### Math 2.0

Thursday, January 28th, 2010 | Author: Konrad Voelkel

The term Web 2.0 was coined by Darcy DiNucci in 1999 and popularised by Tim O'Reilly in a 2004 conference named Web 2.0. In the beginning, it wasn't totally clear what Web 2.0 really meant for the ordinary web consumer. Then it crystallised out that users associate with the term Web 2.0 an interactive internet. During that time, the first large collaborative dynamic websites were seen, such as Wikipedia and YouTube. Web 1.0 are static HTML pages that don't allow interaction.

UPDATE on 2012-11-20: see my compilation of math resources for a much longer list of math 2.0 projects (as well as many cool math 1.0 projects).

For me, it's only natural to ask what's in there for mathematics and mathematicians. Are collaborative websites good for mathematics? (Maybe not, maybe they're just distracting). So let's talk about Math 2.0. One could define the term Math 2.0 to be the mathematical content in Web 2.0, so that would be math blogs, math wikis, math videos. Current math videos on YouTube are just videos captured from ordinary lectures, which could have been on Web 1.0 sites, too. Current math blogs are just like periodic mails on a mailing list, so the concept existed long before Web 2.0, although the make-up has changed and it's easier to find via search engines.

**Let's have a look at some of the best Web 1.0 math websites:**

- The On-Line Encyclopedia of Integer Sequences - look up some short sequence of numbers to see in which patterns they fit.
- John Baez: This Week's Finds in Mathematical Physics - John Baez has been writing his wonderful thoughts about mathematics, physics and the in-between for more years than I know what mathematics is. You can learn a lot from these notes. He has been posting it in sci.physics.research, sci.math.research, sci.physics and sci.math.
- The Mathematical Atlas - a hand-crafted tour through the various regions of mathematics, clustered along the AMS classification, spiced with many useful links. (I hope this will be relaunched as a community-based website one day. It deserves to survive).
- The Mathematics Genealogy Project - find out how half of all professors are descendants of Mersenne: 139335 mathematicians in the database, 61089 descendants of Mersenne. They have nice posters, too.

And now, before I sketch my vision of Math 2.0, for **some of the best Web 2.0 math projects:**

- The n-category café - a group blog about higher algebraic structures (especially n-categories) and physics. There are almost always interesting discussions going on.
- The Catsters - two mathematicians explain category theory (thus the name Catsters) in short, understandable snippets made exclusively for YouTube. Have you ever felt the need to learn what Monads are? String diagrams? Maybe you would be happy if someone would explain you limits and colimits. The Catsters do it, and they do it for free.
- The Open Problem Garden - a collectively maintained list of open problems in mathematics, ranked in difficulty. It's still in an early phase of it's life-time and somehow concentrated on problems with a combinatorial flavour, especially graph theory. Maybe you could enter your favourite open problem there?
- Wolfram Alpha - a mathematical data search and browse engine. You can look up statistics, perform comparisons and calculations and visualise this data. Very nice!
- Complexity Zoo - a website that collects computational complexity classes, with lots of helpful explanations and fact around them. At the moment of writing, they count over 480 complexity classes!
- Rigorous Trivialities - a group blog about algebraic geometry, with a huge series about "Algebraic Geometry from the Beginning" - which I recommend for it's little intuitive text-snippets, where you can pick just what you need.
- The Secret Blogging Seminar - a group blog about algebraic geometry.
- The Unapologetic Mathematician - John Armstrong's high-level educational math blog. You can pick some topic you want to learn and track back the links to the point where you're on safe ground. This way, learning is much more efficient than using a linear book. Covers, for example, some category theory.
- What's new - Terence Tao's blog. He describes it with the words "Updates on my research and expository papers, discussion of open problems, and other maths-related topics". Well said, worth a look!
- Timothy Gowers's blog - currently obsessed with the PolyMath project (see below).

**UPDATE**: For a list less biased by my personal interests, see the thread "most helpful math resources on the web" on MathOverflow

**Okay, now what is Math 2.0?**

Math 2.0 is mathematics done collaboratively in genuine new ways over the internet.

This means, a website qualifies as Math 2.0 if it changed the way mathematicians collaborated.

However, it seems like the school education community, more focused on children, uses the term Math 2.0 as a buzzword for "learning math over the internet".

From the Delicious tag Math2.0 you can see that the term is also used for math blogging.

Keep in mind that all this 1.0, 2.0 buzzword terminology is just tagging some websites. It's not important, and as Tim Berners-Lee says, the web was always about communication from person to person, it's nothing new.

**My favourite Math 2.0 projects:**

- The nLab - the wiki associated to the n-category café, an attempt to structure the discussions and facilitate re-use. This way, the nLab users build an expert encyclopaedia about their subject. Since it's a subject with intense research going on, it's more like their secret lab book than like the consensus-based Wikipedia. The rather inclusive viewpoint instead of the encyclopaedic exclusive viewpoint of Wikipedia has already created a very helpful collection of references. The nLab personal lab wikis have already shaped how people do their mathematical research, thus it truly qualifies for Math 2.0.
- MathOverflow -
*the*mathematical question&answer web site, intended to be used by mathematicians (so, no homework questions on this site). Without MathOverflow you would have to know the right people. With MathOverflow you can just ask them. - PolyMath - the first massively collaborative mathematics problem solving project. It was successful, so they've just recently started the next PolyMath project. Gowers and Nielsen have an article in
*Nature*about PolyMath. - The Tricki - a wiki of problem solving tricks. It's somehow in the spirit of Polya's book about mathematical problem solving, but much more practical, solution-centered in concrete situations. It's something you couldn't get with a book and it's perpendicular to classical literature.

**Usage of the terms "Web 2.0 math" and "Math 2.0":**

I have some ideas in my mind for a future Math 2.0 project, involving creative use of LaTeX, wikis and collaborative/social websites... but it will take another few ~~months~~ years until the idea is ready to go public~~, and I still need to convince some collaborators to help me with the workload~~.

Where they talk about Web 1.0 and Web 2.0, the Web 3.0 is not far. Clearly, somebody must fill the buzzword Math 3.0 with some nonsense! Since this post is already long enough, I will speak about the semantic web, Web 3.0 and the great potential for mathematicians another time.

(And I'm really sorry that I didn't list all good math blogs or other math projects, not even all my favourite ones, like this wonderful blog about motivic stuff. However, if I missed a popular one, I would be happy to hear about it in the comments.)

2010-08-13 (13. August 2010)

Sorry, the DiNucci article is no longer available. For some discussion about this, see