Welcome to the Institute of Mathematics and its Applications (IMA) blog. The IMA is the UK's learned and professional society for mathematics and its applications. We promote mathematics research, education and careers, and the use of mathematics in business, industry and commerce. Among our activities we produce academic journals, organise conferences and engage with government.

In this blog we will publish mathematical articles and news to reflect the interests of our members who come from a multiplicity of different organisations including university academics, industrial mathematicians, financiers, school teachers, scientists, civil servants etc.

Saturday, 10 September 2011

British Science Association 2011

The British Science Association has a long tradition going back to 1831, when it was founded as the British Association for the Advancement of Science to:
give a stronger impulse and a more systematic direction to scientific inquiry; to promote the intercourse of those who cultivate Science in different parts of the British Empire with one another and with foreign philosophers; to obtain more general attention for the objects of Science and the removal of any disadvantages of a public kind that may impede its progress.
According to the British Science Association history website, from which that quote was taken, the early annual meetings included the coining of the word 'scientist' and the first demonstration of wireless transmission.

Today the annual meeting is called the British Science Festival and this is one of Europe's largest science festivals. The 2011 meeting is being held from today until Thursday 15th September in Bradford and is well worth a visit.

The IMA website has more about the British Science Festival and a downloadable Mathematical Sciences Programme of Events. The mathematical sciences programme includes talks on statistics in sport, maths magic, maths of waves, prime number sequences and the impact of maths on science and culture, as well as a chance to catch the maths and stats buskers.

Thursday, 1 September 2011


I've been thinking for some time about what to write in a post on this blog, only I didn't really know what to say.

So I thought I would tell you a little story about how I was inspired by DrMaths (Steve Humble) to do some maths on my fridge last Friday after work.

Steve has been tweeting number facts as @DrMaths for some time and last Friday's was
If you square 1, 5 and 6 you get 62. There are three different numbers you can square to get 62! Its the smallest number with this property
By which I thought he meant there were three sets of three numbers that when squared would add up to 62.

Almost immediately I figured out in my head that 2^2+3^2+7^2=62, but for the life of me I couldn't work out another way.

So I got out my board marker and sat on my kitchen floor and started doing maths on my fridge. You can see photographic evidence of the results below. I am certain that I've proved (by brute force) that there are only 2 ways to this answer and the smallest number with three sets of three summed square numbers is 101.

I wish to add here that DrMaths did clarify in a later tweet to someone who asked about it
too few words used badly! "two distinct squares"
I then went a bit further and started working out prime numbers and decided that 1^2+2^2+6^2=41 is the smallest one of these "sum of 3 squares" numbers that is prime. I then wondered which would be the smallest prime that had two distinct sums. It seems the answer is 89.

While of course 101 is both the smallest integer and the smallest prime number with three distinct sums of this form.