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epicurus comments on Is Scott Alexander bad at math? - Less Wrong
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Definitely less rigorous formalization and more gestalt pattern recognition.
In general, I think of math as dealing with well-defined "things" -- you may not know the shape/properties/characteristics at the moment, but they exist, they are precisely defined, and they are not going anywhere. In contrast to math, statistics deals with fuzzy amorphous "things" that you will likely never know in precise detail, that mutate as more data becomes available, and that usually require interpretation and/or some guessing to fill in the gaps.
Cutting edge math is actually mostly about converting fuzzy stuff, at least the parts of math I am interested in(Algebraic Geometry - Grothendieck/Weil for example). Both the mentioned mathematicians worked in a field where people had some stuff that worked but no foundations.
Also, the foundations of math have been changing for quite a long time and continue to do so. I think your reaction to mathematics might be to badly taught mathematics rather than mathematics as practiced. However, I don't see an easy way to fix it.
To teach mathematics well would require a high amount of mastery and we don't have enough people like that around.
I doubt it -- I generally teach myself things and just ignore bad instruction. The underlying cause is likely to be the curse of the gifted -- I'm lazy and when I run into walls I usually go around instead of starting a wall disassembly project. And I was never attracted to math sufficiently to apply a lot of effort.