The Fields Medal, Goldbach, Twin Primes and fraud

A wonderful month for number theorists: the Weak Goldbach Conjecture is proved [Helfgott], and an enormous inroad is made to the Twin Prime Conjecture [Zhang]. Neither advance owes anything to me.

Kevin then posed an interesting question: is the Fields Medal awarded in the year of the work that merits it? If so, wouldn't you be pissed off to make an advance of huge stature to be pipped by someone else?

I'll delay my publication of a proof of the Riemann Hypothesis until next year, just in case.

More productively, we thought about manufacturing a facsimile of a Fields Medal using the underused 3D printer in Gwyddoniaeth Gyfrifiadurol at Prifysgol Aberystwyth and taking it turns to wear it during excursions to the pubs of Aber.

Kevin, incidentally, is runner-up in the World Outdoor Cribbage Championship.

A tasteful question about M Thatcher's demise

In some parts of the world, care is taken to ensure that places closely associated with less popular ex-leaders do not evolve into shrines attended by the misguided.

Is it true that Grantham is to be demolished?

Mulholland Boyle Leeds Paediatric Surgery Admirals Earl of Orrery

On the BBC this morning, Greg Mulholland MP said (I paraphrase), "Roger Boyle needs to account for his actions".

He meant the other one.

I think. For the record, he is "Professor Sir Roger Boyle", while I am "Visiting Professor Boyle", an eternal disappointment to my sisters. If this baffles you, compare the issue with the hierarchy of Admirals.

(I'm fairly sure Mulholland wasn't referring to the other other one, or indeed his son, also blessed with my name.)

Refugees and the Ace Cafe

There is a route from mid-Kent to West Wales that takes in Liverpool Street station and Stonebridge Park. While not the most direct, it affords two sightseeing opportunities.

1. The Kindertransport memorial at Liverpool Street is only 7 years old: it commemorates the welcoming into Britain of large numbers of Jewish refugees - predominantly children - very shortly before WW2 began. A slick operation saw some thousands received who would very probably otherwise have perished.

   In truth, the sculpture of some children with their few belongings I did not find very striking, but there's no denying the strength of the sentiment.

   

   As Andrea Hammel noted, "How would it be if 10000 refugee children turned up in the UK today? What would their welcome be?". The Daily Mail would surely have a view.

2. 2013 marks the 75th anniversary of the Ace Cafe beside the North Circular at Stonebridge Park: it's famous for being, still, a bikers'/drivers' caff in just the place where such a thing is needed.

   Inside, the experience is of a place that is a monument to itself rather than a cafe, but it's still fun. It's deplorably tidy and clean, with far too many notices promoting Safety (and a few promoting Health). Holding a train ticket from Ashford to Aberystwyth, I had to do some talking to be allowed to alight at the Stonebridge rail station, but it was well worth it. You get a cracking view of the N Circ, and the pointless Wembley Stadium.

   If I'd really been in the groove, I'd have had bacon and eggs &c &c, but actually settled for a pint of Beck's Vier and meatballs in spaghetti (on logo'ed china).

   

The Cheltenham Bayshill: thoroughly saved

When I lived in Cheltenham (1978-79), I visited many pubs (although there is nothing special about Cheltenham in this regard). Head and shoulders above them all was The Bayshill, and when I visited last week I was delighted to find that it remains a top-grade drinking hole in the middle of town.

During my brief tenure as regular there was a demolition scare: it being the sort of place that attracts those sort of people, some musically inclined locals immediately founded The Bayshill Rollers (yes, it's a pun) to release Save The Bayshill, which I bought. The B-side is the rarely heard Cheltenham Ladies - the College Ladies were a frequent topic of conversation in the pub. Presumably they still are.

(Actually this is at least partly nonsense. The Rollers had existed for some time under the name Decameron, a Cheltenham Arts College band founded by Dave Bell and Johnny Coppin, still extant in the early 2000s.)

