[antonfire]

I think a bit of disillusionment with mathematics is healthy, but it's misguided to call this kind of thing "a fundamental flaw in mathematics".

For one thing, in my experience, working on real life problems involves a whole lot more "memorizing problems" than working on mathematics.

And thank goodness for that! When I drive over a bridge or install an app, I really don't want to hear that whoever made it has an aversion to memorizing problems and solutions. Solving a real world problem is usually boring. Making a real life thing well is usually about correctly putting together many pieces that some other people have put together, in a way that's roughly similar to how somebody else has already put a lot of those pieces together before. Most of the work is well-trodden and uncreative.

I think part of the reason mathematics feels like it's about "memorizing problems" is that getting something deeper than that out of it is a habit/skill. A very important aspect of the vague notion of "mathematical maturity" is a habit of looking at a solution to a problem with the mindset of "how could I have come up with this?". That is, unpacking a problem and solution into some deeper understanding or way of thinking that led to it. As opposed to filing the problem and solution away "as is" into some toolbox to be referenced later. A lot of "gotcha!" solutions to mathematical problems are unsatisfying precisely for this reason.

In a lot of cases once you've read a problem and read a solution to that problem, and understood the solution, you've done about 10% of the work. The remaining 90% is this difficult work of unpacking and repacking lessons from that solution into something that actually deepens your understanding of what the problem is about. Sometimes reading the solution is actually doing negative work.

In other words, if you look at this problem and look at this solution and think "neat, but I don't get anything out of it beyond 'neat'", that's normal and fine, and probably correct. But that doesn't mean there isn't anything in it beyond 'neat', and a big part of learning mathematics well is to dig deeper than that even when the problem and solution don't force you to. Whether that digging is worth it is up to you. (It's often kind of a crapshoot in terms of payoff.)

But that's a more complicated situation than "this shows a fundamental flaw in mathematics".