Fermat's last theorem

Everyone knows about the Pythagoras theorem right ?
Well you might not have heard of Fermat's last theorem. have you ?
what does Pythagoras theorem say ? well simple "In a right angled triangle the square of the largest side is equal to the sum of the other two sides".
Fermat's last theorem extends it a bit by saying that it is false for all powers greater than two.well to put it simply we can say Fermat's equation, x^n + y^n = z^n with positive integer solutions, is not true for n greater than 2.the equation also called a diophantine equation.Around 1637, Fermat wrote his Last Theorem in the margin of his copy of the Arithmetica next to Diophantus’ sum-of-squares problem.


 He famously wrote the following sentence in his book.

"It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second, into two like powers. I have discovered a truly marvelous proof of this, which this margin is too narrow to contain".

why did he write that thing and what was that marvelous proof soon became a hot topic among mathematicians. there were even rewards offered to whoever who gave the proof.

 Why did this theorem came to be known as Fermat's last theorem. the answer is simple. as it was the last of Fermat’s asserted theorems to remain unproven hence the name, one that  eluded the mathematicians for nearly three and a half centuries.
 Was the conjecture proven ? yes it was !! It was proven in 1994 by Andrew wiles who spent his entire life devoted to it. the proof was many pages long and used too complicated methods not possible to be known to Fermat at that time.
That's all folks,,,and yes Simon Singh wrote a book covering the entire origin and study of the proof..

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Enigma (WORLD WAR 2)

   
     Hi Everyone, To all who don't know what enigma is, it was a machine used by the Germans for sending their messages in codes during world war 2. continue to read on for more...

       During World War II, Germany believed that its secret codes for radio messages were indecipherable to the Allies. However, the meticulous work of code breakers based at Britain’s Bletchley Park cracked the secrets of German wartime communication, and played a crucial role in the final defeat of Germany.

      The Enigma story began in the 1920s, when the German military - using an ‘Enigma’ machine developed for the business market – began to communicate in unintelligible coded messages. The Enigma machine enabled its operator to type a message, then ‘scramble’ it using a letter substitution system, generated by variable rotors and an electric circuit. To decode the message, the recipient needed to know the exact settings of the wheels. German code experts added new plugs, circuits and features to the machine during the pre-war years, but its basic principle remained the same.

       The first people who came close to cracking the Enigma code were the Polish. Close links between the German and Polish engineering industries allowed the Polish Cipher Bureau to reconstruct an Enigma machine and read the Wehrmacht’s messages between 1933 and 1938. In 1939, with German invasion looming, the Poles shared their information with the British, who in turn established the Government Code and Cipher School at Bletchley Park in Buckinghamshire. Mathematicians and intelligence experts, with the help of primitive early computers, began the complex and urgent task of cracking the Enigma code.

The Germans, convinced their Enigma messages were unbreakable, used the machine for battlefield, naval, and diplomatic communications. Although the experts at Bletchley first succeeded in reading German code during the 1940 Norwegian campaign, their work only began to pay off meaningfully in 1941, when they were able to gather evidence of the planned invasion of Greece, and learn Italian naval plans for the Battle of Cape Matapan. In the autumn, the Allies gained advantage in North Africa from deciphering coded messages used by Rommel's Panzer Army. Information obtained from such high-level German sources was code named ULTRA.

The Germans also enjoyed some noteworthy code breaking successes. The B-Dienst (surveillance service) broke British Naval code as early as 1935, which allowed them to pinpoint Allied convoys during the early stages of the Battle of the Atlantic. Although the US altered its naval code in April 1942, the change came too late to prevent the havoc wreaked by Operation Paukenschlag, the German U-boat campaign off America’s east coast early that year. The Germans also managed to crack Soviet and Danish code systems. But their efforts – fragmented and divided between rival cryptology departments - lacked the consistent success achieved at Bletchley Park.

From 1941 onwards, Bletchley’s experts focused upon breaking the codes used by German U-boats in the Atlantic. In March 1941, when the German armed trawler ‘Krebs’ was captured off Norway complete with Enigma machines and code books, the German naval Enigma code could finally be read. The Allies could now discover where U-boats were hunting and direct their own ships away from danger.

The German Navy, rightly suspicious that their code had been cracked, introduced a fourth wheel into the device, multiplying the possible settings by twenty six. The British finally broke this code that they called ‘Shark’ in December 1942. Using ULTRA always presented problems to the Allies, because any too blatant response to it would cause the Germans to suspect their messages were being read. But nevertheless Bletchley Park and its staff made a crucial and groundbreaking contribution to the defeat of the Axis in the world war 2.
 Another fun fact 
The British tried hard to conceal their code breaking success from the Axis. In 1942, when five Italian ships bound for Africa were sunk due to ULTRA information, Churchill sent a telegram to Naples congratulating a fictitious spy and awarding him a bonus.!!!!

"It was thanks to ULTRA that we won the war."

                      -Churchill to King George VI
   
     And yes there is even a movie made about it. 'The imitation game' starring benedict cumberbatch as alan turing. The movie is slated to release this november 2014.

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Shakespeare's Authorship Debate

The case for Edward De Vere, 17th Earl of Oxford.

