Editorial Ian Stewart

Practising Mathematics Without a License

What would mathematics be like today, if Newton had been able to patent the calculus? In law, it is not possible to patent an idea. But the computer has blurred the line between

ideas and hardware, and the attitudes of lawmakers are beginning to change. The Atari Corporation is attempting to sue anyone using ideas from their video games in software sold on the open market. Recently a group of computer scientists devised a new technique for code-compactification, leading to a 25% saving in memory requirements. A decade ago they would have published it in a journal for anyone to use; today it exists only as a commercial product.

It is a common complaint that mathematics lacks due prestige. The short answer to this is that prestige -- money, so the only way to increase the prestige of the profession is to charge commercial rates. If we think so poorly of our own ideas that we are prepared to give them away free, why should anyone else think better of them? Not so long ago a couple of mathematicians offered to make a statistical analysis of jury selection in the USA. They estimated that proper procedures might save $3,000,000 per annum per county; and offered their services free. They were universally rebuffed (and subjected to repeated lectures on how mathematics couldn't possibly be applied to a random process). I think their mistake was not to have charged $50,000 in consultancy fees and waved great heaps of computer printout.

One can imagine a kind of Utopia for the Mercenary Mathematician, in which the only legal way to get a calculation done is to pay a member of the Guild of Geometers to do it. Five cents for an addition operation, ten for division; a dollar for differentiation, five for solving a differential equation. Diophantine equations subject to a 15% surcharge for an integrity check; reduced rigour on a sliding scale of discounts . . .

No matter that a trained layman could do the job himself. First, we'd have made sure that no layman could get the training. Then, we'd have made it illegal for an unqualified person to practise mathematics. If that sounds ridiculous, try to register for Author's Lending Right in the United Kingdom without the signature of a Notary Public. Or ask in your will that you be buried in your back garden. Or, to put it another way, why will the Inland Revenue believe my accountant, but not me?

Licensing people to practise mathematics wouldn' t necessarily be a bad thing. I am reminded at once of the Case of the Drugged Baboons, pushing a lever at response rate D in comparison with the control rate C of undrugged baboons. A decade's research solemnly plotted D/C against C on logarithmic scales, getting a correlation close to - 1 from a computer package; and interpreted this as showing a dependency of drug effects on the control rate C. Then in 1978 it was noticed that if

log(D/C) ~ - l o g C + k (k = constant) then

D - e k = constant.

If I'd done to baboons what the medics did to my beloved mathematics, I'd be in jail. (Did no one notice D was roughly constant? Just how great are the magic powers of the com- puter?)

THE MATHEMATICAL INTELLIGENCER VOL. 5, NO. 2 �9 1983 Springer-Verlag New York 3

If such a system were introduced now, there would of course be an immediate power- struggle to control it. Judging by public pronouncements, at least one faction would favour the exclusion of all pure mathematicians. But if the system had grown up over a period of time, these people would have been forced to accept what the medical profession learned long ago: the profession as a whole is paramount and it is unseemly to break ranks in public. Nevertheless, ensuring a balanced control would be a serious problem.

It pales into insignificance in the face of outside resistance. Mathematics is far too useful, and the consumers who now get it free would kick up an awful fuss. (Actually, a campaign to introduce a mathematical levy would be one way to remind the outside world of the true value of the subject. If it were as irrelevant as some claim, there need be no outcry. Want to bet? They wouldn' t even let us patent the purest parts of Number Theory. Because (aha!) it might just turn out to be useful, one day.) No, we missed the bus long ago.

Of course, if all rights to the calculus were owned by the Isaac Newton Corporation (after a multi-billion dollar legal action against G. W. Leibniz GmbH) there probably wouldn ' t be much mathematics worth having anyway. Free exchange of information, so vital to the health of our subject, would pretty much have dried up. A few mathematicians would have become rich; but mathematics itself would have become much poorer. We don't get millions of fans beating down the doors of the International Congress trying to get tickets to watch the Fields Medallists; but if we did, the International Congress would have the same scientific importance as the Eurovision Song Contest. It's a heavy price to pay for prestige. Or for the right to stamp out perceived abuses of mathematics.

No: the Licensed Mathematick of the Guild of Geometers is not a practicable proposi- tion---even in fantasy. I suspect we must resign ourselves to continuing along our lonely path, casting pearls of wisdom whither we know not; to be used, abused, or ignored as the whim takes. We can at least find some small consolation in the proverbial nature of those before whom pearls should not be cast.

4 THE MATHEMATICAL INTELLIGENCER VOL. 5, NO. 2, 1983