Johannes Gutenberg’s introduction of the printing press around 1450 was one of the defining moments of the modern age, ushering in a new era where knowledge could be cheaply reproduced and widely distributed. Since then the printed word has come to dominate our understanding of what information is.
Whether it be a book, a pamphlet, a newspaper or magazine article, a letter, a legal document, or these days a pdf or ebook, we have been completely ingrained to understand that information is printed information, and that to learn something means more or less to read it and understand it. This is the bedrock of the educational system, including of course tertiary education; with its heavy reliance on textbooks, libraries and learned journals.
All true, until now.
In only the last five or perhaps ten years, a new paradigm is suddenly upon us, sweeping through the modern world like a wildfire fanned by the deep untapped desire of people to learn by watching and listening, not reading. We are talking about video, my friends: most notably YouTube videos, but also of course iTunesU, Vimeo, Coursera, OpenLearning etc. Young people increasingly go to YouTube as a default if they want to know something; now already the 2nd largest search engine in the world—next only to Google—and moving quickly to become one of the prime repositories of really useful knowledge on the planet.
For one-sentence knowledge, the printed word will remain king. What is the circumference of the earth? Who was the president after Lincoln? Where was the first mammoth discovered? For such tidbits of knowledge, the printed word is optimal. For large-scale knowledge, the printed word may also be harder to replace. But for everyday middle complexity information, which requires, or at least requests, something of an explanation, video will rule.
How do I fix my lawnmower? Who were the greatest conquerors in history and why? What is Rational Trigonometry, and why is it so superior? Where are the best surfing spots in Sydney? What is the best way of chatting up a girl? For this kind of important info, and much, much else besides, most of us would rather get the answer from a person, using a combination of audio and visual representations. Video cannot be beaten here in my opinion.
While MOOCS and all kinds of fancy e-learning systems are much the rage in tertiary education these days, it is useful to keep in mind that the key ingredients are almost always the videos themselves. We are returning to the rhythm and logic of an earlier vocal tradition, where knowledge was memorized and passed on from father to son, from mother to daughter, from leader to followers—by talking, explaining, showing. This is far closer to our biology than the current arcane system of letters and numbers that form our printed sentences, like this one. If I was reading this out loud on a video, then my emphasis, pauses, expressions and posture would convey just as much, maybe more, than the words themselves. As it is, you have only the words.
Video as information is an idea which may well prove to be more interesting and important than video as entertainment. It is happening now, as we speak. When I started posting math videos on YouTube in 2007, most of my colleagues thought it was a strange use of my time. Don’t academics spend all of their energy writing furiously to continuously augment their all-important list of printed publications? What’s the point of posting videos that you will get little academic credit for?
Some of my colleagues probably still feel this way, but I bet they are a lot less confident now. They are perhaps starting to acknowledge something that students have long known—that even interesting and pretty mathematics may be difficult or painful to learn from an article or book! And some of them are starting to realize that if you don’t join the video revolution, your work runs the risk of being left behind, forgotten and unused, no matter how good it looks officially on a CV.
A salutary story for me: when I was a graduate student at Yale, I had a desk in the annex of the library on 11 Hillhouse Avenue; a somewhat dark and hard-to-find room in the basement which was stacked to the rafters with ancient math journals (for which there was no more room in the main library upstairs). Late at night, bleary from too much mathematical pondering, I would pull down a volume from on high and have a look into journals from the 1800’s. Creakily the dusty tome would relinquish its grip on its neighbours, having been unmoved in at least half a century: then I would skim these lovely, elegant articles, thinking—why is no one reading this great stuff anymore?, and— is this what will happen to my work once I am gone?
This need not be the future of today’s mathematicians. Well-presented videos of interesting topics embodying deep understanding will be regarded like gems of classical music to future generations of students and scientists, is my guess. Maybe this is a tad poetical, but I really do believe in the huge potential for broadening understanding and interest in the general public towards mathematics—that most beautiful of disciplines!
So, young mathematicians, take my advice—by all means play the game of oft and repeated publication in learned journals, but also spend some time developing your skills at explaining and presenting your knowledge and work through videos, so that your ideas will be accessible, useful and engaging to a wide spectrum of listeners. It is the future of publication, as much as it is the future of knowledge distribution.
njwildberger: tangential thoughts 
I listened yesterday to a speech by Guy Pfefferman, CEO of the Global Business Schools Network, which tries to improve managerial skills in developing countries. When water or goods or medicines aren’t delivered simply because of untrained incompetence, progress is crippled.
Here’s what’s relevant to your post:
He said that in Africa, 2/3 of the population now has access to mobile phones, many of which are smart phones, and that the impact has been revolutionary, more than anything else he has ever seen. Wireless phones have facilitated improvements in efficiency and all kinds of new entrepreneurship. Yet higher level management education has been neglected for 20 years. He hopes that someone develops a business model for the mobile video delivery of education in basic, badly-needed areas like accounting, supervising human resources, etc.
Your video lectures are models of simplicity and clarity, yet reflect years of teaching experience. Your inexpensive 8-10 prepared posters are much better than, say, looking over the shoulder of some amateur fumbling along. Operations analysis may not be as beautiful as hyperbolic number theory, but if other teachers emulate your methods and provide free YouTube video lectures to the world, they’ll be doing a real service to humanity, too.
I think you are right. I was at an education conference in South Africa a few years ago, and it was clear that mobile phones, not computers were the go to technology for reaching people across a wide spectrum. It is going to be huge–people anywhere just being able to watch and learn stuff on so many interesting things, and connecting with others with similar interests.
