1) Among adults, maths is "sexy"; Fermat's Last Theorem, Simon Singh's book explaining how a British mathematician solved the eponymous long- standing problem, headed the bestseller lists; the film Good Will Hunting revolved around a maths genius; two British mathematicians last week won international prizes; and books on maths as a pastime are a publishing mini-boom.
2) This year, the proportion of children failing maths GCSE doubled, and the proportion obtaining grades between A* and C fell.
3) Recruitment of maths teachers this year is 60 per cent below target.
If that seems like a headscratcher of a question, you only have to talk to a few teachers and academics who follow the trends in mathematics education to see which of those three facts is the crucial one. It's the third: we don't have enough maths teachers, and pupils are losing out because of it. Yet at the same time, people's unfulfilled interest in maths means that later in life they like to indulge themselves in it - to participate vicariously, without the risk that they will ever be examined on it.
But although the lack of maths-qualified teachers is serious, it is also old news to some. "The recruitment of maths teachers has always been a problem," says Ted Wragg, professor of education at Exeter University. "In fact, I can't remember a year when people have ever said, 'Well, we're flush with maths teachers'."
Following the recruitment graphs backward shows that there haven't been enough maths teachers coming into the profession for 20 years or more. The only time recruitment picks up is during a recession - because there are fewer job opportunities in the commercial sector.
"Maths is such a useful degree that it opens up a huge variety of jobs," says Professor Ian Stewart, director of Warwick University's Mathematics Awareness Centre and author of successful maths books. "Faced with the choice of banking, computing, research, or teaching, what would you go for?"
The financial rewards for a mathematician in the City can soon reach six figures. Compare that with the salary of a maths teacher, who will start on pounds 14,000 and might never be paid more than pounds 30,000.
In fact, the only time within living memory when Britain had enough qualified maths teachers was in the recession of the 1930s, although recruitment did rise in 1983 and 1991. But in all the intervening years, the problem of finding sufficiently able teachers to help pupils to understand one of the few subjects for which you can't cram - because you either understand a mathematical concept or you don't - has meant that standards have fallen.
Professor Wragg comments: "The problem is endemic in many schools. They get people teaching maths who aren't specialists. The trouble is that it has always been a subject where people get roped in to teach it - 'Oh, just take 4A and teach them this, it's in the syllabus' - so that the real shortage of maths teachers turns into an imaginary shortage, because there's always somebody actually turning up in front of the class."
But at the grass roots, the teachers are also frustrated on two fronts: the "dumbing down" of the syllabus, and the reams of administration they now have to handle as part of the process of teaching.
"The biggest problem today is that you have to entertain the pupils," says Ian Tyce, 49, who lives in Maidstone, Kent, and has taught maths at secondary level for the past 20 years. "Before, you could present facts and the pupils would learn them. Now, everything has to be dressed up. You can't just get them learning a times table; you have to make it into something with rewards where perhaps they split into groups and ask each other questions, and if they get the answer right they can ask a question back."
Examining boards are prickly at the suggestion that they are lowering their standards, but the evidence exists: a growing number of universities teaching maths-related subjects have to run remedial courses to try to get their students up to speed.
"The syllabus now has nothing like formal proofs," Mr Tyce says. That matters because proving theorems, or conjectures, is essentially what mathematics is all about; it's the only way to create the building blocks that will advance the subject. "Even at A-level it has really changed in terms of the way it is being taught. It used to be that even at GCSE you had to get them able to prove a proposition. But some A-level boards now certainly don't have proofs. They would know what proof by induction is, they might not know what complex numbers are, or second-order differential equations."
Even if those sound like car parts, they have been part of the mathematical armoury for centuries. The idea that our examining boards might be abandoning them can only, in a mathematician's eyes, be a retrograde step.
But the problem exists because, Mr Tyce reckons, that is where society is going.
"It's a tendency in all subjects, in all society," he says. "Just look at the way that on TV you never see people talking face to face any more. Something will flash up every 20 seconds."
The change is a reduction in attention span: "Children now don't have much concentration. You can't retain their attention without some form of entertainment."
But the biggest problem for the individual teachers is the tide of forms that now engulf them in the name of accountability.
"It stifles your style," says Mr Tyce. "At one stage in this business, I could pretty much do my own thing in the classroom. Now there's a syllabus to follow and if you fall behind it there's not much you can do to catch up."
Professor Stewart, at least, is in no doubt what should be done. "Get rid of public-sector bureaucracy, which is now Kafkaesque in its lunacy. Pay is a secondary issue - excessive paperwork and unintelligent management is primary. I know a lot of teachers who have left teaching because of it.
"Stuff all those idiotic forms, assessment exercises, league tables, and 'quality assurance' - a misnomer if ever there was one - and let the teachers get back to teaching."Reuse content