You have put things out of context.matt grime said:Ok, let me put it this way.
When I read your arguments this is what I see.
1. Physics/Engineering is so cool because it lets you model all these things. I like solving problems by putting in numbers to formulae.
2. Mathematics is so bad because its just following rules without any reason why.
What I said is that I prefer formulae over proof techniques beacuse I get a result from the formulae that I can see in real world where doing a proof has no visible results.
I would never have claimed that putting numbers into equations is stimulationg, I am sorry if I have missled you to believe soo, but I do think that putting numbers into equations can give you sometimes results that you can observe in the real world compared to nothing that you get from doing proofs that were already done and are stated as theorems. If something was false it would not be allowed to be a theorem would it???
What I mean by understaning is this. You should know the meaning of what is it that you are trying to achieve. Take for example this:
32 = 2^x
find the value of X, if you are a Math teacher, just for fun, ask somebody to give you the result. If somebody would understand what it is that you are trying to achive, that is you need to find the value of x, one would answer 5 because (2*2*2*2*2 = 16 * 2 = 32). But probably they would want to do things with logarithms. Why? Beacuse they have learned a technique on how you obtain the value of x in such a circumstance and they see the pattern. But that is just knowing, if you would understand you would just say the answer is 5. But you as a mathematician would probably say that is just GUESSING??? You got the solution using arithmetic and not algebra! But hey just doing the logarithms needs no understanding from you. Doing it the way I have show had to do with understanding the problem.
Sorry for giving you more of an calculation example but I do hope you did get my point I was trying to make.
Here one example with definitions.
I was surprised that when I said to a colleage who had the highest grade ever possible in Math, I said jokingly that you can aswell make a recursive definition for faculty, and he said, "Wow, that is interesting, I did not KNOW you can do that.". See if he would understood what was the thing he tried to achive he would have know that you can write
n! = 1*2*...*(n-1)*n as
n! = (n-1)!*n
0! = 1
That is what I had in mind with understanding and not knowing.
I think Mathematics are wonderful, but Mathematics lessons are just a horror. Things that could be explained in plain English are all wrapped in some formalities and proofs. And the focus is on formalites oh, better say the Mathematical rigor, everything must be rigorus. Why? Mathematics are wild west. Take a look at geometry. If I recall there is no one "correct"
axiomatization of geometry!! It varies from textbook to textbook! And then you dare questioning people on the rigor, yet you don't even have your facts straight!
For example, If I were to take a physics lessons in Japan or in South Africa the content would be the same, the explanation is bound to differ from professor to professor. But the 2nd newton law will be the same everywhere. Yet if I were to take geometry lessons there are bound to be some differences in the content. If in some scheme you can take something as an axiom and in another sheme you can take that as a theorem, where is the rigor? If Math is "universal" as in universally the same, how can there be no correct axiomatization of geometry?
You have artificial rigor. How can a mathematician preach about precision yet he is usually late for his lessons. That is just being a hippocrit.