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Paul Erdős
Paul Erdős at a student seminar in Budapest (fall 1992)
Paul Erdős at a student seminar in Budapest (fall 1992)
Born March 26, 1913(1913-03-26)
Budapest, Hungary
Died September 20, 1996 (aged 83)
Warsaw, Poland
Residence Hungary
United Kingdom
United States
Israel, then itinerant
Nationality Hungarian
Fields Mathematics
Institutions Princeton
Purdue
Notre Dame
Then itinerant
Alma mater University of Pázmány Péter
Doctoral advisor Leopold Fejér
Doctoral students Bonifac Donat
Joseph Kruskal
Alexander Soifer
Known for Combinatorics
Graph theory
Number theory
Notable awards Wolf Prize (1983/84)
AMS Cole Prize (1951)
Notes
Note that he has an Erdős number of zero. Events 1026 - Pope John XIX crowns Conrad II as Holy Roman Emperor. Year 1913 ( MCMXIII) was a Common year starting on Wednesday (link will display the full calendar of the Gregorian calendar (or a Common Budapest ( also /ˈbʊ-/) is the capital city of Hungary. As the largest city of Hungary it serves as the country's principal Political, Hungary (Magyarország 'mɔɟɔrorsaːg) officially in English the Republic of Hungary ( Magyar Köztársaság, literally Magyar (Hungarian Republic Events 451 - The Battle of Chalons takes place in North Eastern France. Year 1996 ( MCMXCVI) was a Leap year starting on Monday (link will display full 1996 Gregorian calendar) Warsaw (Warszawa; also known by other names) is the Capital and Largest city of Poland. Poland (Polska officially the Republic of Poland Hungary (Magyarország 'mɔɟɔrorsaːg) officially in English the Republic of Hungary ( Magyar Köztársaság, literally Magyar (Hungarian Republic The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom, the UK or Britain,is a Sovereign state located The United States of America —commonly referred to as the For a topic outline on this subject see List of basic Israel topics. Hungary (Magyarország 'mɔɟɔrorsaːg) officially in English the Republic of Hungary ( Magyar Köztársaság, literally Magyar (Hungarian Republic Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Princeton University is a private Coeducational research university located in Princeton, New Jersey. The University of Notre Dame du Lac (or simply Notre Dame) (ˌnoʊtɚˈdeɪm is a private Roman Catholic Research university located in Alma mater is Latin for "nourishing mother" It was used in Ancient Rome as a title for the mother Goddess, and in Medieval A doctorate is an Academic degree that indicates the highest level of academic achievement Lipót Fejér (or Leopold Fejér) ( February 9, 1880, Pécs – October 15, 1959, Budapest) was a Hungarian Joseph Bernard Kruskal Jr (born January 29 1928) is an American Mathematician, Statistician, and Psychometrician. Alexander Soifer is a Russian born American Mathematician and Mathematics author Combinatorics is a branch of Pure mathematics concerning the study of discrete (and usually finite) objects In Mathematics and Computer science, graph theory is the study of graphs: mathematical structures used to model pairwise relations between objects Number theory is the branch of Pure mathematics concerned with the properties of Numbers in general and Integers in particular as well as the wider classes The Frank Nelson Cole Prize, or Cole Prize for short is one of two Prizes awarded to Mathematicians by the American Mathematical Society, one The Erdős number (ɛrdøːʃ honoring the late Hungarian mathematician Paul Erdős, is a way of describing the "collaborative distance" between a person

Paul Erdős (Hungarian: Erdős Pál, in English occasionally Paul Erdos or Paul Erdös, March 26, 1913 – September 20, 1996) was an immensely prolific (and famously eccentric) Hungarian mathematician. Hungarian ( magyar nyelv) is a Uralic language (more specifically a Ugric language) unrelated to most other languages in Europe. English is a West Germanic language originating in England and is the First language for most people in the United Kingdom, the United States Events 1026 - Pope John XIX crowns Conrad II as Holy Roman Emperor. Year 1913 ( MCMXIII) was a Common year starting on Wednesday (link will display the full calendar of the Gregorian calendar (or a Common Events 451 - The Battle of Chalons takes place in North Eastern France. Year 1996 ( MCMXCVI) was a Leap year starting on Monday (link will display full 1996 Gregorian calendar) Hungary (Magyarország 'mɔɟɔrorsaːg) officially in English the Republic of Hungary ( Magyar Köztársaság, literally Magyar (Hungarian Republic A mathematician is a person whose primary area of study and research is the field of Mathematics. With hundreds of collaborators, he worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory. Combinatorics is a branch of Pure mathematics concerning the study of discrete (and usually finite) objects In Mathematics and Computer science, graph theory is the study of graphs: mathematical structures used to model pairwise relations between objects Number theory is the branch of Pure mathematics concerned with the properties of Numbers in general and Integers in particular as well as the wider classes Analysis has its beginnings in the rigorous formulation of Calculus. In Mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with Quantitatively Probability theory is the branch of Mathematics concerned with analysis of random phenomena

