This week’s Article of the Week features Alan Beardon on Fractional Calculus (I, II, III). Find out how do integrate 2-and-a-half times!
The articles are from the website NRICH. It’s aimed at schoolkids, so goes gently enough. So if, for example, you already know what the Gamma function is, you can skip the first part. But I learned something, nonetheless.
In Article of the Week, I intend to post something that I’ve enjoyed reading in the last the last seven days, but don’t really have anything to say about. So it will usually be outside my areas of study.
To kick us off, Fields medalist Tim Gowers asks Cuspomms (Cambridge University society for the philosophy of maths and the mathematical sciences) Does mathematics need a philosophy?
I would like to advance a rather cheeky thesis: that modern mathematicians are formalists, even if they profess otherwise, and that it is good that they are.
This is the sort of evidence I have in mind. When mathematicians discuss unsolved problems, what they are doing is not so much trying to uncover the truth as trying to find proofs. Suppose somebody suggests an approach to an unsolved problem that involves proving an intermediate lemma. It is common to hear assessments such as, “Well, your lemma certainly looks true, but it is very similar to the following unsolved problem that is known to be hard,” or, “What makes you think that the lemma isn’t more or less equivalent to the whole problem?” The probable truth and apparent relevance of the lemma are basic minimal requirements, but what matters more is whether it forms part of a realistic-looking research strategy, and what that means is that one should be able to imagine, however dimly, an argument that involves it.
Another next week!
