I’m fascinated by mathematics, though my own understanding of it peaked at 18, when I was merely competent, never precocious. I wonder from time to time, as we all do, what mathematicians are actually ‘doing’ when they retreat to think and squiggle.
I touched on the philosophy of mathematics when I was at university and I remember reading about Bertrand Russell’s and Alfred North Whitehead’s massive three-volume Principia Mathematica, which sought to derive mathematics from the basic principles of logic (an undertaking that Kurt Godel later showed to be impossible). Though it may not be true, I was amused by the story that it’s only after about 500 pages that you reach a sentence that reads ‘..and so therefore 1 = 1′. I never read the book, nor will I, not least because you need a wheelbarrow to carry it around.
I am fascinated not by the squiggles but by the mathematical struggle itself, and I recently read a layman’s account of Andrew Wiles’ heroic 1995 proof of Fermat’s Last Theorem (after 358 years of effort by the mathematical community) with great excitement but little understanding. Proofs are like ‘discoveries’, akin to the discovery of the South Pole, or the first landing on the moon. The outer reaches of mathematics are uncharted territories, waiting to be found, mapped and possessed. Wiles’ proof was like the discovery of the North West Passage, the finding of a route from one impossible mathematical place to another.
But of course mathematics isn’t anything like ‘discovery’ in the geographical sense. There isn’t any mathematical ‘reality’ out there for mathematicians to explore. It’s just a game with symbols, perilously constructed on a simple foundation of 1,2,3,4,5,6…. and so on. Who chose, for example, to extend the rules of that game to allow the square root of a negative number?
But the wonderful thing, I am told, is that it’s not a pointless game at all, not just a form of amusement for very clever people. Mathematics, together with all those improbable extensions that take it well beyond what most of us can grasp, and well beyond any use that most of us might have for it, has proven a useful tool for science. Those flights of fancy and intellect have practical applications in areas such as quantum theory.
So, I was excited to read yesterday that another of the great unproven hypotheses of mathematics had finally been proved – Riemann’s Hypothesis, which has to do with the distribution of prime numbers. Indeed its mere statement, unlike Fermat’s Last Theorem (no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two), is beyond most of us.
Riemann’s Hypothesis is one of the seven somewhat difficult Millenium Problems listed by the Clay Mathematics Institute. Solve any one of these and you’ll win a million dollars.
What I read yesterday was that Riemann’s Hypothesis has been proved by a university lecturer in Nigeria, Opeyemi Enoch, who was inspired by the enthusiasm of his students to give it a try.
But apparently it isn’t true, and the Clay Mathematics Institute still lists the problem as unsolved. Other sources report that the theoretical papers Opeyemi Enoch had referred to were neither his nor an accepted proof of Riemann’s Hypothesis. Probably a case of plagiarism. See Not Proven.
Plagiarism seems so foolish nowadays, so unlikely to succeed. There are many tools to hand (one of them being Google) that will quickly determine if a paragraph of text has been ‘borrowed’. You wonder why anyone still bothers. It’s a risky practice. But accusations of plagiarism still bring down the high and mighty, or, in some cases, should do so if the plagiarist possessed a modicum of shame.
Romania’s former Prime Minister Victor Ponta, who resigned a couple of weeks ago, currently stands accused of corruption and may face trial, but some years ago he blithely sailed through very plausible accusations that large parts of his doctoral thesis were copied.
Plagiarism, one must remember, is a time-honoured tradition in Romania. Elena Ceausescu, wife of the former dictator, received a number of academic awards for her work on polymer chemistry, though when she left primary school she was proficient only in needlework. It is unlikely that she could have understood even the first page of her 162-page thesis.