I don't believe much of anything.
Except that you don't believe much of anything. And much more.
I find it to be mostly an egocentric waste of time.
Egocentric waste of time? I've spent decades curating my belief set in an effort to accumulate knowledge about how the world works including how to function in it. And maybe it was all just luck, but I got to where I wanted to be - hardly a waste of time.
Nor do I care much if I'm "right" or not.
That's unfortunate.
I ran to the store because I intuitively determined that that was then next thing for me to do.
I don't BELIEVE that. You ran into the store because you BELIEVED that there are items there that you BELIEVED you wanted because you BELIEVED that they would facilitate you achieving your immediate goal. All of that was based in empirical knowledge acquired from prior experience. Your choices were deductions based in applying inductions to specific situations. For example, you've enjoyed chocolate ice cream several times, and your induction is, "Chocolate ice cream tastes good to me." You arrive at a store and realize that you can buy some right now. sing that generalization, and deduce the specific conclusion, "This is going to be good."
"The Earth is flat" is demonstrably correct given a specific information set and practical objective.
No, it's not demonstrably correct. All you can say is that wherever you're standing seems flat more or less, and it does, and that error might be a close enough approximation that it works for you most of the time, but that does not make the earth flat.
Most humans do not expend so much time and energy worrying about the correctness of what's happening in their brains.
I know, but many that I know do, especially other physicians and bridge players.
That's a good think if the biases are rational, but not so good when irrational. Knowledge is rational bias. Preferring that chocolate ice cream to a flavor that you haven't liked in the past as well is a rational bias. You might want to reconsider ... never mind. You don't have beliefs or care about being correct. Carry on.
"New math" is as irrelevant as "old math"
I'll bet banking and doing taxes is a nightmare around your home.
It's always the same thing ... "Come stand before me in my kangaroo court so I MAY JUDGE THEE AND DISMISS THY "EVIDENCE"!!!
That's what trained, analytical minds do well. Besides evaluating evidence, they evaluate the claims and arguments of others. And if they do it faithfully according to the laws of inference (reason/logic), they can arrive at ideas that are demonstrably correct and can be used to anticipate outcomes, like the experience of eating chocolate ice cream - what I call knowledge.