Contents

Biography

Paul Erdős was born in Budapest, Hungary, as Erdős Pál. Budapest ( also /ˈbʊ-/) is the capital city of Hungary. As the largest city of Hungary it serves as the country's principal Political, Hungary (Magyarország 'mɔɟɔrorsaːg) officially in English the Republic of Hungary ( Magyar Köztársaság, literally Magyar (Hungarian Republic (Erdős is pronounced [ˈɛrdøːʃ], similar to Air-doesh. ) After his siblings died before his birth at the ages of 3 and 5, he was the only child of Anna and Lajos Erdős. His parents were both Jewish mathematicians, from a vibrant intellectual community. PLEASE TAKE NOTE************ [1] At the age of three, he could calculate how many seconds his family's friends had lived (Hoffman 1998). Erdős showed early promise as a prodigy, and soon became regarded as a mathematical genius by his peers. List of child prodigies|Fictional child prodigies A child prodigy is a one who masters one or more skills or arts at an early age A genius is a person of great Intelligence or remarkable abilities in a specific subject who shows an exceptional natural capacity of intellect and/or ability especially

Both of Erdős's parents were high school mathematics teachers, and Erdős received much of his early education from them. Erdős always remembered his parents with great affection. At 16, his father introduced him to two of his lifetime favorite subjects—infinite series and set theory. During high school, Erdős became an ardent solver of the problems proposed each month in KöMaL, the Mathematical and Physical Monthly for Secondary Schools. Erdős later published several articles in it about problems in elementary plane geometry. [2]

In 1934, he was awarded a doctorate in mathematics. [3] Because anti-semitism was increasing, he moved that same year to Manchester, England, to be a guest lecturer. Antisemitism (alternatively spelled anti-semitism or anti-Semitism; also rarely known as judeophobia) is the Prejudice against or hostility England is a Country which is part of the United Kingdom. Its inhabitants account for more than 83% of the total UK population whilst its mainland In 1938, he accepted his first American position as a scholarship holder at Princeton University. Princeton University is a private Coeducational research university located in Princeton, New Jersey. At this time, he began to develop the habit of traveling from campus to campus. He would not stay long in one place and traveled back and forth between mathematical institutions until his death.

Possessions meant little to Erdős; most of his belongings would fit in a suitcase, as dictated by his itinerant lifestyle. Awards and other earnings were in general donated to people in need and various worthy causes. Philanthropy is the act of donating money goods services time and/or effort to support a socially beneficial cause with a defined objective and with no financial or material He spent most of his life as a vagabond, travelling between scientific conferences and the homes of colleagues all over the world. A vagabond is an Itinerant person Such people may be called Tramps rogues or Hobos A vagabond is characterised by almost continuous travelling He would typically show up at a colleague's doorstep and announce "my brain is open", staying long enough to collaborate on a few papers before moving on a few days later. In many cases, he would ask the current collaborator about whom he (Erdős) should visit next. His working style has been humorously compared to traversing a linked list. In Computer science, a linked list is one of the fundamental Data structures and can be used to implement other data structures

His colleague Alfréd Rényi said, "a mathematician is a machine for turning coffee into theorems", and Erdős drank copious quantities. Alfréd Rényi (20 March 1921 &ndash 1 February 1970 was a Hungarian Mathematician who made contributions in Combinatorics and Graph theory CoFFEE is an Open source Software for computer supported collaborative learning (CSCL in a digital classroom In Mathematics, a theorem is a statement proven on the basis of previously accepted or established statements (This quotation is often attributed incorrectly to Erdős. )[4] After 1971 he also took amphetamines, despite the concern of his friends, one of whom (Ron Graham) bet him $500 that he could not stop taking the drug for a month. Amphetamine, and related drugs such as Methamphetamine are a group of drugs that act by increasing levels of Norepinephrine, Serotonin, and Dopamine Ronald Lewis Graham (born October 31, 1935) is a Mathematician credited by the American Mathematical Society with being "one of the principal [5] Erdős won the bet, but complained during his abstinence that mathematics had been set back by a month: "Before, when I looked at a piece of blank paper my mind was filled with ideas. Now all I see is a blank piece of paper. " After he won the bet, he promptly resumed his amphetamine habit.

