Archive for mathematics

R.I.P. John M Stewart (1943-2016)

Posted in Biographical, Education, The Universe and Stuff with tags , , , on November 23, 2016 by telescoper

john-stewartI was very sad this morning to hear of the death of distinguished mathematical physicist Dr John M. Stewart (left). Apart from a few years in Munich in the 1970s John Stewart spent most of his working life in Cambridge, having studied there as an undergraduate and postgraduate and then returning from his spell at the Max Planck Institute to the Department of Applied Mathematics and Theoretical Physics for forty years.

John’s research mostly concerned relativistic fluid dynamics. Indeed, he was one of the pioneers of numerical relativity in the United Kingdom, and he applied his knowledge to a number of problems in early Universe cosmology and structure formation. I think it is fair to say that he wasn’t the most prolific researcher in terms of publications, which is perhaps why he only got promoted to Senior Lecturer in 2000 and never made it to a Chair, retiring as Reader in Gravitational Physics in 2010. However, his work was always of a very high technical standard and presented with great clarity and he was held in a very high regard by those who knew him and worked with him.

The tributes paid to John Stewart by King’s College (of which he was a Life Fellow) here and his colleagues in the Centre for Theoretical Cosmology here give a detailed account of his research achievements, so I refer you to them for more information about that aspect of his career.

I just wanted to add a personal note not about John Stewart’s research, but about something else mentioned in the obituaries linked to above: his teaching. I was fortunate enough to have him as a lecturer when I was studying Natural Sciences at Cambridge during the early 1980s. In the second year (Part IB) I specialised in Physics and Mathematics, and John taught part of the Mathematics syllabus. He was an absolutely superb teacher. For a start he was superbly well organized and had clearly thought very deeply about how best to present some quite difficult material. But it wasn’t just that. He projected a very engaging personality, with nice touches of humour, that made him easy to listen. His lectures were also very well paced for taking notes. In fact he was one of the few lecturers I had whose material I didn’t have to transcribe into a neat form from rough notes.

I have kept all the notes from that course for over thirty years. Here are a couple of pages as an example:

wp-1479909754508.jpeg

Anyone who has ever seen my handwriting will know that this is about as neat as I ever get!

When I was called upon to teach similar material at Cardiff and Sussex I drew on them heavily, so anyone who has learned anything from me about complex analysis, contour integration, Green’s functions and a host of other things actually owes a huge debt to John Stewart. Anything they didn’t understand was of course my fault, not his..

I also remember that John came to Queen Mary to give a seminar when I worked there in the early 90s as a postdoc. I was still a bit in awe of him because of my experience of him in Cambridge. His talk was about a method for handling the evolution of cosmological matter perturbations based on an approach based on the Hamilton-Jacobi formalism. His visit was timely, as I’d been struggling to understand the papers that had been coming out at the time on this topic. In the bar after his talk I plucked up the courage to explain to him what it was that I was struggling to understand. He saw immediately where I was going wrong and put me right on my misconceptions straight away, plucking a simple illustrative example apparently out of thin air. I was deeply impressed, not only by his ability to identify the issue but also with his friendly and helpful demeanour.

Rest in Peace, Dr John M. Stewart (1943-2016).

Computable Numbers, 80 Years on..

Posted in History, mathematics, Uncategorized with tags , , , , on May 28, 2016 by telescoper

There’s been rather a lot of sad news conveyed via this blog recently, so I thought that today I’d mark a happier event. Eighty years ago today (i.e. on 28th May 1936), a paper by Alan Turing arrived at the London Mathematical Society. Entitled “On Computable Numbers, with an Application to the Enstscheidungsproblem“, this was not only enormously influential but also a truly beautiful piece of work. Turing was only 23 when he wrote it. It was delivered to the London Mathematical Society about 6 months after it was submitted,  i.e. in November 1936..

Here’s the first page:

Turing

The full reference is

Proc. London Math. Soc. (1937) s2-42 (1): 230-265. doi: 10.1112/plms/s2-42.1.230

You can find the full paper here. I heartily recommend reading it, it’s wonderful.

