In the previous post I linked to a video lecture by Jean-Pierre Sierre on writing mathematics. However I should also have linked to a series of lectures on Mathematical Writing by Donald Knuth and others given nearly 20 years ago in the Autumn of 1987 at Stanford University. To quote from Don Knuth: Musings and More “I also gave a class called Mathematical Writing, just for one quarter,” says Knuth. “The lectures are still of special interest because they feature quite a few important guest lecturers.” This collection contains thirty-one tapes. If you haven’t got the time to sit through all the videos you can download a transcript of the course (or buy the book) in plain TeX format on Donald Knuth’s site: Mathematical Writing
On a slightly different tack there are a couple of papers on mathematical research that would be useful to postgraduate students:
- Advice to the beginner by Alain Connes
- What is good mathematics? by Terence Tao Some personal thoughts and opinions on what “good quality mathematics” is, and whether one should try to define this term rigorously. As a case study, the story of Szemerédi’s theorem is presented.
I’d be very interested if there are any more online resources on mathematical writing or beginning research.
Thanks to Noncommutative Geometry for the links to the two papers above.
PS Gooseania has mentioned that Nick Higham’s Handbook of Writing for the Mathematical Sciences is good.
eon mentions Some Hints on Mathematical Style by David Goss which has been recently updated with suggestions by Jean-Pierre Serre. It contains a number of references to other papers and books on writing style.
Jean-Pierre Serre (and also see Wikipedia) is one of the most eminent mathematicians alive; he was part of Bourbaki in the later stages, and he has been awarded many mathematical prizes. So it is a pleasure to watch a video of him explaining how to write good mathematical papers. He does this by explaining how to not to write mathematics which is why his talk is entitled How To Write Mathematics Badly.
You can forgive the amateurishness and poor sound quality of the 56-minute video for the sageness of the advice he gives. I don’t know when the talk was given but if it was recent he is doing very well for a man in his eighties.
You can find the video on Google video at Jean-Pierre Serre – How To Write Mathematics Badly and is a must see for postgraduate students who appear to make up the bulk of the audience.
Thanks to ComplexZeta for the link.
The number of maths blogs has risen dramatically in the last year, I am delighted to say. It started just a few years ago when Isabel’s math blog was one of the few (though sadly it has now vanished) to today when we there are thousands out there. Whether it is undergraduates blogging like Me Or My Maths, postgrads like Gooseania or professor (in the British sense so higher status than a lecturer) at Mathematics under the Microscope, all at Manchester University.
There are blogs like NeverEndingBooks which covers advanced topics like Noncommutative Geometry as well as being in the forefront of technical innovations (he is currently converting to using MathML and has a command line version which is fascinating). Then there are large collections of maths related blogs such as those at Art of Problem Solving and the huge number of blogs by Warwick University students and staff at Warwick Blogs.
Many such blogs deal with the writer’s experiences but if it is mathematics you are after then a good place to start is at Carnival of Mathematics: Inaugural Edition. This has links to mathematics blogs at all levels, such as mathematics quotes, mathematical objects like Klein bottles that you can buy, a hotly debated probability paradox (well worth reading for an insight into the intricacies of this subject) all the way up to group cohomology. Do visit Carnival of Mathematics: Inaugural Edition – you may never have time to read anything else once you’ve explored the links and the links to the links …