Everyone of us know Shakespeare as the greatest poet the English language has ever known. but wait !!!
you are in for a surprise here, the Shakespeare authorship debate is most discussed and argued one over the 20th century. Continue to read on for more

Many Oxfordians believe that the true author of Shakespeare’s plays was an aristocrat named Edward De Vere. The evidence for this comprehensive, ranging from Edward de Vere’s aristocratic knowledge of the upper classes through to his education and the structural similarities between his poetry and Shakespeare’s. As regards authorship of Shakespeare’s plays and sonnets, it has been suggested that Edward wrote these under the pseudonym of Shakespeare, both to avoid breaking a voluntary convention against aristocrats publishing poetry and plays and to escape the consequences of the subject matter he was writing about. George Puttenham's 1589 book, The Arte of English Poesie explains this further.

Below are the major reasons Oxfordians claim Edward De Vere was well qualified to write 37 plays and 154 sonnets.

Edward De Vere and Elizabethan Theater.

Edward De Vere, Earl of Oxford is known to have composed, directed and acted in plays around the same time as Shakespeare. Like Shakespeare he was part of an acting troupe but unlike Shakespeare, Edward managed his acting troupe called "Oxford’s Boys". Furthermore, Edward De Vere was a leaseholder of the Blackfriars Theater, a rival to The Globe.

Edward De Vere’s poetry and its similarities to Shakespeare.

Whilst most academics agree that Edward De Vere’s poetry was better than the Sir Francis Bacon’s (the other contender for replacing Shakespeare), few believe it is of a standard necessary to prove De Vere wrote the 154 sonnets claimed to have been authored by Shakespeare.

Similarities in Edward De Vere’s verse to Shakespeare’s suggest however that such a leap in poetry composing was possible. Specifically six-line pentameter stanzas in Venus and Adonis reoccur only in Edward de Vere’s early poems and yet are not repeated by other poets of Shakespeare’s time. Both Joseph Sobran and J. Thomas Looney have noted the close similarities in form between Edward De Vere’s work and that claimed to be Shakespeare’s.

Edward De Vere’s knowledge of Elizabethan Courts and his superior education.

It is recognized by Oxfordians and Stratfordians alike that writing about royal courts, Italy and law required a certain prerequisite level of education. Edward De Vere fits the bill here since he is known to have graduated from Cambridge University at age 14, becoming master of arts at age of 16. Furthermore in view of plays like The Merchant of Venice which discussed law, De Vere studied law at Gray's Inn. Account books clearly showed that Edward De Vere had an extensive library underlining his qualifications to write as knowledgeably as Shakespeare.

Underlining this argument is the fact that Venus and Adonis, derived from Ovid's Metamorphoses, could only have been possible with Arthur Golding’s translation of this work. Arthur Golding was Edward De Vere’s uncle and his translation was said to be dedicated to Edward De Vere.

To further prove that Edward De Vere was qualified to write settings ascribed to Shakespeare, Edward De Vere is known to have traveled to Italy in the 1570s, putting him in an ideal position to write knowledgeably about Venice (The Merchant of Venice / Othello).

Similarities between Edward’s life and the character Hamlet.

Similarities between Edward De Vere’s life and Hamlet suggest that Hamlet was almost an autobiographical play about the Earl’s life. Notably Polonius’ line of "young men falling out at tennis" is believed to refer autobiographically to Edward De Vere’s notorious tennis court squabble with Sidney. Notably Edward De Vere’s father-in-law, William Cecil, Lord Burghley is said to be have been parodied as the character Polonius. Only a person intimately knowledgeable of Lord Burghley’s life could parody this man convincingly in Hamlet.

Furthermore only Edward De Vere fits the historical assertion in sonnet 125 that Shakespeare "bore the canopy" over Queen Elizabeth in her victory celebration over the defeat of the Spanish Armada.

The parallels continue between Edward De Vere’s life and subject matter in Henry IV, Part One. It is known that in 1573 Edward De Vere and company did routinely play practical jokes on ill-fated travelers on the same stretch of road as Prince Hal does in the play.

The similarities between life and sonnets, continues as Edward De Vere’s poem "Anne Vavasor's Echo", composed for Anne Vavasor is likely to have been the elusive "dark lady" of the Shakespeare’s sonnets. Furthermore, Anne Vavasor’s Echo has more than a passing resemblance to the echo verses in Venus and Adonis.

Shocked, right ?? well there's even a movie made regarding this debate. The movie's name is "Anonymous".Seriously consider watching it.

Who do you think might be the author of the plays and poems. it's left for you guys to decide the truth...!!!

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BOTTICELLI'S MAP OF HELL

At first look the painting may seem like a spinning top. but wait, have a closer look. observe keenly. you are about to see 9 levels and stairs get you from one level to another. what you are seeing is a map of hell, yes a map as described by Dante and given life by Botticelli

The Map of Hell is a painting depicting Dante's nine ring of hell as described in Dante's Inferno. 

Dante's Inferno, widely hailed as one of the great classics of Western literature, details Dante's journey through the nine circles of Hell. The voyage begins during Easter week in the year 1300, the descent through Hell starting on Good Friday. After meeting his guide, the eminent Roman poet Virgil, in a mythical dark wood,the two poets begin their descent through a baleful world of doleful shades, horrifying tortures, and unending  lamentation.

Botticelli conjured up a wonderful ,vivid and intense painting that correctly fit the description of the hell as told by Dante in his book 'the divine comedy'.
Recently Dan brown authored a book adapting Dante's inferno, using the best pieces and made it into a story that fits the contemporary era.

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