[dalke]

"If you’re going to get anywhere in learning mathematics, you need to learn to be comfortable not understanding something."

This is true for all research.

And I don't mean just the physical sciences either. Historians and sociologists are also chronically "lost and confused." Otherwise it wouldn't be a topic worth of study.

This is why students who are "good at X", whether it be math, German, sports, or programming, may become frustrated when they find out that "good at researching X" is a very different matter.

[j2kun]

I think it's a good point, but I still think the kind of lost and confused in mathematics is more embarrassingly extreme. Imagine a few hundred historians trying to discern when King George I died, and after 50 years of work they conclude, "All we know for sure is that it was between the day he was born and yesterday." A startlingly large part of mathematics feels like this.

And I think the reason is that "prevailing theories" mean nothing in mathematics.

[dalke]

That's a poor comparison. I find it hard to believe that mathematicians are still trying to decide if the set {1, 2, 3} is finite or infinite.

A "startling large part" of all science fields like this.

Physicists don't even know if the gravitational mass of an object is really the same as its inertial mass. Or if there are true magnetic monopoles. And that's after over a century of trying.

Immunologists have barely scratched the surface of how that field works.

Economists make lots of conjectures, with lots of math to back it up, but it's not a perfect predictor of the human economic system.

Biological evolution still surprises us, 150 years after Darwin and nearly 100 years after the neodarwinian synthesis.

Chemists still don't come close to handling some of the reactions that natural systems have figured out.

And so on.

[j2kun]

Good point.