It was splendid to see a copy of the disc mounted on the pub wall. Alongside it was a picture of the public bar mural which had featured a number of well known locals (not me - insufficient length of service). It photographs badly but fourth from the right (bow tie) is Aubrey Lewis, with whom I used to work at GCHQ. He was 60-ish in those days, drank beer prodigiously, and smoked lots of Capstan Full Strength cigarettes: a model for us all.

On age, perfection, semi-primality and being 142

Some years ago, the Frau was 28 years old: one day she became 29 and I cockily wrote in her birthday greeting "No longer perfect, but irreducible", and since that date have paid close attention to the primality or otherwise of our respective ages.

She was pleased and impressed when I noted that both before and after our recent birthdays (many thanks for your cards and gifts), both our ages were semiprime: which is to say all four numbers have precisely 2 prime factors (but you knew that already).

Which leads to the obvious questions:

1. What is the density of semiprimes?
2. What is the density of consecutive semiprimes: in particular is it asymptotically >0?

It took some web-searching to determine that an answer to the first question is x log log x / log x - a result I was unable to prove myself that is predictably due to Landau, although this is reported as a poor approximation, and better, less quotable, asymptotic formulae exist.

There does not seem to be a clear answer to the second question, which it need not surprise us pre-occupied the ubiquitous Paul Erdös (did I mention I once beat him at chess?). A simple computer program suggests there are many consecutives, and indeed triples (clearly, 4 in a row is no-go). Heath-Brown has shown there is an infinite number of such pairs [1] but I am unsure of their density.

Anyway, if I live to be 141-142, the pair of us can enjoy this happy numerological event again.

References

1. D. R. Heath-Brown, The divisor function at consecutive integers, Mathematika 31, 141–149, 1984.

<pun> A routine step for Man </pun>

Bar-room chat with Armando and Pierre very naturally turned to the Isle of Man moon-shot plans.

Having in the past authored a documentary piece mistaken by some as spoof or fiction, I saw an immediate opportunity to create an entertaining scam. But truth, as ever, is stranger than fiction, and it seems that the Isle of Man does indeed have a place near the front of the moon-shot peloton. The island state is variously listed as fourth (Hyperbola Flightglobal blog) or fifth (Daily Mail) most likely nation to mount the next personed lunar expedition.

It seems that the combination of the tax regime (well-known) and the Island's active encouragement of space industry (less well-known - to me anyway) combine to give Excalibur Almaz real plausibility of returning humans to the moon. The firm will use ex-Soviet former space stations; details are available.

Geeks are referred to the aforementioned Hyperbola blog, where technicalities are discussed in a measure of depth - I did like their observation Big rockets, complex spacecraft, and (lots of) money needed for manned lunar return. I think I had guessed that already.

Notable quotations on this hot topic:

• IOM.com writes: A three legged lander is a stable configuration as NASA’s unmanned Lunar Surveyor landers found in the 1960s.
• Hyperbola notes: While at first sight sensible, the plan does present other problems ... .
• The Daily Mail reports: Industry insiders have already said the island is already ‘punching above its weight’ in the 21st century space race.
• IOM today said: The Isle of Man is another step closer in the race to the Moon, according to space industry experts.
• The FTsays: Excalibur Almaz will charge wannabe astronauts an average of £100m for a six-eight month journey exploring deep space, and The company also hopes to drive revenues by emblazoning adverts across its space station, and If you make a mistake in space, it will kill you
• The IoM blogger ShareCrazy notes I am afraid of heights so will not be volunteering ... which UK citizen would you nominate? We offer up a choice in our Poll: Tony Blair (war criminal, serial liar), Cherie Blair (freeloader, parasite, ‘uman Rights persecutor), Lady Thatcher (Greatest PM we ever had, please come out of retirement), Wayne Rooney (congenital idiot, scumbag) and Bob Diamond (fat cat casino banker).

(I understand the Sark cold-fusion project has stalled).
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