He had his own idiosyncratic vocabulary: he spoke of "The Book", an imaginary book in which God had written down the best and most elegant proofs for mathematical theorems. God is the principal or sole Deity in Religions and other belief systems that worship one deity. Lecturing in 1985 he said, "You don't have to believe in God, but you should believe in The Book. " He himself doubted the existence of God, whom he called the "Supreme Fascist" (SF) [6]. Fascism is a totalitarian nationalist and corporatist ideology He accused the SF of hiding his socks and Hungarian passports, and of keeping the most elegant mathematical proofs to himself. A passport is a document issued by a national government which certifies for the purpose of international travel the identity and nationality of its holder When he saw a particularly beautiful mathematical proof he would exclaim, "This one's from The Book!". Many Mathematicians derive aesthetic pleasure from their work and from Mathematics in general This later inspired a book entitled Proofs from THE BOOK. Proofs from THE BOOK is a book of Mathematical proofs by Martin Aigner and Günter M

Other idiosyncratic elements of Erdős' vocabulary include: children were referred to as "epsilons" (because in mathematics, particularly calculus, an arbitrarily small positive quantity is commonly denoted ε); women were "bosses"; men were "slaves"; people who stopped doing math had "died"; people who died had "left"; alcoholic drinks were "poison"; music was "noise"; people who had married were "captured"; people who had divorced were "liberated" and to give a mathematical lecture was "to preach". Epsilon (uppercase Ε, lowercase ε; Έψιλον is the fifth letter of the Greek alphabet, corresponding phonetically to a Close-mid front unrounded Also, all countries which he thought failed to provide freedom to individuals as long as they did no harm to anyone else were classified as imperialist and given a name that began with a lowercase letter. Imperialism has two meanings one describing an action and the other describing an attitude For example, the U.S. was "samland" (after Uncle Sam), the Soviet Union was "joedom" (after Joseph Stalin), and Israel was "israel". The United States of America —commonly referred to as the Uncle Sam is a National personification of the United States (US with the first usage of the term dating from the War of 1812 and the first Joseph Stalin ( ნამდვილი გვარი ჯუღაშვილი|Iosif Vissarionovich Dzhugashvili; March 5 1953 was General Secretary of the Communist Party For his epitaph he suggested, "I've finally stopped getting dumber. An epitaph (in Greek, &mdash literally " on the gravestone " is a short text honoring a deceased person strictly speaking that inscribed on " (Hungarian: "Végre nem butulok tovább"). (Hoffman 1998)

In 1952, during the McCarthy anti-communist investigations, the U. Joseph Raymond McCarthy (November 14 1908 – May 2 1957 was an American politician who served as a Republican U S. government denied Erdős, a Hungarian citizen, a re-entry visa into the United States, for reasons that have never been fully explained. [1] Teaching at Notre Dame at the time, Erdős could have chosen to remain in the country. Instead, he packed up and left, albeit requesting reconsideration from the Immigration Service at periodic intervals. The government changed its mind in 1963 and Erdős resumed including American universities in his teaching and travels.

Hungary, then a Communist nation, was under the hegemony of the Soviet Union. Although it curtailed the freedoms of its citizens, in 1956 it gave Erdős the singular privilege of being allowed to enter and exit Hungary as he pleased. Erdős exiled himself voluntarily from Hungary in 1973 as a principled protest against his country's policy of denying entry to Israelis. [7]

During the last decades of his life, Paul Erdős received at least fifteen honorary doctorates. He became a member of the scientific academies of eight countries, including the U. S. National Academy of Sciences and the U. The National Academy of Sciences (NAS is a corporation in the United States whose members serve Pro bono as "advisers to the nation on science K. Royal Society. The Royal Society of London for the Improvement of Natural Knowledge, known simply as The Royal Society, is a Learned society for science that was founded in 1660 Shortly before his death, he renounced his honorary degree from the University of Waterloo over what he considered to be unfair treatment of a colleague. The University of Waterloo (also referred to as UW and Waterloo) is a comprehensive Public university in the city of Waterloo, Ontario He died 'in action' of a heart attack on September 20, 1996, at the age of 83, while attending a conference in Warsaw, Poland. Myocardial infarction ( MI or AMI for acute myocardial infarction) also known as a heart attack, occurs when the blood supply Events 451 - The Battle of Chalons takes place in North Eastern France. Year 1996 ( MCMXCVI) was a Leap year starting on Monday (link will display full 1996 Gregorian calendar) Warsaw (Warszawa; also known by other names) is the Capital and Largest city of Poland. Poland (Polska officially the Republic of Poland Erdős never married and had no children.

