Using Mathematica vs pen and paper in Physics

[ohannuks]

Hi!

I'd like to discuss your experiences with pen and paper vs software. Especially young people are welcome to join the discussion :)

I'm wondering if there are people who do *most* of the symbolic calculations on a computer. I am very familiar with pen and paper and I've been wondering whether it would be worth a try to see if I can get familiar enough with symbolic software such as SageMath or Mathematica that I could use it for most of my work. Do you think this makes sense?

My current way of working is with pen and paper and occasionally Mathematica (when I need to e.g. simplify long expressions of if I know an integral has an answer I plug it in). I see obvious pros and cons to using software (pros being that it's programmable, it's very good at pattern matching and has a large database for doing stuff, cons being that it's not always very flexible, can't draw pictures and some say it makes the user dumber)

 

[ohannuks]

I'm especially curious if there are any people who actually start off with Sage/Mathematica, e.g. they want to solve a problem and they open up Mathematica and start working on it right off the bat without first formulating the problem on pen and paper.

 

[nuuskur]

I do formulate the problem with pen and paper, often times, the problems are quite trivial, I know exactly what to do when I want to solve it with Mathematica/Matlab or what have you.

 

[jackwhirl]

[...]can't draw pictures[...]

Every symbolic mathematical computation program that I've heard of, including Mathematica, can plot graphs. They draw better pictures than any human.

[...]some say it makes the user dumber[...]

Using a computer won't make you better at solving problems by hand, but it will make you better at solving problems by computer, which is not dumber.
Tangent in the spoiler.

Spoiler

There's another recent discussion thread asking about the greatest mathematicians ever. My reply was basically that present day mathemagicians are capable of so much more than their predecessors that it is hard to even compare them. One of the reasons for this is the printing press. We have the collected knowledge of everyone who bothered to publish their work. The other reason is computers. They extend our abilities, particularly with math, to levels that... (I'm having trouble thinking of something appropriately hyperbolic and all that's coming back is "to infinity, and beyond!")

 

[mkay]

I don't think one should use mathematica as an alternative to pen/paper. It complements it. There are some stuff that you absolutely cannot do with pen/paper, for example, computational work. However, for managing some integrals and such, I'd say that pen/paper should be your 1st go-to.

 

[Ben Niehoff]

Mathematica is not capable of doing most of the calculations I do. I work things out by hand, and use Mathematica for incidental things like doing integrals or making graphs.