I have recently bought Edward Frenkel’s new book Love and Math: The Heart of Hidden Reality. The article that was sent to me that provoked me to buy the book appeared in the New Scientist and was very interesting but one link that particularly caught my attention was an article written by Frenkel critiquing E.O Wilson’s advice to young scientists about mathematics. Wilson basically says that he did not need mathematics for his scientific career and so young scientists should not worry if they are challenged by mathematics. Frenkel picks this apart and lays bare the grand fallacy Wilson’s position with both precision and passion. And he is right to do so, however revered and loved is E.O Wilson.
The core of the problem it seems is a total misunderstanding of what mathematics actually is. The idea that it is number crunching, algebraic manipulation and advanced arithmetic seems inherent in society mainly because that is about as far as most people got in their mathematical career. Yes, we all have had mathematical careers, even if we left school at 11 years old!
Frenkel explains how mathematics is so much more than that. “The laws of Nature are written in the language of mathematics” as Frenkel quotes Galileo who knew a thing or two about using mathematics to go beyond our the physical limitations of our biology. Charles Darwin spoke of math endowing us “with something like a new sense”. Frenkel discusses three dimensional curved space, a universe with more dimensions than we can see. The fact is that our own biology limits what we can see and experience, and it is if we are looking at our universe through a keyhole, with a view limited by our own physical and cognitive limitations. The only avenue beyond this biology is mathematics. Not only is it beautiful but it is also attainable. The idea of going outside our bodies to achieve a higher plane of understanding is present in many religions. Mathematics has much in common with this goal and it perhaps no surprise that in India, the home of meditation, that mathematical prowess is respected as in no other country.
So what has this got to do with mathematics in schools? Well, first of all let’s start to listen to top mathematicians about what mathematics actually is. Marcus du Sautoy (and others) conceive of mathematics as the science of pattern. This leads to a neat understanding of why our universe and mathematics seem to match up so well. It a fundamental assumption that the universe we inhabit behaves in the same way wherever we are in that universe, this could be regarded as a definition of being human. This is also the basis of human learning, including when we are babies. We assume that when we knock over a glass of milk the milk will spill, and will always spill. This pattern in the universe is what we see in the mathematics that is the language of science. When we study and understand pattern in the universe we are almost by definition doing mathematics.
Mathematics is moving so fast and the science that accompanies it is following on the same path that by not urgently taking our curricula beyond number crunching and arithmetic we are creating a new illiteracy in society. The few who understand mathematics will control the mass that do not. This is not fair and a society that relegates mathematical insight to a luxury for the few is on a dangerous path.