation, meaning we our ancestors who thought the rubyduby fruit theory was idiotic got eaten by lions, while the credulous saps who filled sacks with 50 pounds of inedible crap and carried it across the plain were fine.

This is a just-so story, but the point is illustrated, which is that not only do humans have terrible reasoning ability when it comes to money and anything remotely scary, it's quite possible we evolved specifically towards irrationality in certain situations. There is billions of dollars spent studying this every year, it's called marketing.