[buescher]

They included the FFT.

Also, you'd think computer algebra systems would make the list. Macsyma, Mathematica, etc.

Mathematica has had a notebook interface since before I could personally afford a machine that could run Mathematica, but somehow the newer and inferior Ipython/Jupyter system makes the list?

[Y_Y]

Mathematica is not much liked in science. If you aren't careful or good at programming (most scientists) it's very slow, and it's much too easy to create a forkbomb the crashes the UI with a trillion red errors.

Plus the language is an ugly lisp and looks weird to people who understand log tables and calculators and Fortran.

And it's expensive and the guy most associated with it (Stephen something) has a bad rep.

But Jupyter is hot at the moment (for good and bad reasons) and it's FOSS and is easy to install as long as you can get your grad student to install conda for you.

[buescher]

Somebody's buying enough licenses to keep them in business. You either find a computer algebra system useful for what you do or you don't. My needs are pretty simple and Wolfram Alpha works well for me when I need something like that. Better than GNU Maxima, which I also like.

Stephen Wolfram made his early reputation in part by being one of the first people to seriously use Macsyma for physics. No, I don't know any physicists that take A New Kind of Science that seriously, but that's a different story.

Jupyter is hot, but it's not novel. The Mathematica notebook interface was an innovation and is still best-in-class in my opinion.

[dekhn]

I wasn't very good at solving integrals in grad school, so I bought Mathematica because I had the impression it could solve them. What I found was interesting. First, for all the integrals I dealt with, computers can't solve them using the rule systems that exist. Instead, you need a Physics Grad Student who knows how to solve integrals. Mathmeatica will just take your integral and spit out a more complicated one.

However, Mathematica is really good for symbolic algebra! I wrote a Python-Mathematica bridge many, many years ago, and learned that not only could it decompose numeric matrices, it could do it for matrices with symbols. Mind=blown.

[SiempreViernes]

That's the thing, there is essentially one FFT algorithm. If you want to include a big family of algorithms as Monte Carlo you better make place for it further down the line after Euler integration or possibly just numerical integration, and it's starting to become a question if maybe the list should simply be "addition and multiplication but with computers".