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The Hungarian mathematician Paul Erdős was a partial exception. He overcame severe obstacles early in his life: his father had been deported to Siberia after the first World War and his mother had to work all day, so as a child he was left on his own for long periods with nothing to do but read the maths books around the house. He was Jewish, and when the Nazis came to power he had the foresight to leave for the United States while he still could. He devoted his entire life to mathematics, was called "The Oddball's Oddball" by Time magazine, and is widely believed to have described himself as "a machine for turning coffee into theorems" (although actually that was another Hungarian mathematician, Alfréd Rényi). But he was intensely sociable, at least when it came to doing maths, publishing over 1,500 papers with over 500 coauthors.

This prolific publication record led mathematicians and other scientists to assign themselves Erdős Numbers. Your Erdős number is the number of steps, via coauthored papers, between you and Erdős (yes, this is weird, but only a little). Erdős himself was the only person with an Erdős number of 0. His 500 coauthors all had an Erdős number of 1. Anyone they in turn had coauthored a paper with (who had not also coauthored one directly with Erdős himself) had an Erdős number of 2. And so on.

My Erdős number is, I think, 5 - it might be less, but it's definitely not more. This means that tutoring could help you get not only an A-level but also an Erdős number of 6, because if you go on from your A-level course to do a first degree and a PhD and start publishing, you are welcome to get back in touch with me and offer to add my name to a paper you are about to submit, even if I know nothing about its content, which I probably won't (this is remarkably common practice in academia). And an Erdős number of 6 is not to be sneezed at - the average for Nobel Prize winners is 5.3, and Peter Higgs, of Higgs Boson fame, allegedly has an Erdős number as high as 9. Clearly he should get out more.

*I also heard this joke told recently (by an engineer) with "engineer" substituted for "mathematician". Perhaps they are sensitive souls too, and they only wear those hard hats because they feel emotionally vulnerable.