always busy counting, doubting every figured guess . . .
In 1981, the Soviet mathematician V. I. Arnold wrote a little book attempting to explain catastrophe theory to a general audience. It was translated into English by R. K. Thomas and published with the title Catastrophe Theory by Springer in Continue reading
Last night some of the strands of gamgee inside my skull connected up and I remembered something I learned nearly 14 years ago, which I think is relevant to the discussion of AI in mathematics, and in particular to the Continue reading
In the last two hours, the following three news items have appeared on the BBC website: Be very afraid!
I have not been well for a while; my brain has turned to gamgee, and I find it difficult to concentrate on hard mathematics. So let me try to get things working by an easier warm-up exercise. There has been Continue reading
A week in the Oude Abdij Drongen, near Ghent in Belgium, accompanying Rosemary to the mODa14 conference. The name of this conference gives a double role to the initials OD: model-oriented design and analysis, and optimal design, hence the typography. Continue reading
Not THE famous ABC conjecture, but a conjecture of mine with Mohammed Aljohani and John Bamberg. A simple counting argument shows that, in any vertex-transitive graph, the product of the clique number and the independence number is at most the Continue reading
I am now retired, and nearly 80. My brain does not work at the same clock speed that it used to, and I am no longer paid for things which were part of the job sucuh as refereeing, conference attendance Continue reading
Take a right-angled triangle with hypotenuse c and the other two sides a and b. Pythagoras Theorem tells us that c2 = a2+b2. Let the area of the triangle be A. We know that A = ab/2 (since an a×b rectangle is cut into Continue reading
Imagine you are in the following situation. You are the foreign minister of your country. You are in New York for a meeting of the General Assembly of the United Nations. A powerful enemy has been deploying troops on the Continue reading
Graphs and groups, in my view, are two subjects engaged in a wide-ranging dialogue at present. Graphs can be used to describe interesting classes of groups, and groups to construct interesting graphs. But I am delighted that recently, in a Continue reading