What maths A-level doesn’t necessarily give you

I had a mathematical conversation yesterday with a 17-year-old boy who is in his second year of doing maths A-level. Although a sample of size 1 should be treated with caution, I’m pretty sure that the boy in question, who is very intelligent and is expected to get at least an A grade, has been taught as well as the vast majority of A-level mathematicians. If this is right, then what I discovered from talking to him was quite worrying.

The purpose of the conversation was to help him catch up with some work that he had missed through illness. The particular topics he wanted me to cover were integrating , or as he called it, and integration by parts. (Actually, after I had explained integration by parts to him, he told me that that hadn’t been what he had meant, but I don’t think any harm was done.) But as we were starting, he asked me why the derivative of was , and what was special about .

What actually happened

The short version is that I’ve had the ablation (see previous post) and the surgeon who did it says that he has a good feeling about it. It’s taken till now to write this because, unlike most people who have ablations, I felt terrible for two days after it — with a headache (normal) and a fever (less normal but not unheard of). The fever was not very high, but high enough to be unpleasant, and meant that the only thing I could bear to do was go to bed, except that on the second night after the operation I had to spend part of the night sitting up on a sofa because my chest hurt too much when I was horizontal. (That was normal, and nothing to worry about.) So today is the first day that I am well enough to do anything as strenuous as writing a blog post.

Mathematics meets real life

I’ve been in two minds about whether to post this. On the one hand, I try to keep personal matters out of this blog — though there has been the occasional exception — but on the other hand I have a topic that fits quite nicely with some of what I’ve been writing about recently, since it concerns a fairly important medical decision that I have had to make based on what felt like inadequate information. Since that is quite an interesting situation from a mathematical point of view, and even a philosophical point of view, and since most people have to make similar decisions at some point in their lives, I have opted to write the post.

The background is that over the last fifteen years or so I have had occasional bouts of atrial fibrillation, a condition that causes the heart to beat irregularly and not as strongly as it should. It is quite a common condition: I’ve just read that 2.3% of people over the age of 40 have it, and 5.9% of people over 65. Some people have no symptoms. I myself have mild symptoms — I can feel a slightly strange, and instantly recognisable, feeling in my chest, and I experience a few seconds of dizziness almost every time I stand up from a relaxed seated position — otherwise known as orthostatic hypotension, which I often used to get anyway (as do many people).