In glancing through the pages of this book, you may notice that it contains some symbols, including x’s, ω’s (omegas), and even the odd א (aleph). You’ll find an occasional equation or an unfamiliar-looking combination of characters, such as 3↑↑3↑↑3 (especially in the chapters on large numbers and infinity). If you’re a non-mathematician, don’t be put off. They’re just shorthand for ideas that, hopefully, we explain well enough in advance and thereby help us delve a little faster and deeper into the subject than would otherwise be possible. One of us (David) has taught maths privately to students for many years and has yet to come across one who can’t be good at it once they believe in themselves. The fact is we’re all natural mathematicians, whether we realise it or not. So, with that in mind, let’s take the plunge…