My dad taught Philosophy and Sociology all of his professional life, and in his retirement continues to study and think about these subjects. He recently gave a talk about the work of John Gray to the Erasmus Darwin Society in Lichfield, Staffordshire.

John Gray is currently Professor of European Thought at the LSE, and has been an outspoken and controversial academic throughout his career. He has written about a great breadth of topics, but the thread of thought that ties his work together is his rejection of our contemporary belief in the progress of mankind.

The prepared text of my dad’s overview of Gray’s views is an excellent introductory text, with a good bibliography pointing towards further reading. I would strongly recommend this text to students as an overview of his thought.

John Gray, An Appreciation

The new Bowland Maths Website is the website of a new project which seeks to ground maths in an explorative, problem solving environment.

Bowland Mathematics seeks to develop meta-cognitive skills and promote an analytical, quantitative attitude towards problem solving. These goals are worthy, and important life skills, but they are difficult to measure cleanly. With curricula that separate the strands of mathematics in a way that encourages their their teaching to be separated also, and with testing that aims at accountability over intelligence, school mathematics has become ever more piecemeal and disconnected with reality. Bowland is an important project that seeks to reclaim some of the lost ground.

I urge, in the strongest possible terms, that anyone involved in mathematics education take this initiative seriously. I have no vested interest in the scheme, but simply I believe that it is crucial that initiatives such as this succeed and are built upon.

Dr Ron Knott in the Department of Mathematics at Surrey University is not a name I recognised, but reading his resume, I now realise that I have heard him talk a few times about Mathematics on Radio 4, both on Simon Singh’s 5 Numbers series, and in Melvyn Bragg’s In Our Time podcast.

I was looking for some information about exact values of trigonometric ratios, and came across his most informative site. I was extremely pleasantly surprised to discover that for some values the trigonometric functions give exact solutions in terms of phi, the golden ratio, among other information.

For example, did you know that the cosine of 27 degrees is exactly a half of the square root of (two plus the square root of (two subtract phi)). (One day when I finish writing my own equation display movies, I’ll write that out in a prettier way, Dr Knott’s website tries a little harder than I do). I love that the number 27, which clearly wants to be prime so much it tricks generations of children into thinking it is, the square root of two and the golden ratio are connected inextricably through the circle-based cosine function. Fantastic!

The whole page, indeed the whole of his site in general, is steeped in extremely interesting, and relatively accessible mathematics with Fibonacci numbers, Egyptian Fractions and so on and so forth. It’s mostly a site for KS4 and beyond (14 years old +), with most material for the older students. Some of it is not for the faint-hearted. However, it is a valuable resource for mathematicians of all hues, and well worth a look.