Mathematical work

Erdős was one of the most prolific publishers of papers in mathematical history, second only to Leonhard Euler; Erdős published more papers, while Euler published more pages (Hoffman 1998). He wrote around 1,500 mathematical articles in his lifetime, mostly with co-authors. He had 511 different collaborators (The Erdős Number Project Data Files), and strongly believed in (and obviously practiced) mathematics as a social activity.

In terms of mathematical style, Erdős was much more of a "problem solver" than a "theory developer". (See The Two Cultures of Mathematics[8] by Timothy Gowers for an in-depth discussion of the two styles, and why problem solvers are perhaps less appreciated. William Timothy Gowers FRS (born 20 November 1963, Wiltshire) is a British mathematician )   Joel Spencer states that his place in the 20th-century mathematical pantheon is a matter of some controversy because he resolutely concentrated on particular theorems and conjectures throughout his illustrious career. Joel Spencer (born April 20 1946)is an American Mathematician. [9] Erdős never won the highest mathematical prize, the Fields Medal, nor did he coauthor a paper with anyone who did,[10] a pattern that extends to other prizes. The Fields Medal is a prize awarded to two three or four Mathematicians not over 40 years of age at each International Congress of the International Mathematical [11] He did win the Wolf Prize, where his contribution is described as for his numerous contributions to number theory, combinatorics, probability, set theory and mathematical analysis, and for personally stimulating mathematicians the world over. [12] In contrast, the works of the three winners before were recognized as outstanding, classic, and profound, and the three after as fundamental or seminal.

Of his contributions, the development of Ramsey theory and the application of the probabilistic method especially stand out. This article provides an introduction For a more detailed and technical article see Ramsey's theorem. This article is not about Probabilistic algorithms which give the right answer with high probability but not with certainty nor about Monte Extremal combinatorics owes to him a whole approach, derived in part from the tradition of analytic number theory. Extremal combinatorics is a field of Combinatorics, which is itself a part of Mathematics. In Mathematics, analytic number theory is a branch of Number theory that uses methods from Mathematical analysis to solve number-theoretical problems Erdős found a proof for Bertrand's postulate which proved to be far neater than Chebyshev's original one. Bertrand's postulate (actually a Theorem) states that if n > 3 is an Integer, then there always exists at least one Prime number p Pafnuty Lvovich Chebyshev (Пафну́тий Льво́вич Чебышёв ( –) was a Russian Mathematician. He also discovered an elementary proof for the Prime number theorem, along with Atle Selberg, which showed how combinatorics was an efficient method of counting collections. Atle Selberg ( June 14, 1917 &ndash August 6, 2007) was a Norwegian Mathematician known for his work in Analytic number Combinatorics is a branch of Pure mathematics concerning the study of discrete (and usually finite) objects

