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I am a graduate student in mathematics, and I recently got the question why there isn't a press release to the general public whenever we publish a paper (to advertise mathematics and increase interest).

Now, every paper is a bit extreme, but forced me to ask several questions:

Would arxiv be a good place to put math text aimed to the general public? (I am currently trying to explain an article in a very metaphorical, but accessible to non-mathematicians).

Would it be considered strange to explain research for non-mathematicians either in a separate abstract in a paper, or also writing a shorter non-math version? (I fear that this is considered slightly odd, and metaphors sometimes dumbs down the problem so that the question seems very silly. Also, will professors think it is a waste of time?).

A partial goal is to be able to explain what I've done the last five years to my family at the dissertation, but also get some experience in explaining math for grant applications. It would be nice if news from the world of mathematics appeared more often in the news, (local news for smaller achievements, explanations etc).

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    Posting "general audience" math papers to the arxiv would be reasonable, but I'm not sure if you'd reach much of your target audience. How many non-mathematicians do you know who have ever visited that site? – Dan C Oct 14 '12 at 20:29
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    Well, putting it on arxiv and linking to it, would attract non-mathematicians to the site, and some might be curious on how other articles look like. This gives a glimpse in the world of math, as arxiv is a central piece in the research process, imho. Also, it is more permanent than a personal web page at an institution. – Per Alexandersson Oct 15 '12 at 5:59
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    Would arxiv be a good place to put math text aimed to the general public? — Speaking as an ArXiv moderator: Yes! – JeffE Oct 15 '12 at 15:10
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I would recommend blogging. This seems like the standard procedure for explaining your papers both to the lay audience and to other mathematicians (potentially ones that don't work on your specific problem). The blog format is preferable over arXiv or journal publications for reaching the lay audience because it is more accessible. Links to blogs are easier to share and faster to read than journals (which might be behind paywall!) or pdfs from arXiv. A blog setting also allows you to interact with your audience through the comments, this is the best way to help guide them through any confusion.

A blog setting can also be used to provide casual tours through proofs for experts and graduate students. This has recently started in TCS. Since this is aimed at the slightly technical audience, it is more appropriate to put on the ArXiv, although I would still advocate blogs.

  • +1 I do some version of this myself, but I write my summaries mostly for non-expert mathematicians rather than non-mathematicians. – Willie Wong Oct 15 '12 at 9:32
  • I highly recommend blogging if you have time for it. ArXiv is not the best place for it as few non-academic know of the site, but if you blog about it in plain language and provide a link to the original article, it might be the best of both worlds. If you don't want to set up a blog yourself, then see if you have friends who have a blog on relevant topics and would not mind letting you do a guest post. – Theresa Liao Mar 18 '13 at 3:03
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This is a great idea, and it does happen. For years, Martin Gardner wrote a column in Scientific American called "Mathematical Games". He took interesting mathematical ideas and made them accessible to a wide audience. Another example is Keith Devlin, who is known as the Math Guy on NPR (National Public Radio) in the U.S. A third example is Ian Stewart. His book "Letters to a Young Mathematician" explains a typical mathematical career arc to a general audience in a fun and engaging way. Along the way, he touches on many important mathematical ideas.

So why don't we see more of this? The short answer is because it's really hard to do well. You have to really understand the math, and you have to be very good at explaining to people who think very differently from the way you've spent the last 15 years or more being trained to think. Furthermore, much of the general public doesn't really want to know more about math. Another reason is that this type of writing is typically not well-rewarded at research schools. The culture of research mathematics tends to say that exposition is fine, but it's not really hard, like research. So it shouldn't be rewarded at the same level.

I agree with you, that the world would be better off if more people understood what we (research mathematicians) do. The problem is, I don't know how to make it happen.

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    To add to this, not only is it hard to do, the audience is vanishingly small as the topics become more specific. – eykanal Oct 15 '12 at 0:10
  • @eykanal So true. It's hard to get many mathematicians to read most math papers (even when they have all the needed background). – Dan C Oct 15 '12 at 0:22
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    The culture of research mathematics tends to say that exposition is fine, but it's not really hard, like research. — Unfortunately spot on. – JeffE Oct 15 '12 at 15:15
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Would it be considered strange to explain research for non-mathematicians either in a separate abstract in a paper, or also writing a shorter non-math version?

It would come across as strange to include a separate abstract for non-mathematicians in a math research paper, partly because it's unconventional and partly because it might be interpreted as an assertion that this paper was likely to be of unusual interest for the general public. That's not to say it's a bad idea, but I'd recommend that grad students not try it, since you don't want readers to focus on this instead of your research contributions.

Writing a companion piece aimed at a general audience is less likely to attract any negative attention, especially if it's in the form of a blog post (as Artem suggests) rather than a formal paper. If you spend too much time on this, you risk having it look like a distraction from your research, but that's not likely to come up except in fairly extreme cases.

Also, will professors think it is a waste of time?

Some will, but others won't. I'd recommend not focusing just on your own papers: if you advertise other people's work as well to a general audience, they may or may not think it is worthwhile, but they are likely to feel flattered, and it will avoid the risk that this could come across as self-promotion on your part. Once again, you don't want to let this overshadow your scholarly accomplishments, but it can be a nice counterpoint to them.

It would be nice if news from the world of mathematics appeared more often in the news, (local news for smaller achievements, explanations etc).

Certainly. If you are a decent writer, it may not be too difficult to get your local newspaper to publish periodically about math news (this would require going well beyond your own work, of course). That would be a service for the community and an interesting line on your CV.

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You could make Youtube videos as well, e.g. start a video blog. Perhaps not like Khan Academy, which is mainly for instruction, but perhaps just to discuss new and cool ideas.

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