A grande cappuccino costs £2.40 at Starbucks in Oxford, but on arrival in Geneva, I found the price here is £4.60 (6.80 Swiss francs).  Swiss prices are sky-high, and for a week or two, every time I bought anything in this city I had a painful sense of money slipping through my fingers.

Two weeks later, I had mostly stopped feeling the pain.

On the face of it, there’s irrationality here. Either I was irrational to be so disturbed by the high prices originally, or I am irrational to be so blasé about them now. Which is it, then?

And yet, maybe the deeper rationality consists precisely in being disturbed at first and less disturbed later. Changes in our environment may bring danger, and we must be vigilant in detecting and responding to them. Yet these costly cappuccinos will not break my bank account, and one must get through life. If you’re alert to everything, you’re alert to nothing.

[22 February 2014]

In a spectacular breakthrough, Yitang Zhang proved that there are infinitely many pairs of primes differing by at most 70 million.

This is the opening line of the advertisement for the upcoming LMS-CMI Research School on Bounded Gaps Between Primes.

[16 April 2014]

English pronunciation is notoriously underdetermined. Here’s an example. I guess we all know how to pronounce

    A tear in the eye.

Well, I would have thought so anyway, but last weekend I had an ophthalmic scare that introduced another possibility. It seemed I had

    A tear in the retina.

[27 March 2014]

Is mathematics about numbers?

Is the law about money?

I think the two situations are much the same.  In principle, mathematics is concerned with all kinds of logical relationships, not just numerical ones.*  Yet many of the most powerful things we do with logic involve numbers, and mathematicians are the experts in their use.

As for the law, in principle, it is concerned with all kinds of human relationships, not just financial ones.  Yet so much of human relationships is regulated by money that inevitably lawyers have a special interest in this area.

*The Independent reassures Sudoku players: “There’s no maths involved.  You solve the puzzle with reasoning and logic.”

[30 December 2013]

Why did the Lord send his son to earth?  I was embarrassed to realize last night that it took me to age 58 to notice how I’d been hoodwinked by the standard narrative.

The line we’re fed is that he did it to help us sinners out, since we can be redeemed through Christ.

And yet if you look at it from God’s point of view, well, let’s face it, in the BC years he was nobody, with just a few Jewish believers.  Sending Jesus down changed that completely, a brilliantly successful advertising ploy.  Jesus made God go viral.

[22 February 2014]

It’s October, start of a new year.  Having purchased my blue Oxford diary for 2013-2014, I’ve just put 2012-2013 on the shelf.  The stack is 16 high now, beginning with 1997-1998.

Life has its rhythms, on different time scales.  You get a cup of coffee every few hours, go to bed once a day, put the trash out each Friday… and put the old diary on the stack each October.  The top of my stack is rising around one centimeter per year, so its velocity is slightly less than that of your average tectonic plate.

As a youngster I used to imagine with fascination the plateau of adulthood, that unending time of regular habits, one day after another, year stretching on year.  Who could comprehend such an infinity?  Here at age 58, I think I’ve reached it.

[25 October 2013]

Slowly, over the generations, cultures adapt to the conditions they face, but year on year we mostly do what we’re used to.

And so it is that among the hundreds of mathematicians here in Oxford’s Andrew Wiles building, there are two who habitually wear short trousers, even in the winter.  Both of these young men get plenty of good-natured kidding on the subject of their dress habits.  Maybe you guess that Cameron and Anthony are from Iceland or northern Russia, finding Britain balmy in comparison?  Of course the truth is just the opposite.  One of them is from sun-baked Queensland, and the other from steamy Texas.

[10 December 2013]

The two most important things I’ve worked on in the past seven years are Chebfun, a software package that people are using around the world, and Approximation Theory and Approximation Practice, a bestselling SIAM book that is changing perceptions of the mathematical properties of polynomials.  It’s a safe bet that among my “outputs” of the past seven years, these two will have the greatest impact.

Not according to the UK’s assessment scheme known as the Research Excellence Framework, however.  Our department has just sent in its REF submission, reporting for each of 147 researchers their four best outputs from the past seven years.  In theory, the REF welcomes nonstandard outputs, including software.  In practice, everybody is scared to death of deviating from the safe pattern of specialist papers in specialist journals.  Luckily I’ve produced enough of those too.

So neither Chebfun nor ATAP has been included in our REF submission.  Among the more than 500 outputs of Oxford Mathematics for the period 2007-2013, they do not appear.

[13 December 2013]

My cycling safety jacket exploits two different technologies to be visible.  I can’t resist wondering, are the two analogous?  What I find is that no, in a sense they are opposite.

One technology is directionality, which makes the silver strips on the vest shine bright in headlights. The trick here is that the fabric reflects light in the same direction it came from, making the strips appear magically bright to oncoming drivers.  (Traffic signs have used this technology for years.  I remember once as a kid being amazed when my father said, look, I can turn off all those signs up ahead on the highway just by switching off our car’s headlights!  My mother wasn’t pleased with this experiment.)

The other is fluorescence, which gives the fabric of the jacket its unnatural brightness.  The physics here is that ultraviolet light hitting the fabric is converted by quantum mechanical effects to a visible wavelength and radiated out again.   So my jacket emits more yellow light than it receives.  Our eyes see the magic in this, and in the last year or two people have started wearing “neon” shirts and shoelaces.

Here is what I mean by saying that the two technologies are opposites.  Fluorescent fabrics work by bending incident light from one wavelength to another.  Reflective strips work by preventing the bending of incident light from one direction to another.

[21 October 2013]

As we know, the heart has two atria, of unequal sizes, with a barrier between them.  The smaller right atrium is involved with pumping blood through the lungs, while the larger left atrium handles the rest of the body.

This is pretty much the setup in our new Andrew Wiles mathematics building at Oxford, which will open officially next week.  The pure mathematicians have offices in the right atrium, and the applied ones on the left.  I guess this means pure maths is the lungs, bringing in the oxygen of new ideas, and applied maths is the body, applying the oxygen to do some work?  With a cafeteria in-between.

[30 September 2013]