 

The Terror of Maths

Posted in History, The Universe and Stuff with tags , , , , on May 9, 2016 by telescoper

I’m not sure whether to be amused or appalled by the story of the Professor whose flight was delayed in order for him to be interrogated because a fellow passenger saw him doing some mathematical calculations. I know some people who find mathematics scary but that’s taking things too far! I wonder if the passenger was Simon Jenkins?

I was wondering whether the calculation was concerned with plane geometry but that seems not to be the case. The academic concerned is an Economist and he was studying a differential equation. That surprises me. I hadn’t realised economists knew about calculus. Or about anything else, for that matter.

The BBC coverage of the story used the following image:

scary_maths

The physicists among you will recognize this as a representation of some of Maxwell’s Equations. I very much doubt they played a part in the work of  our Economics Professor, so presumably this is just one of the  BBC’s stock of generic “scary maths” images.

Other things worth noting are that this version of Maxwell’s Equations isn’t written in SI units, the standard notation in the UK and Europe. As a matter of fact it uses cgs units, which suggests it may be an American import. Nor is it really correct anyway, because the time derivative inside the brackets should surely be partial.

All of which goes to demonstrate how Mathematics is usually viewed in the media and, by extension, the public at large: like an arcane book written in an incomprehensible  language that should be viewed with suspicion or ridicule by any sensible person.

There is nothing new about this, of course. I’m reminded that in 1870, during the Franco-Prussian Way, Norwegian mathematician Sophus Lie was arrested in France on suspicion of being a German spy because the authorities thought his mathematical notes were coded messages of some sort.

In reality, mathematics is the most open and universal language of all and, as such, is a powerful force for human good. Among many other things, quantitative reasoning and proper logic help to defend us against those who lie and distort the facts in order to gain power. Mathematics may not be the easiest language to learn, but it’s well worth the effort, even if you can only master the basics.

 

 

Geometry, by Rita Dove

Posted in Poetry with tags , , on February 23, 2016 by telescoper

I prove a theorem and the house expands:
the windows jerk free to hover near the ceiling,
the ceiling floats away with a sigh.

As the walls clear themselves of everything
but transparency, the scent of carnations
leaves with them. I am out in the open

and above the windows have hinged into butterflies,
sunlight glinting where they’ve intersected.
They are going to some point true and unproven.

by Rita Dove

 

17 Equations that Changed the World

Posted in History, The Universe and Stuff with tags , , on December 14, 2015 by telescoper

Yesterday I posted about a map that “changed the world”. Clearly the world changed a lot and for many different reasons because when I got home I noticed the following picture on Facebook, depicting 17 equations that also “changed the world”:

 

17 Equations

This is from a book by mathematician Ian Stewart.

Of course it’s actually 20 equations, because there are four Maxwell Equations. It is an interesting selection. Are there any surprising omissions?

 

 

Helping Blind Students with Mathematics and Physics

Posted in Education with tags , , , , on October 16, 2015 by telescoper

This short video clip features Daniel Hajas, a third-year theoretical physics student in the Department of Physics & Astronomy at the University of Sussex who has been working on technology intended to help visually impaired students to   engage with the charts, graphs and equations involved in studying mathematics and physics. Here is a news item arising from a recent poster competition for which Daniel, who is himself visually impaired, highlighted the challenges faced by blind students by exhibiting a completely blank poster, explaining that this was how a blind person would experience a complex equation. In the video he explains a little more about the work he has been doing.

 

The Crocodile Maths Challenge

Posted in Cute Problems, Education with tags , , , , on October 14, 2015 by telescoper

I’m indebted to an anonymous informant (John Peacock) for drawing my attention to a BBC Scotland story about an allegedly challenging examination question that appeared on a “Higher Maths” paper. For those of you not up with the Scottish examination system, “Highers” are taken in the penultimate year at school so are presumably roughly equivalent to the AS levels taken in England and Wales.

Anyway, here is the question that is supposed to have been so difficult. For the record, it’s Paper 2, Question 8 of the SQA examination 2015.

crocodile_questionCall me old-fashioned, but it doesn’t seem that difficult to me  but I never took Scottish Highers and there have been many changes in Mathematics education since I did my O and A-levels; here’s the O-level Mathematics paper I took in 1979, for example.  I wonder what my readers think? Comments through the box if you please.

Feel free to give it a go. If you get stuck here’s a worked solution!