Here’s a phrase you don’t read much these days: David Lammy, the Labour politician, got me thinking last week. I will explain later how the same trick was pulled off by John Humphrys and half a dozen eggs, but first things first.

Lammy is the minister in charge of universities but is perhaps best known for his unfortunate appearance on Celebrity Mastermind just over a year ago. Here are a couple of the questions he was asked, along with his replies. You should remember, as you read them, that the future of our greatest learning institutions was in his hands. And still is.

Q: What was the married name of the scientists Marie and Pierre, who won the Nobel prize for physics in 1903 for their research into radiation?

A: Antoinette

Q: Which fortress was built in the 1370s to defend one of the gates of Paris, and was later used as a state prison by Cardinal Richelieu?

A: Versailles.

Lammy shrugged off this humiliation with good nature and has kept his head down since then. I’d barely heard a squeak out of him until he appeared on Radio 5 Live last week, defending the government’s record on universities and selling the benefits of a degree.

Essentially, his argument was this. If you are a graduate, you will dwell upon soft couches in the lush gardens of paradise. At the very least, you will earn more money, be promoted more quickly and drive a BMW. Meanwhile, those without degrees will suffer eternal torment in the flames of hell and be forced to drive Toyotas at high speed down mountain passes.

I may have got one or two of the details confused, you understand, but the core of the message was unmistakable: degrees are pretty much essential to a modern career.

For me, this is very depressing news. I am not a graduate in much the same way that Lammy is not an expert in physics or French history. Imagine how this feels. Most of my colleagues at The Sunday Times seem to have gone to either Oxford or Cambridge.

There are two PhDs in the office, to my certain knowledge; possibly more. Many of my closest friends also went to Oxford or Cambridge. I sometimes wonder how the colleges managed to fit everybody in: it must have been five to a bed. In contrast to all this academic excellence, I failed rather spectacularly to get into Keele.

Keele no doubt has a fine academic record. It has produced Chris Woodhead, who was once England’s chief inspector of schools; Richard Mottram, the former permanent secretary at the Ministry of Defence; Michael Mansfield QC; and the Bishop of Lichfield. But at my school it was known as the college that would accept even the most hopeless of cases: “I’m afraid the University of Lundy can’t find you a place either. I think it’s time to try Keele.”

You can perhaps now appreciate the extent of my shame. For most of my life this hasn’t bothered me. In fact, I’ve carved out a bit of a career from warning hopeless A-level failures each August that all is not lost. No employer has even asked where — and certainly not whether — I went to university. But over the years things have changed.

Many jobs are now closed to non-graduates, and I can’t help thinking this is not a change for the better. Not having a degree didn’t seem to worry Alan Sugar, Richard Branson, Jeremy Clarkson, John Major or Charles Dunstone, who rejected a place at Liverpool University and went on to found Carphone Warehouse. A young IT and business graduate, speaking on Radio 5 Live not long after Lammy, recounted how he left university to work in a call centre, where some of his colleagues had masters degrees and doctorates.

Degrees are good — all knowledge is good — but they’re not as important in the world of work as ambition, drive, personality, luck and good communication skills (and perhaps several family friends who are the directors of hedge funds or investment banks).

Such is the modern pressure to get a degree that I’ve been thinking for a while that I might have a stab at the Open University, probably in maths (which got me into such trouble at A-level). But John Humphrys and those half a dozen eggs may have scuppered that idea.

As a bit of light relief from MPs’ expenses, the war in Afghanistan and interviews with Lord Mandelson, listeners to Radio 4’s Today programme last week debated the probability of finding six double-yolked eggs in a single box. I was late to the debate but just caught Humphrys reading a listener’s email.

“Chance has no memory,” the listener explained, going slightly off the egg-yolk topic and using the analogy of children. The probability of having three daughters, he explained, is one in eight. Yet if you already have two daughters, the probability of a third child being a girl is one in two. What he did not explain is this: how can the probability of what is essentially the same event be both one in eight and one in two?

I have a sinking feeling that the answer to this is very simple, GCSE stuff. Yet I’ve spent most of the week looking like Alan Davies does on QI when Stephen Fry is trying to explain the fascinating connection between, say, dark matter and male pattern baldness. I’m now wondering whether it’s worth studying for years only to repeat the errors of my youth.

It very much looks as if I am destined to burn in the eternal fires of hell after all, while David Lammy — who has a law degree from London and a masters from Harvard — dwells upon silk cushions in the gardens of paradise. Even though he seems never to have heard of Marie Curie.

Jeremy Clarkson is away

Times Recommends

• Remember the Crimea. Look after the Army
• Prepare for the fourth transport revolution
• If interest rates rise, our prospects plummet