I’m a computer science student and I stumbled upon your videos on quaternions which helped me a lot in making sense of the math involved. Videos are the way of the future of learning.
I have two thoughts on this.
Firstly I’m reminded of Marshall McLuhan. My knowledge of him is still scant and consists entirely of the Wikipedia article, a few blurbs, Amazon reviews and video clips from interviews on YouTube. I’ve not read a word of his books, so I make no claim to be an expert on him, but it seems like while he mostly stated very confidently various assertions which seem like exalted intuition rather than science, and might be dismissed by some, there might still have been something to his viewpoint. I learned American companies and advertisers had paid him a fortune for his advice about how to use TV to their advantage, since he was among a few people in the 60’s with very clear notions of how to effectively use TV, which at that time was still a new medium.
In any event, his most famous proclamation, as you may recall, was that “the medium is the message”, which seems like a dramatic way to express a more modest claim, namely that _what_ you choose to communicate via a given medium is far overshadowed by the effect of the medium via _which_ you chose to communicate it. Personally, I second your assertion that it can be much easier to grasp math via a TV program than a book, because I’ve thought the same thing after watching your videos and contrasting the experience to reading math books, which I tend to do alongside them. I think YouTube videos better resemble aspects of the classroom lecture experience than a book can, even without that other important aspect– student teacher interaction– which books similarly lack.
I’m led to wonder what McLuhan’s observations and intuitions might have been regarding this recent proliferation of all sorts of new media. Let me add to your list blogs, MMO gaming, Twitter, Wii consoles, Smartphone apps, Google Glass, and Second Life, with still more sure to come. I’m not sure people have even considered how one might, say, conduct education over some of these mechanisms. Perhaps even the more preposterous (e.g., trying to conduct a literature discussion over something similar to Twitter?) might lead us someplace interesting, who knows?
My second thought relates to recently having come upon some great content from British TV in the 1970’s, clips from Bryan Magee’s discussions with philosophers about philosophy. I’m not sure that sort of discussion even leaves college campuses these days! And as an American, especially today, it’s difficult to imagine anything so intellectual ever having appeared on TV at all!
I think it must be the case that major broadcasters show so much sex, squalor, scandal, violence, song and dance, glitter and general stupidity as they do because it seems a surer way to make money from a big random crowd than attempting to appeal to their respective intellects. But then YouTube would seem to afford this new opportunity for viewers and content providers who are seeking something smarter or more practical to actually be able to find one another, in quantity, and so raise the bar a bit, at least somewhere. Consider TED Talks. I wouldn’t call them education, per se, but they are more informative than Gangnam Style and Miley Cyrus on a wrecking ball. I suppose most of YouTube users (and to be fair, some of us, too, some of the time!) will still choose to watch the pabulum, so that will continue to reign supreme, but it’s new and exciting that other content is even making it to TV. And increasing its availability to people around the world, for those motivated to find it, does seem hopeful. I feel I’ve benefited from it myself. It’s pointed me to people and ideas and books and other YouTube content I doubt I’d have found at my local library.
Lots of good ideas there, thanks. I wonder if those Bryan Magee talks are accessible these days?
Hello Professor Wildberger, I’m sorry that this has nothing to do with the topics here but I want to know your opinion on this post on physics exchange by the user Ron Maimon. Maybe you could do some video about it? Or just say your what you think 🙂
http://physics.stackexchange.com/questions/14939/does-godel-preclude-a-workable-toe/14944#14944
(you have to scroll down a bit to see the answer of the user
uargh sry for typing mistakes….
I appreciate your thoughts. Your foundational videos on mathematics was a huge influence on my thinking, and has gotten me MORE interested in MATH BOOKS. I also find myself frequently looking for HOW TO videos/articles on things that I know little about, in which cross referencing can be VERY important. Another valuable and much less promoted resource is: https://archive.org/index.php
Another thing to consider is the medium of the computer and the ability to run programs on it which can emulate environments in which we can learn. Geometry It seems, may be THE prime example I have at this time. For example, I can take an old text about geometry off the internet for free, read about these seemingly complicated relationships, and then build them and play with them in a great free program, like Dr. Geo. What a wonderful way to self educate!
I also love to program, and the link between mathematical research and heritage is something that I think is very valuable to grounding the programmer into the conceptual framework of the nature of computation. I think perhaps the most important thing about your approach for me, was that you seemed to invite me to to mathematical research, with MY obligation as the challenge of working with the framework to gain some level of proficiency so that I could defend these foundational arguments on my own. Oh, and your thinking on the subject is as clear as I’ve ever seen! And you shared that with me!
All the best Mr. Wildberger!
Hi Adam, Thanks for the comment. You are spot on in identifying geometry programs as a great way for amateur mathematicians to make interesting and even possibly important observations and discoveries. Hope you keep on exploring.
As a consumer of your great Youtube content, let me just say that I wholeheartedly agree with this post! 🙂
I wanted to take some of the information you presented in math foundations and make some python functions out of them. The problem was the pace of the videos is pretty slow, I had already seen them and wasn’t really in a mood to go through them twice. Then I remembered that you number all your slides, and each slide was pretty complete in the information you covered verbally. All I had to do was get near to where I wanted to begin, pause the video, read the slide and then fast forward on to the next slide. If I had *any* questions on what the written material covered I just played the video at normal speed. You friendly voice covered in detail each line of the slide and quickly brought me back in line. I have to admit it was both expedient and enjoyable. Like having a book that took the time to detail any questions, but allowed me to go at a pace I was more comfortable with.
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