I have a tenuous relationship with math. Or maybe I should come right out and say it : I hate math.
First of all, I really hate the prime numbers, for the same unpredictability that fascinates the true mathematician.
I see no point in riddles like Fermat's last theorem, anymore than I would ever let myself be locked in an escape room or try to solve a crossword puzzle. These are just man made challenges, and I don't like the competitive spirit they breathe. And I hate losing.
I am also terrible at rote calculation. I cannot copy a single line of math without making an error. Manipulating and simplifying equations is a real pain for me. I have no sense of direction in trigonometrical manipulations, and after many random steps I sometimes end up at the starting point ( if I am lucky ).
This is a problem for someone who loves physics, because physics and mathematics go hand in hand. But then we are talking about applied mathematics, the continuous kind with the nice smooth real numbers, not the jumpy kind with the natural numbers.
Mathematicians come in two flavors : the ones who do abstract logical manipulations in their head, and the ones with a geometrical mindset. Even though I am not a mathematician, I am firmly in the latter group. I can only accept a result if I can "see" it in a more or less geometrical way.
I do not see my way forward at all in purely abstract reasoning. But once I have found a more or less geometrical view, I believe it gives me a good bullshit detector. I will not easily be fooled into a fallacy. I know when I don't know something for sure, and I will not accept a "known" fact just because all the other lemmings do too.
There are ways of getting out of the roadblocks and vicious circles that lesser mortals encounter when trying to solve a mathematical puzzle. Charming examples include Polya's book "How to solve it", and De Bono's book on "Lateral thinking". These books are well worth reading, and they helped me understand the design process of mechanical artefacts. Unfortunately, they did nothing for me in the field of mathematics.
Symbolic logic held great promise for me. For someone getting lost in copying one line of equations to the next, a tool with commands like "simplify" or "collect" would seem to be the ideal solution.
So far, it has not worked for me. Tools like Mathematica, and before that Maple and its incarnations in Matlab, have proved unreliable not in their results, but in their continuity of support due to commercialization.
And worst of all, somehow they do not seem to simplify the equations to the forms that I can relate to. These are the kind of tools that "help" you on their own terms, but cannot be persuaded to tweak the equations to your own idiosyncratic taste. I'm afraid I am still on my own here. I suppose AI might come to the rescue now, if I can ever bring myself to learn the gentle art of prompting.
There is one field where AI, or something like it, has already been very useful to me. In propeller theory I came across an number of analytical integrals, one of those subjects where I know some of the tricks ( like clever substitutions ) and most, but not all solutions can be looked up in big books of tables.
I recently found that simply typing the integral into a search engine gives one or more perfect solutions with all the steps to get there. This has been very useful in working my way through the viscous optimization of the propeller, which turned out to be analytically simple enough, but which presented a number of analytical integrals which I would never have been able to solve myself in any finite amount of time.
This is a long winded introduction to a short section on math. I hope to make life easier for those with limitations similar to mine, and who also like to take the road less travelled.
Much of the received knowledge in physics and technology is quite complex, and in the worst cases an impenetrable article of faith. A simpler, often more geometrical view occasionally makes these relations immediately and intuitively obvious. This is a wonderful sensation.
It may even allow you to take next steps, or at the very least to do some light hearted, friendly, quick sanity checking on other people's wonderful new ideas.