Many years ago I asked Robin Gandy about Andrew Hodges' biography of Turing. He said it was very accurate. There are some more biographies of him now, but I've not read them.
The problem with mathematical notation is that it is usually designed by accountants, physicists, and, of course, mathematicians. None of which groups are noted for their prowess in graphic design or cognitive psychology. (Ok so Robert Recorde's equals sign is an example of superb graphic design but I agree with Turing on Leibnitz' notation for calculus.)