You will have seen in the paper the other day that Bill Clinton believes in the need to move away from zero-sum solutions ("where, in order for me to win, you have to lose") to the non-zero-sum solution, where, "in order for me to win, you have to win too."
Indeed. This might explain Mr Clinton's rather pedestrian golf game (though his outing at Ballybunion was not all that disastrous). And Tiger Woods is fairly obviously a zero-sum man. But at the risk of sounding pedantic (always a risk worth taking), Bill doesn't have it quite right. The zero-sum equation means that whatever is gained by one side is lost by the other so that the net change is always zero. This is hardly what happens when wars are won and lost, or agreements brokered, or disputes settled, or even when trade deals are made.
As for the non-zero-sum equation, some clearly win more than others, and the biggest winners are surely more delighted than anyone about that. I don't imagine that at the close of last week's lucrative Deutsche Bank Open in Heidelberg, stunned runner-up Michael Campbell and third-placed Sven Kjeldsen were admiring their petty prizes of a couple of hundred thousand dollars while gaping at winner Tiger Woods's appearance fee of some $2.5 million and shouting "Yeah! Non-zero-sum solution! Way to go, Tiger!"
Even in politics, and business, the non-zero-sum equation has surely operated for centuries, in the sense that most practitioners try to ensure that their close colleagues share in their success (though not necessarily to the same extent). Nothing new there, Bill.
But the theory does draw attention to the importance of maths. In our EL supplement on Tuesday, an NUI Galway lecturer in mathematics warned that, considering our technological needs, we are neglecting the subject at our peril. Maths teachers are apparently a "dying race" and the politicians aren't interested in giving the subject any priority.
Technological needs are only half the story (or perhaps less - the figures haven't been worked out). And it is an unhelpfully reductive exercise to simply emphasise the practical applications of mathematics to everyday life.
If maths enthusiasts want more attention paid to their subject, they need to raise their game, and get away from arguments that are clearly not impressing the politicians. They might start with a new emphasis on the joys of mathematical knowledge - such as being able to refute the assertions of former American presidents, improve performance at the poker and roulette tables, make millions out of junk bonds and keep an accurate score in a tennis match (not as easy as it seems).
They might also be well advised to separate mathematics from the dreary science of economics, with which it has been linked for far too long. The sheer beauty of pure maths must be emphasised more, and the last desperate efforts to justify the certainty of mathematics must finally be abandoned: this (of course) will mean doing away with Frege and Russell's logicism, Hilbert's formalism and Brouwer and Heyting's intuitionism.
But - you cry in horror - what will we be left with then? Why, the fallibilist epistemology of Philip Kitcher, that's what. If it's good enough for Philip, it should be good enough for you.
One thing is sure, there must be no truck with the formalists. These are the people (and I could name names) who believe mathematics is invented rather than discovered, and disdainfully treat it as a meaningless game: they play it according to certain rules, but do not admit to rules governing the construction of these rules.
These people are not quite the anarchists of the mathematical world, but they still need a close eye kept on them. For some odd reason they tend to proliferate in middle management, tennis clubs, backstreet garages and at Formula One race meetings.
As for Bill Clinton, he may or may not be aware of the theory that "mathematics can be used to make the invisible visible" but still, as a former Fulbright Scholar, he could probably deliver off the cuff a one-hour lecture on why dimples help a golfball fly.
bglacken@irish-times.ie