94
votes
What programming language should a professional mathematician know?
Python, so they can use Sage.
From their website:
SageMath is a free open-source mathematics software
system licensed under the GPL. It builds on top of many existing
open-source packages: NumPy,
...
80
votes
What programming language should a professional mathematician know?
Depends on their specific field.
In numerical mathematics, Matlab is the de-facto standard (unless you need high performance computing, but then you start to become more a computer scientist than a ...
76
votes
On proof-verification using Coq
Coq is a proof assistant, and not the only one. Other popular ones are Agda, Isabelle and the related HOL light. They all use type theory as a mathematical foundation (as opposed to first-order logic ...
- 48k
61
votes
What programming language should a professional mathematician know?
LaTeX
This is perhaps not the answer you are looking for, but it is indeed a programming language (it is Turing complete), and it is also a language that every professional mathematician needs to ...
47
votes
Is there a database for tracking the dependencies of mathematical theorems?
The reverse mathematics zoo, founded by Damir Dzhafarov and with recent development by Eric Astor, aims to be a database showing the relations and dependencies of mathematical theorems as described in ...
- 225k
43
votes
What programming language should a professional mathematician know?
One should probably also mention functional programming languages based on some form of typed lambda calculus such as Haskell. There is quite a bit of category theory going on in the type systems of ...
35
votes
What programming language should a professional mathematician know?
My answer is: TikZ
This is a programming language, often used in combination with
LaTeX, for producing high-quality graphics.
I view this language as important for mathematicians, not because
...
34
votes
Is there a database for tracking the dependencies of mathematical theorems?
It's important to distinguish between two types of "dependencies."
The cleanest type of dependency is the kind that is studied in reverse mathematics: Theorem T depends on Axiom A if T is actually ...
- 78.7k
24
votes
Accepted
Software for symbolic matrix calculus?
Indeed, I was having the same problem. Hence, I implemented a matrix calculus toolbox myself. You can find it at www.matrixcalculus.org. It can compute vector and matrix derivatives and will return ...
- 256
23
votes
What programming language should a professional mathematician know?
this language should be very useful for mathematics applications
As already said, this is a bit vague – maths applications are extremely different across fields, and most fields have their specialist ...
21
votes
Is there a database for tracking the dependencies of mathematical theorems?
The Stacks Project provides an example of what you're looking for. Every definition, lemma, theorem, etc. is given a tag, and the tags are used as references in proofs. They even provide an API for ...
- 28.8k
21
votes
What computer program for automorphic forms
The only CAS's that have built-in support for modular and automorphic forms, as far as I know, are Sage and Magma. [Edit: I had forgotten Pari/GP, which will introduce substantial modular forms ...
- 36.2k
21
votes
How do we explain the use of a software on a math paper?
Welcome to MO! I believe the answer to your question depends on what Mathematica command(s) you used to find the maximum.
If you used the command Maximize[], then its output is exact and, in my view,...
20
votes
How do you generate math figures for academic papers?
TikZ (a self-referential acronym for Tikz Ist Kein Zeichenprogramm) is an excellent, and extremely versatile drawing program. I highly recommend it.
There's an extensive manual. It might be ...
- 42.5k
18
votes
Is there a database for tracking the dependencies of mathematical theorems?
Not an answer, just
a diagram from the Stacks Project, mentioned by Paul Siegel,
illustrating dependencies of "the results needed to prove Chow’s Lemma" (the Noetherian case):
&...
- 149k
18
votes
How do we explain the use of a software on a math paper?
As is evident from the responses, different mathematicians have different attitudes towards computer calculations. If the computer calculation is not actually logically necessary for your proof, then ...
18
votes
Accepted
How do you generate math figures for academic papers?
To complement Kostya's answer, here is a way to turn hand-drawings into something looking vaguely professional using inkscape, very quickly (and for free).
Draw something on paper.
Take a photo in ...
- 5,565
15
votes
Mathematical software wish list
A wiki-like mathematical structure/example data base
I can imagine this better as an online service than a locally running software, but nevertheless I imagine it to be very useful.
You ever ...
13
votes
How do we explain the use of a software on a math paper?
The answer to this will differ from one field of math to another. In my opinion (I work primarily in combinatorics and algebraic geometry) a paper should contain enough data that the reader could ...
13
votes
How do we explain the use of a software on a math paper?
25 years ago I published a paper where there were computer-based enumerations of certain combinatorial objects. Unfortunately I did not publish the code (in GAP, an OSS system) and it vanished after a ...
13
votes
How do you generate math figures for academic papers?
In the case you prefer to draw pictures on a computer without entering the source code manually, I recommend Inkscape, which is a free, opens source vector graphics editor. It has a Latex plugin that ...
- 8,672
12
votes
What programming language should a professional mathematician know?
I'll start with a meta-answer: given the large (and growing) number of programming languages out there, how do you decide where and how to invest your time?
The answer turns out to be quite simple, ...
12
votes
Is there a reasonable "text-to-speech" solution for math papers?
Most formula-to-speech software only works with MathML, so you would first need to convert the LaTeX you find on arXiv.
There may be an alternative, under development for AWS:
Tex2Speech takes LaTeX ...
- 178k
11
votes
Mathematical software wish list
[In short, a place we can find a more modern proof, or a proof with a different approach, than the original paper that is customary to cite.]
One of the comments mentioned moving LaTeX from PDF to an ...
11
votes
Accepted
A closed form for an integral expressed as a finite series of $\zeta(2k+1)$, $\pi^m$ and a rational?
I think the following articles can give a clue:
http://www.tandfonline.com/doi/abs/10.1080/10652460701688125?journalCode=gitr20 (Closed-form evaluation of some families of cotangent and cosecant ...
- 16.4k
11
votes
Accepted
Instructions for using Coxeter 3.0 software
If you type "help" immediately on entering the program, you'll get a fairly long and useful introductory message. At whatever level you are, you are supposed to be able to type "help," and then the ...
- 541
11
votes
What programming language should a professional mathematician know?
More and more I am becoming convinced that one should know at least one programming language very well as a mathematician of this century. Is my conviction justified, or not applicable?
All of the ...
11
votes
Accepted
Software for detecting Brauer-Manin obstructions?
I strongly disagree with the assertion that "the language of modern algebraic geometry [...] is unfamiliar to many people who might otherwise have the right skills to write the software". ...
- 36.2k
10
votes
Accepted
What kind of computer tools topologists/geometrists use to visualize the objects they deal with?
Here is one case study:
An impressive animation of the Hopf fibration created by Niles Johnson using only open-source tools, available for all platforms: The Python-based mathematics program Sage was ...
- 178k
10
votes
How can we be sure that results that rely heavily on extensive computations are correct?
In the long run, the best we can probably do is to develop computer algebra packages whose computations are formally verified. To my knowledge, there has not been a lot of effort in this direction. ...
Only top scored, non community-wiki answers of a minimum length are eligible