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It’s been a while since I’ve added to my career advice and writing pages on this blog, but I recently took the time to write up another such page on a topic I had not previously covered, entitled “Write in your own voice“. The main point here is that while every piece of mathematical research inevitably builds upon the previous literature, one should not mimic the style and text of that literature slavishly, but instead develop one’s own individual style, while also updating and adapting the results and insights of previous authors.
I’ve added some new pages to this blog. Firstly, I’ve moved my old page on my books to a new page on this blog, so that each book now has its own page for publication information, errata, etc., as well as its own comments section for feedback (including the inevitable reports of future errata).
Finally, I added some links on the sidebar of this blog to some of the more popular of my older posts and articles, and reorganised the categories slightly. In particular, my expository articles were moved out of the “short story” category (they didn’t fit particularly well with the other wordpress articles in this category) and into the “expository” category. (Now that there are a number of wordpress blogs in research mathematics, it might eventually be worth trying to establish some standards for use of mathematical tags, but this is hardly an urgent concern.)
For the last year or so, I’ve maintained two advice pages on my web site: one for career advice to students in mathematics, and another for authors wishing to write and submit papers (for instance, to one of the journals I am editor of). It occurred to me, though, that an advice page is particularly well suited to the blog medium, due to the opportunities for feedback that this medium affords (and especially given that many of my readers have more mathematical experience than I do).
I have thus moved these pages to my blog; my career advice page is now here, and my advice for writing and submitting papers is now here. I also took the opportunity to split up these rather lengthy pages into lots of individual subpages, which allowed for easier hyperlinking, and also to expand each separate topic somewhat (for instance, each topic is now framed by an appropriate quotation). Each subpage is also open to comments, as I am hoping to get some feedback to improve each of them.
[Update, June 10: Of course, the comments page for this post, and for the pages mentioned above, are also a good place to post your own tips on mathematical writing or careers. :-) ]