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Recreational maths

I have been getting into the puzzles section at the tail end of The Guardian newspaper which I get each week. Last week it asked you to prove that there are infinitely many different pairs of numbers (a,b) for which a+b=ab.

This is easy to prove but I admit I had to work at it […]

Googol, googolplex & Google

Someone asked me the other day where the word “google” came from and I responded that I thought it was a corrupted version of the word “googol” which Stephen Krasner in his book “Mathematics and the Imagination” attributed to his (then) 9-year old nephew. A googol is 10 raised to the 100th power. Krasner’s nephew […]

MathematicaAlpha

From time-to-time I use the Mathematica software mainly for much lower level types of applications than it is designed for. This is quite expensive software – around $1400 – and involves a substantive learning effort to use. It is a grand hassle to install and upgrade as I have grizzled about in the past and […]

‘No self-defeating object’ arguments

Can an omnipotent being create a rock so heavy that he cannot lift it? I got through the elementary parts of this post by Terry Tao but some of the applications were hard. ‘Strategy stealing arguments’ in game theory are a subset of this class of results. Note the amazing subsequent discussion.

Way of the Tao

Professor Terry Tao (born 1975) is an Australian mathematician now working in the US. Tao was a child prodigy who taught himself arithmetic at age 2. He received his PhD at age 20, was appointed a full professor at UCLA at age 24 and won the Field’s Medal in mathematics at age 31. This award […]

William’s maths question

I have always enjoyed maths and used to try to solve elementary maths problems as a school kid. I can remember with joy finally solving a simple-to-state problem after hours of thinking about it. Often the solution popped out of my head almost involuntarily after I had spent a lot of time thinking about it* […]