There's something to be said about time investment. You're suggesting that tinkering takes time. If I want to keep current on all the math I learned in school, I'd have to invest a significant amount of time in addition to the time I already invest in keeping up-to-date with languages/frameworks/platforms/algorithms/datastructures/databases/etc.
How often would I use this level of math? I know I use the others on an almost daily basis. Coming up with something I need linear algebra for, though? Few and very far between. Maybe you use linear algebra often, but most of us don't have a need for it.
And if you disagree, then I think you should actually know abstract algebra, number theory, topology, etc., so that when the next problem comes along, you can 'quickly come up with an optimal solution'.
Sorry if this comes off as snarky, but I'm not sure of a better way to explain it. To me your comment sounds like:
"I have been walking through mazes my whole life with my eyes closed, and I make progress by feeling the walls with my hands. In order to get through each maze I need to remember lots of facts about how the walls in the different mazes feel when I touch them. If I opened my eyes now, it would take too much time, and be too painful to adjust to the light. I never tried to open my eyes, and even though a lot of people keep telling me it's a lot easier to get through mazes with your eyes open, I think they are wrong. Besides, the few and far between times I get stuck, I can always ask one of the people who can see where I should go next. And if you think I need to keep my eyes open, then the next thing you are going to tell me is I should use my sense of hearing and smell too."
Is that really the best you can do? That analogy has absolutely nothing to do with baak's point.
If you must reword and put his entire argument into a bad analogy, try this one:
"I've been walking through mazes all my life. This one time, I had to recognize a particular brand of poison flower, but I didn't know my flowers very well because flowers are rare in the maze."
And the answer?
"I asked my friend who was also in the maze: 'Is this flower poisonous?' He said yes. I said okay. We skipped the flower and moved on."
Pretty much this. Except you should also add that while he dedicated time to learning poisonous flowers that are encountered almost never, I spent that time getting in shape to move through the maze quicker, a skill/attribute used way more often.
How often would I use this level of math? I know I use the others on an almost daily basis. Coming up with something I need linear algebra for, though? Few and very far between. Maybe you use linear algebra often, but most of us don't have a need for it.
And if you disagree, then I think you should actually know abstract algebra, number theory, topology, etc., so that when the next problem comes along, you can 'quickly come up with an optimal solution'.