In 1693, Christiaan Huygens was struggling to learn the new calculus developed by his former student Gottfried Leibniz. He wrote to Leibniz asking for “any important problems where they should be used, so that this give me desire to study them”. Ever since, ‘when will I ever use this?’ is a common refrain, especially among engineering students — right?
A study published in 2020 had found engineering students preferred pure problems without context, but we weren’t sure — it turns out defining when a problem is and isn’t placed in context isn’t as easy as we thought. We wrote some questions that were either just ‘solve this equation’ or were dressed up with an engineering context, and asked students what they preferred and why.
We found pretty split preferences between contextual and non-contextual problems, and learned a lot about why different students prefer different sorts of problems and how they solve them (the quotes in the title give a flavour of this). The resulting article has just been published in Teaching Mathematics and its Applications. Check it out!
I’m aperiodically working my way through Martin Gardner’s cover images from Scientific American, the so-called Gardner’s Dozen, attempting to recreate these in the LaTeX drawing package TikZ. View the previous attempts.
This time I chose January 1974. The cover image relates to the article ‘The combinatorial basis of the “I Ching,” the Chinese book of divination and wisdom’, reprinted as chapter 20 in the book Knotted Doughnuts and Other Mathematical Entertainments.
There seem to be a lot of numerical coincidences bouncing around concerning the new year 2025. For example, it’s a square number: \( 2025 = 45^2 \). The last square year was \(44^2 = 1936\), and the next will be \(46^2=2116\).
The other one you have likely seen somewhere is this little gem: that 2025 equals both \((1+2+3+4+5+6+7+8+9)^2\) and \(1^3+2^3+3^3+4^3+5^3+6^3+7^3+8^3+9^3\).
The UK Government have announced the latest list of honours, and we’ve taken a look for the particularly mathematical entries. Here is the selection for this year – if you spot any more, let us know in the comments and we’ll add to the list.
Alison Etheridge, Professor of Probability, University of Oxford, and President, Academy for the Mathematical Sciences, becomes a Dame for services to the mathematical sciences.
Francis Keenan, Professor (and former Head of School of Mathematics and Physics) at Queen’s University Belfast. Appointed MBE for services to higher education.
John Westwell, Director, System Leadership, National Centre for Excellence in the Teaching of Mathematics. Appointed MBE for services to education.
Adam McCamley, Senior Analyst, Liverpool City Council. Appointed MBE for services to social care data.
Jineon Baek claims a resolution to the moving sofa problem. This considers a 2D version of turning a sofa around an L-shaped corner, attempting to find a shape of largest area. (There are some nice animations at Wolfram MathWorld.) Baek offers a proof that the shape above, created by Joseph L. Gerver in 1992, is optimal.
One thing that’s new, apart from the prime itself, is that the work was done on a network of GPUs, ending “the 28-year reign of ordinary personal computers finding these huge prime numbers”. Also this was the first GIMPS prime discovered using a probable prime test, so the project chose to use the date the prime was verified by the Lucas-Lehmer primality test as the discovery date. In other computation news, the fifth Busy Beaver number has been found, as well as 202 trillion digits of pi.
Finite Group is a friendly online mathematical discussion group which is free to join, and members can also pay to access monthly livestreams (next one Friday 20th December 2024 at 8pm GMT and recorded for viewing later). The content isn’t at the level of the research mathematics in this post, but we try to have a fun time chatting about interesting maths. Join us!
