>>13292892>Anything that isn't arithmetic>The basic calculus stuff like limits, derivatives, integrals have to be solved via numerical methods (Simpson's rule, central difference, etc.) which do not give exact answers, they are approximations.no, this is wrong. we have many computer algebra systems that do symbolic computation like you and I would, and many times, they're very, very, very good at it. Finding closed forms for "the basics" is well solved, but the reason people go to numerics comes down to many reasons:
1) it's faster
2) they don't care about closed forms as much as making a complicated calculation fast
3) you want to get easy visuals or reinterpret the equations via what laws they govern (ie fluid simulation). you could just as easily have a solver - but you give up a lot of flexibility of numerics.
If you're gonna make a fuss about real numbers and floating point representations, it's easy to point out that people don't write down arbitrary real numbers in their closed form solutions or even when writing down a problem. The mathematics "computers can't do" has slowly diminished because mathematicians are literally pushing to have the computer work for them and help them in proving theorems as problems get harder and harder. This is the whole aim of papers in the prestigious journal Experimental Mathematics.
>If it isn't addition, subtraction, multiplication, or division, the computer has no idea what the fuck you want.There is no distinction between a computer and the algorithms you run on a computer. If you have an algorithm to solve something, you can do it on a computer.
>uhhh but what about integration you mean automating methods for identifying antiderivatives in the Reimann case?
I swear, it's always the midwits that have the most *mundane* ideas of what math is who think a computer "can't do math." Computers have been invaluable in math and science research precisely in the places where traditional methods have failed.
