That’s sum problem!
QUESTION Have any of the Millennium Prize problems, a series of maths challenges, been solved? CLAY Mathematics Institute (CMI) of Cambridge, Massachusetts, founded in September 1998, by Boston businessman Landon T. Clay, and his wife, Lavinia D. Clay, aimed: ‘ To increase and disseminate mathematical knowledge.’
To celebrate the Millennium, CMI established its Prize Problems, seven fundamental problems straddling the mathematical disciplines which continued to bamboozle even the greatest scientific minds.
Any solution positively verified by CMI’S Scientific Advisory Board stood to win a prize of $1,000,000. Since the competition began, just one of the problems has been solved. These problems are beyond simple explanation and the proposed answers so intractable that they could baffle even the finest brains for months:
1. P vs NP problem: Introduced in 1971 by Stephen Cook in his seminal paper The Complexity Of Theorem Proving Procedures, this asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.
2. The Hodge conjecture: Formulated by Scottish mathematician William Hodge in 1940, it stands on the intersection of several fields — geometry, algebra, calculus and topology. It involves the technical problems of building shapes by ‘gluing’ geometric blocks together.
3. The Riemann hypothesis: Proposed by Bernhard Reimann in 1859, its solution would explain the apparently random pattern of prime numbers — numbers such as 3, 17 and 31, which are divisible only by themselves and one. Prime numbers are the atoms of arithmetic. 4. Yang–mills Existence and Mass
Gap: In 1954, Ning Yang and Robert Mills introduced a framework to describe elementary particles using structures that also occur in geometry. The successful use of the theory depends on a quantum mechanical property called the ‘mass gap’. While its predictions have been proven scientifically, its mathematical foundations remain unclear.
5. The Navier- Stokes equation: named after Claude-louis Navier and George Stokes, these describe the motion of fluid (that is, a liquid or a gas) in space. While used in many practical applications, the mathematics behind them is not resolved, particularly in relation to turbulence, one of the great unsolved problems in physics, despite its immense importance in science and engineering. 6. Birch and Swinnerton- Dyer
conjecture: Devised in the Fifties, this is a complex problem of algebraic number theory relating to arithmetic data associated to an elliptic curve.
7. The Poincare conjecture: Postulated by French mathematician Henri Poincare in 1900, it involves the problem of understanding the shapes of spaces — topology. It asserts that any three-dimensional space without holes in it is equivalent to a stretched sphere. This problem was solved by eccentric Russian mathematician Dr Grigori Perelman.
In August 2006, Perelman was awarded the coveted Fields Medal (officially known as International Medal for Outstanding Discoveries in Mathematics) for ‘his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci Flow’. Perelman declined the award, stating: ‘I’m not interested in money or fame, I don’t want to be on display like an animal in a zoo.’
He solved the Poincare Conjecture in 2003, but it was not until March 2010 that it was announced that he had met the criteria to receive the first Millennium Prize.
Despite living in poverty, he turned down the prize, saying that he considers his contribution to proving the Poincare Conjecture to be no greater than that of U.S. mathematician Richard Hamilton, who had introduced the geometric theory of Ricci Flow. Perelman has since given up mathematics.
Dr Ian Smith, Cambridge.
QUESTION
Did Charles Dickens ever refer to Queen Victoria in his novels? ACCORDING to the recently published Dickens Dictionary, by John Sutherland, throughout his many novels Dickens doesn’t mention Victoria once. He wasn’t antagonistic towards the monarchy — he concludes A Child’s History Of England (1851) with: ‘Queen Victoria . . . came to the throne on the 20th of June, 1837. She was married to Prince Albert of Saxe Gotha on February 10, 1840. She is very good, and much beloved. So I end, like the crier, with “God Save the Queen!”’
But neither was Dickens in awe of the monarchy. Victoria, for her part, was known to admire Dickens and considered Oliver Twist ‘excessively interesting’.
She spent many years trying to secure a meeting with the author while Dickens, renowned for his gargantuan ego, gave her the runaround for more than 20 years. He thought the Queen no more than ‘merely a provincial devotee’.
Victoria even attended several plays in which Dickens starred (as a keen amateur actor), but each time he cried off meeting her, citing ‘emotional fatigue’. When she asked for a private reading of A Christmas Carol, his excuse was that he couldn’t do the story justice outside of a proper theatre.
Dickens finally met the Queen in March 1870, just months before his death. She was told that he wasn’t well enough to travel to Windsor and so made the concession of travelling to Buckingham Palace to receive him. Protocol demanded Dickens stand for the monarch in an audience which lasted one-and-a-half hours. In a sign of the respect in which she held the author, she remained standing also. At the end of the audience, the Queen presented Dickens with a copy of her own Leaves From The Journal Of Our Life In the Highlands, in which she had inscribed: ‘ From the humblest of writers to one of the greatest.’
Annie Walker, Guildford, Surrey.
QUESTION
If an AA bra cup is smaller than an A cup, why is a DD bigger than a D? TWO immigrant Russians in the U.S., Ida and William Rosenthal, revolutionised the brassiere industry. In the Twenties, women wore a towel-like brassiere with hooks in the back which didn’t flatter them.
The Rosenthals, who ran a small tailoring firm, recognised that a woman paying more than $100 for a custom-made dress should have it fit well around the bosom, and designed a bra with two pockets or ‘cups’ which produced a better fit.
Women’s clothing became more stylish and Maidenform Brassieres became a roaring success.
In 1928, William devised the first standard cup sizes, along with the first maternity and nursing bras. His system was numerical: it was another firm, S.H. Camp and Co, which first correlated band size around the woman’s torso with an alphabetical system for volume or cup size, introducing the letters A,B,C and D. Other companies such as Warners, Model and Fay-miss soon followed suit.
Over time, it became apparent that not all women fitted well into these cup sizes and a degree of variation was required.
This was achieved by adding letters, e.g. AA or DD. The simplest way to understand the system is to prefix the size with the word ‘extra’. In clothing we have XS or extra small, S small, R regular L, large, XL extra large XXL etc. In the same way you have AA, i.e. extra A (extra small), A,B,C,D, DD or Extra D (extra large), DDD etc.
Gina Williams, Edinburgh.
QUESTION
Some years ago I saw a driving school car with two steering wheels, one for the learner (of course) and one for the instructor. Does any driving instructor today use a similarly equipped car? FURTHER to the earlier answer, The Midland Red bus company, for which I once worked, built many of its own vehicles. These included the C1 coaches of circa 1949.
After withdrawal in the Sixties, several were converted to dual control driver training vehicles.
One, No 3327 ( KHA327), was equipped with twin steering wheels, with both columns connected by a drive shaft below the dashboard. I passed my company driving test on this vehicle. It was sold for scrap in about 1979.
M. Hunt, Nuneaton.