Mathematician Keith Devlin thinks the cellphone and 3D gaming technology are the watershed technologies for learning mathematics. I don’t agree on the $100 laptop — it’s impossible to anticipate the innovative ways that technology will be exploited.

For the first time since Euclid started the mathematics education ball rolling over two thousand years ago, we are within a generation of eradicating innumeracy and being able to bring out the mathematical ability that research has demonstrated conclusively is within (almost) everyone’s reach. The key to this development (actually two developments, one in the developing world, the other in affluent, technology-rich societies) is technology (actually two technologies).

First the developing world. Forget the $100 laptop, which I think has garnered the support it has only because of the track record and charisma of its principal advocate (Nicholas Negroponte), the ubiquitous computing device that will soon be in every home on the planet is the mobile phone. Despite the obvious limitations of a small screen and minimal input capability, with well-crafted instructional materials it will provide the developing world with accessible education in the basic numerical and quantitative reasoning skills that will enable them to escape from the poverty trap by becoming economically self-sufficient. Such a limited delivery system would not work for an affluent consumer who has choices, but for someone highly motivated by the basic desires of survival and betterment, who has no other choice, it will be life transforming.

At the other end of the economic spectrum, the immersive, three-dimensional virtual environments developed by the gaming industry make it possible to provide basic mathematical education in a form that practically everyone can benefit from.

We have grown so accustomed to the fact that for over two thousand years, mathematics had to be communicated, learned, and carried out through written symbols, that we may have lost sight of the fact that mathematics is no more about symbols than music is about musical notation. In both cases, specially developed, highly abstract, stylized notations enable us to capture on a page certain patterns of the mind, but in both cases what is actually captured in symbols is a dreadfully meager representation of the real thing, meaningful only to those who master the arcane notation and are able to recreate from the symbols the often profound beauty they represent. Never before in the history of mathematics have we had a technology that is ideally suited to representing and communicating basic mathematics. But now, with the development of manufactured, immersive, 3D environments, we do.

Good stuff — enjoy.