The significance of his contribution to the war makes the way he was treated all the more sad and regretful. I hope his work and achievements will be more generally appreciated.

If I were to ask you to count to infinity, what number would you start on? And what would be your next number?

Cantor thought about it. If you count the Natural numbers (that is 1, 2, 3, …) then you will eventually count to infinity. But if you count all the integers, including minus numbers as well, (0, 1, -1, 2, -2, …) then you will count infinitely many numbers again: but surely you will have counted more numbers this way.

If you keep changing the way you count, you can begin to see that you count a different infinity each time. In theory, there are an infinite number of infinities. That sounds odd, doesn’t it?!

The engineer carefully manoeuvers the sheep into a neat circle and attempts to build a fence round them. It works. But the physicist notices that he can make the circle smaller. So he builds a fence of infinite radius then draws it in and makes it as small as possible with the sheep inside. Satisfied he challenges the mathematician to do better.

The mathematician sighs and puts a fence round himself and declares "I am outside". He wins.

That’s what mathematicians learn. We have conventions that we make without really realising. Why is the centre of the circle thought to be on the inside? Why is there no square root of a minus number? Why is there only one infinity? If you can’t answer those questions then keep an open mind, and you’re half way to being a mathematician.

Of course, you’re also half way to madness.

But this one does. It highlights the problem of a lack of teachers of Mathematics in secondary schools, and how such a negative view of Mathematics by adults and children alike are damaging the chances of finding raw mathematical talent.

I had once been drawn to teaching, and particularly of Mathematics at secondary school. However, there is little that draws me there now. All those things that attracted me to the profession are the same ones that make me feel that teaching Mathematics privately is a more attractive option. It is of little wonder that the turnover of teachers in the field is so frequent, when quite frankly the prospect of teaching is financially uncompetitive and offers far more in terms of drawbacks than perks.

Yesterday, I gave a presentation on my project to four or five staff and eight or nine students. To be honest, I didn’t really concentrate on the audience! However, I must have done quite well, having been given a provisional mark of 8.5/10. I am particularly pleased since being awarded a nine has been deemed "rare" and one of the two judges must have awarded it a 9. As long as it doesn’t change I guess!

So next week, I’m off to Kent! But not before dying my hair black… again… and this time… it’s permanent!