Mathematics journals publish papers by mathematicians on their research discoveries, or sometimes expository works that overview an area. They have traditionally been the main repositories of innovation and development in mathematics—the advance guard of mathematical knowledge—with books being the support troops that bring up the rear and consolidate the progress made.

Mathematics journals used to be published by Academies or Societies, often with a strong regional affiliation. Crelle’s journal was an important journal initiated by a single individual. These days most journals are associated with a Mathematical Society and run as a service to the community, or are commercial enterprises run for a profit.

Modern technology, in particular the internet, is putting the entire enterprise under investigation. Will the mathematics journal in its present form survive? Recently the ArXiV and other online repositories mean that people can upload research papers before they are officially published, and indeed can circumvent the entire publishing process if they so choose. What happens when everything is online and no-one really reads the bound journals? What will be the role of other means of relaying information, in particular video?

Can commercial publishers maintain the (seemingly) exorbitant prices that they have historically been able to charge the main institutional (library) buyers of their wares? How are the roles of editor, referee, typesetter, distributor going to change?

Before the onslaught of the internet, we had already seen a major shift in the world of journals with Donald Knuth’s celebrated creation of TeX, and then LaTeX, which allows authors to typeset their mathematical papers themselves. I use Scientific Workplace to access LaTeX, and it is easily the most useful toolbox that I use as a professional mathematician (I will have to sing its praises in a separate blog sometime). So us mathematicians no longer need typists or typesetters, and in fact we don’t really need the printing and distribution capabilities of traditional journals, since papers only really get published in one place these days, namely the internet, and if someone wants a printed copy, they print it out themselves.

What about editors and referees? Don’t they still perform a valuable function? Yes certainly they do, but their roles are also looking increasingly unclear. Is the refereeing system really working? There are ranges of opinion. As gatekeepers to prestige and success, editors and to a lesser extent referees have been able to shape and direct the course of mathematics. Now increasingly there is a sense that mathematics will go where it will, without supervision, and with powerful people having less of a handle on promoting one area at the expense of others.

But I believe that the real game changer will be coming from video. Already if people want to know something in depth, they are as likely to look it up on YouTube as find a printed explanation. The reality is that we can learn most efficiently when someone who knows what they are talking about explains it to us in a visual way at a level that is appropriate to us. Increasingly mathematicians are going to start to realize that if they really want to engage with a wide audience, and promote their ideas in the broadest possible way, they will have to augment their paper productions with video explanations.

In fact if done well, a video presentation can easily become the primary resource, with an associated pdf as a secondary resource for those who want to pore over the details. Most of us don’t want to pore over the details. So we are going to see an increasing number of academics thinking not so much about their paper CV, but rather about their video CV.

I have already made this transition some years ago. It is just so much more satisfying to explain a good idea by making a video about it, without the onerous obligation of getting every word just right and jumping through all the publishing hoops. Every word doesn’t really have to be right. The ideas have to be right, and they have to be visually interesting and engaging.

And what about the importance of having someone else to `approve’ my ideas for publication? Bah. For me, this is completely unnecessary. I am perfectly capable of deciding myself whether my work is worthy of publishing. If I make a mistake and someone points it out, I can change the video. If someone discovers a better way of working through some point, they can make a comment or publish their own video. And ultimately it will be the public, the viewers, that decide whether videos are worth watching, not some anonymous referee.

Want an example? I am working on revolutionizing hyperbolic geometry. I am slowly doing that with a series of traditional papers in excellent journals. But I am also doing that on YouTube, right here: