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Hardy and Littlewood
Hardy and Littlewood showed that all sufficiently large numbers are the sum of at most 19 fourth powers.
A stronger form of the twin prime conjecture, the HardyLittlewood conjecture, postulates a distribution law for twin primes akin to the prime number theorem.
The HardyLittlewood conjecture ( after G. H. Hardy and John Littlewood ) is a generalization of the twin prime conjecture.
Pursuing this type of analysis more carefully, Hardy and Littlewood in 1923 conjectured ( as part of their famous HardyLittlewood prime tuple conjecture ) that for any fixed c ≥ 2, the number of representations of a large integer n as the sum
# redirect Twin prime # First HardyLittlewood conjecture
This ( along with much else ) led to quantitative progress on the Waring problem, as part of the HardyLittlewood circle method, as it became known.
This was a major factor in the development of number theory as a system of conjectures ; examples are the first and second HardyLittlewood conjectures.
In a 1947 lecture, the Danish mathematician Harald Bohr reported a colleague as saying, " Nowadays, there are only three really great English mathematicians: Hardy, Littlewood, and HardyLittlewood.
A heuristic estimate ( due to G. H. Hardy and J. E. Littlewood ) for the number of Sophie Germain primes less than n is 2C < sub > 2 </ sub > n / ( ln n )< sup > 2 </ sup > where C < sub > 2 </ sub > is the twin prime constant, approximately 0. 660161.
In 1923, Hardy and Littlewood showed that, assuming the generalized Riemann hypothesis, the odd Goldbach conjecture is true for all sufficiently large odd numbers.
John Edensor Littlewood ( 9 June 1885 – 6 September 1977 ) was a British mathematician, best known for the results achieved in collaboration with G. H. Hardy.
Together they devised the first HardyLittlewood conjecture, a strong form of the twin prime conjecture, and the second HardyLittlewood conjecture.

Hardy and listed
* Thomas P. Hardy House-Frank Lloyd Wright house listed on the National Register of Historic Places
Lloyd's is not publicly traded, though some of its members are listed companies, such as Hiscox Ltd, Catlin Group Ltd and Hardy Underwriting Bermuda Ltd.
Apart from Unfinished Dialogue and the 4th edition of Karl Marx, all publications listed from 1978 onwards are compilations or transcripts of various lectures, essays, and letters, edited by Henry Hardy.
* Hickory Hill ( Petersburg, West Virginia ), listed on the NRHP in Hardy County, West Virginia
" Seminole " is listed as one of the Muskogean languages in Hardy's list, but it is generally considered a dialect of Creek, rather than a separate language ( as she herself comments: Hardy 2005: 70 ; see also Mithun 2005: 462, Crawford ).
The Orlando Sentinels Gregory Hardy listed it as the seventh best episode of the show with a sports theme.

Hardy and their
Stan Laurel and Oliver Hardy, who had made a number of very popular short silent films, used the arrival of sound to deepen their well-formed screen characterizations and enhance their visual humour, and went on to great success in talking films.
The most famous of these assertions is by the History Channel in their " True Horror " series ( produced by Hardy Pictures in 2009 ) which states Aldini specifically as one of the sources for Mary Shelley's novel.
A tag team match in progress-Jeff Hardy kicks Eddie Fatu | Umaga, while their respective partners, Triple H and Randy Orton, encourage them and reach for the tags.
The bowlers and other broadly comic aspects of their personas have reminded modern audiences of Laurel and Hardy, who occasionally played tramps in their films.
The English author Thomas Hardy used a fictionalised Wessex as a setting for many of his novels, adopting his friend William Barnes ' term Wessex for their home county of Dorset and its neighbouring counties in the south and west of England.
Hirschfeld said that modern film stars were more difficult to depict, that silent film comedians such as Laurel and Hardy and Keaton " looked like their caricatures ".
" She once characterized their marriage as Love Finds Andy Hardy.
*" Magic Act " introduced by Jack Benny, featuring Laurel and Hardy as magicians in a comedy skit ( their first appearance in a sound feature film )
It was parodied by Laurel and Hardy in their film Bonnie Scotland.
She tells the manager her address-1127 Walnut Avenue-and he hires the Laurel and Hardy Transfer Company to deliver the piano in their freight wagon.
While at Roach, McCarey cast Stan Laurel and Oliver Hardy together and guided development of their onscreen characters, thus creating one of the most enduring comedy teams of all time.
* The British comedy troupe Monty Python mention Tess of the d ' Urbervilles on their 1973 comedy record album Monty Python's Matching Tie and Handkerchief on the track " Novel Writing ", in which Thomas Hardy writes Return of the Native before a live audience.
Originally Morecambe and Wise objected to sharing a bed ( which would become one of their most popular and fondly remembered character traits ), but Braben countered that if it was good enough for Laurel and Hardy it was surely good enough for Morecambe and Wise.
Moreover, Hardy deliberately pointed out in his Apology that mathematicians generally do not " glory in the uselessness of their work ," but rather – because science can be used for evil as well as good ends – " mathematicians may be justified in rejoicing that there is one science at any rate, and that their own, whose very remoteness from ordinary human activities should keep it gentle and clean.
" Hardy also rejected as a " delusion " the belief that the difference between pure and applied mathematics had anything to do with their utility.
In the late 1950s the Scopitone, a visual jukebox, was invented in France and short films were produced by many French artists, such as Serge Gainsbourg, Françoise Hardy, Jacques Brel, and Jacques Dutronc to accompany their songs.
In 1992 and 1993, Robert Crumb was involved in a project by a Dutch formation, The Beau Hunks, and for both their albums " The Beau Hunks play the original Laurel & Hardy music "
The 1929 film Berth Marks stars the comedy legends Laurel and Hardy as they attempt to reach Pottsville by train for one of their booked performances.
While Kenneth R. Hall suggests that Champa was not able to rely on taxes on trade for continuous revenue, but instead financed their rule by raiding neighbouring countries, Hardy argues that the country's prosperity was above all based on commerce.

Hardy and I
" I Know My Mind " b / w " Laurel & Hardy " ( Warner Bros. 7219 )-( JB )
* Hardy once told Bertrand Russell " If I could prove by logic that you would die in five minutes, I should be sorry you were going to die, but my sorrow would be very much mitigated by pleasure in the proof ".
* Moses Hardy, formerly oldest living American man, one of the oldest veterans of World War I.
In a 1947 lecture, the Danish mathematician Harald Bohr said, " To illustrate to what extent Hardy and Littlewood in the course of the years came to be considered as the leaders of recent English mathematical research, I may report what an excellent colleague once jokingly said: ' Nowadays, there are only three really great English mathematicians: Hardy, Littlewood, and HardyLittlewood.
R. H. N ( Dick ) Hardy: Beeching-Champion of the Railway ( 1989 ) ISBN 0-7110-1855-3 and Gerard Fiennes: I Tried to Run a Railway ( 1967 ) ISBN 0-7110-0447-1.
On May 27, 1928, Peer had the group travel to the Victor Camden, New Jersey studios, where they recorded many of what would become their signature songs, including: " Meet me by the Moonlight Alone "; " Keep On the Sunny Side "; " Can the Circle be Unbroken "; " Little Darling, Pal of Mine "; " Forsaken Love "; " Anchored in Love "; " I Ain't Goin ' to Work Tomorrow "; " Will You Miss Me When I'm Gone "; " Wildwood Flower "; " River of Jordan "; " Chewing Gum "; and " John Hardy Was a Desperate Little Man ".
He is best known for his radio work, particularly on The News Quiz, I'm Sorry I Haven't a Clue and his long-running series of monologues Jeremy Hardy Speaks to the Nation.
Laurel later said, " Hardy and I were always planning to do something on TV.
:" I do not think that G. H. Hardy was talking nonsense when he insisted that the mathematician was discovering rather than creating, nor was it wholly nonsense for Kepler to exult that he was thinking God's thoughts after him.
The series featured two other actors, regular I'm sorry I haven't a clue panelist Jeremy Hardy, and Alison Steadman.
Also, an " I Quit " match took place featuring Jeff Hardy defeating Matt Hardy.
I have called it " Slapstick " because it is grotesque, situational poetry -- like the slapstick film comedies, especially those of Laurel and Hardy, of long ago.
In a rematch at Backlash, however, Hardy defeated Matt in an " I Quit " match.
After appearing in more than a dozen B-movies, as well as supporting roles, as FBI agent Steve Daniels in the espionage series I Led Three Lives and as LAPD Sergeant Vince Cavelli in The New Breed, he was offered the role of Dr. Steve Hardy on the soap opera General Hospital.
At Backlash 2009, Jeff Hardy defeated his brother Matt Hardy in an " I Quit " match after threatening to jump off a ladder onto Matt, which he did after the match.
" Hardy wrote of the review, " alas ... the Spectator brought down its heaviest leaded pastoral staff on the prematurely happy volumes ... the bitterness of that moment was never forgotten, at that moment I wished I was dead.
Hardy wrote in a letter to Edmund Gosse on Dec. 10, 1882, “ I get most extraordinary criticisms of T. on a T. Eminent critics write & tell me in private that it is the most original thing I have done ... while other eminent critics ( I wonder if they are the same ) print the most cutting rebukes you can conceive -- show me ( to my amazement ) that I am quite an immoral person ...”

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