Erwin Schroedinger lies buried in a grave in the Austrian village of Alpbach. Best known for the cat that existed only in theoretical physics, so cannot have been simultaneously alive and dead, Schroedinger was one of the greatest thinkers of the Twentieth Century. The winner of the Nobel Prize in 1933, he fled his native Austria to escape the Nazis and was a professor in Dublin for fifteen years. His grave is unremarkable, easily missed. It was a decade ago that an English physicist, who had given up science to become a policeman, pointed out the distinctive inscription at the top of the memorial. “That is the Schroedinger Equation,” he said, “it is derived from the Hamilton constant.”
“Of course,” I said, having no more clue whether he was talking about physics or a regular member of a Scottish football team.
Perhaps inscribed equations were the hallmark of mathematical geniuses for the Irish mathematician William Rowan Hamilton, upon whose work Schroedinger drew, was walking one day with his wife beside the Royal Canal one day in 1843 when the idea of quaternions occurred to him. Taking out his pen knife, he carved i2 = j2 = k2 = ijk = −1 into the side of Broom Bridge.
Saying one or more things are equivalent to one or more other things is at the heart of science; it is also at the heart of numerous other activities, from farming to shopping, from medicine to decorating. Equations are unavoidable, anyone who works out what they can afford to buy with the money they have in their pocket engages in working out equations. Even deciding how time is best spent is a matter of deciding on the relative worth of various activities, it is saying spending this much doing this equals spending that much doing that, it is to do an equation.
Equations being so much a matter of everyday life, it is necessary that they be part of school mathematics, part of the national curriculum for 11-16 year olds. So it is that I spend hours trying to work out the values of x and y and to determine whether equations have one, infinite or no solutions. Starting teacher training in the autumn there is a need to understand what is being taught, but there are moments when its abstract nature is challenging, even headache inducing. Schroedinger and Rowan Hamilton would shake their heads in disbelief that anyone could fail to understand things so elementary.