Mathematics research, like any worthwhile challenge, is demanding, but it is great fun. Like an athlete, a research mathematician puts enormous commitment into the hunt for the prize (which might be a significant new idea, or theorem proved, or new proof of a known theorem, or new promising technique, or problem solved); also like the athlete, the mathematician experiences great excitement in the chase, and finds huge satisfaction in reaching the goal. Most scientists and many mathematicians work in teams and feel themselves part of a wider community of fellow-researchers; so do most athletes. Some mathematicians are more like long-distance runners - they work alone a lot of the time. Andrew Wiles (now the most famous living mathematician, following his long-awaited proof of ``Fermat's Last Theorem" - see Zimaths 2.3) is one of these. Here are his own words about his experiences during the long years he battled in secret to find his way to proving Fermat's Last Theorem. His comparison of his mental adventures with the exploration of a huge mansion plunged in darkness, expresses well what many other researchers feel like:
Much of the time I would sit writing at my desk, but sometimes I could reduce the problem to something very specific - there's a clue, something that strikes me as strange, something just below the paper which I can't quite put my finger on. If there was one particular thing buzzing in my mind then I didn't need anything to write with or any desk to work at, so instead I would go for a walk down by the lake. When I'm walking I find I can concentrate my mind on one very particular aspect of a problem, focusing on it completely. I'd always have a pencil and paper ready, so if I had an idea I could sit down at a bench and start scribbling away...One enters the first room of the mansion and it's dark. Completely dark. One stumbles around bumping into the furniture, but gradually you learn where each piece of furniture is. Finally, after six months or so, you find the light switch, you turn it on, and suddenly it's all illuminated. You can see exactly where you were. Then you move into the next room and spend another six months in the dark. So each of these breakthroughs, while sometimes they're momentary, sometimes over a period of a day or two, they are the culmination of, and couldn't exist without, the many months of stumbling around in the dark that precede them.
Does that inspire you all to persevere with the much easier problems in this magazine?!