Collaborators

Among his frequent collaborators were

Erdős number

Main article: Erdős number

Because of his prolific output, friends created the Erdős number as a humorous tribute; Erdős alone was assigned the Erdős number of 0 (for being himself), while his immediate collaborators could claim an Erdős number of 1, their collaborators have Erdős number at most 2, and so on. Yousef Alavi is a Mathematician who specializes in Combinatorics and Graph theory. Béla Bollobás (born August 3, 1943 in Budapest, Hungary) is a Hungarian Mathematician who has worked in various areas of mathematics Fan Rong K Chung Graham (金芳蓉 pinyin Jīn Fāngróng (born October 9, 1949 in Kaohsiung) known professionally as Fan Chung, is a Václav (Vašek Chvátal (born 1946 (ˈvaːt͡slaf ˈxvaːtal is a professor in the Department of Computer Science and Software Engineering at Concordia University in Ralph J Faudree is a Mathematician who specializes in Combinatorics; specifically Graph theory and Ramsey theory. Péter Frankl (born 26 March 1953 in Kaposvár, Somogy county Hungary) is a Hungarian Mathematician and Ronald Lewis Graham (born October 31, 1935) is a Mathematician credited by the American Mathematical Society with being "one of the principal Richard Kenneth Guy (born 1916 Nuneaton, Warwickshire) is a British mathematician Professor Emeritus in the Department of Mathematics András Gyárfás (born 1945 is a Hungarian Mathematician who specializes in Combinatorics and Graph theory. Ke Zhao or Chao Ko ( April 12 1910 – November 8 2002 was a Chinese Mathematician born in, People's Republic of China. In Combinatorics, the Erdős–Ko–Rado theorem of Paul Erdős, Chao Ko, and Richard Rado is a theorem on Hypergraphs specifically Carl Pomerance (born in 1944 in Joplin, Missouri) is a well known number theorist. Richard Rado ( April 28 1906 &ndash December 23 1989) was a Jewish German Mathematician. Alfréd Rényi (20 March 1921 &ndash 1 February 1970 was a Hungarian Mathematician who made contributions in Combinatorics and Graph theory Cecil Clyde Rousseau is a Mathematician and author who specializes in Graph theory and Combinatorics. Joel Spencer (born April 20 1946)is an American Mathematician. Endre Szemerédi (born August 21 1940) is a Hungarian Mathematician, working in the field of Combinatorics, currently professor of Paul (Pál Turán ( ( August 18 1910 &ndash September 26 1976)was a Hungarian Mathematician who worked primarily in Peter Winkler is a noted research mathematician author of more than 125 research papers in mathematics and patent holder in a broad range of applications The Erdős number (ɛrdøːʃ honoring the late Hungarian mathematician Paul Erdős, is a way of describing the "collaborative distance" between a person Some have estimated that 90% of the world's active mathematicians have an Erdős number smaller than 8 (not surprising in the light of the small world phenomenon). The small world experiment comprised several experiments conducted by Stanley Milgram examining the Average path length for Social networks of people in It is jokingly said that Baseball Hall of Famer Hank Aaron has an Erdős number of 1 because they both autographed the same baseball when Emory University awarded them honorary degrees on the same day. Henry Louis "Hank" Aaron (born February 5 1934 in Mobile Alabama) nicknamed "Hammer" "Hammerin' Hank” or "Bad Henry” is a retired Emory University is a Private university located in the metropolitan area of the city of Atlanta and in western unincorporated DeKalb County, Erdős numbers have also been humorously assigned to an infant, a horse and several actors. For details see the "Extended Erdős Number Project" [2]

The Erdős number was most likely first defined by Casper Goffman, an analyst whose own Erdős number is 1. Analysis has its beginnings in the rigorous formulation of Calculus. [13] Goffman published his observations about Erdős's prolific collaboration in a 1969 article entitled "And what is your Erdős number?"[14]

Notes

  1. ^ The Budapest Jewish community of that day produced at least six remarkable thinkers besides Erdős: physicist and mathematician Eugene Wigner (Wigner Jenő in Hungarian), physicist Edward Teller (Teller Ede), physicist Leó Szilárd (Szilárd Leó), mathematician and polymath John von Neumann (Neumann János), physicist Dennis Gabor (Gábor Dénes), and philosopher Georg Lukács (Lukács György). Eugene Paul "EP" Wigner ( Hungarian Wigner Pál Jenő) ( November 17, 1902 &ndash January 1, 1995) was a Edward Teller (original Hungarian name Teller Ede) (January 15 1908 &ndash September 9 2003 was a Hungarian -American theoretical Physicist Leó Szilárd (Szilárd Leó February 11, 1898 – May 30, 1964) was an Hungarian - American Physicist who A polymath ( Greek polymathēs, πολυμαθής "having learned much" is a person whose knowledge is not restricted to one subject area Dennis Gabor (original Hungarian name Gábor Dénes) FRS, ( June 5, 1900, Budapest &ndash February 9 György Lukács (pronounced in IPA dyɶrdyə ˈlukɑtʃ) ( April 13, 1885 – June 4, 1971) was a Hungarian
  2. ^ www. cs. uchicago. edu/files/tr_authentic/TR-2001-11. ps
  3. ^ Erdős's thesis advisor at the University of Budapest was Leopold Fejér (or Fejér Lipót), who was also the thesis advisor for John von Neumann, George Pólya and Paul (Pál) Turán. Lipót Fejér (or Leopold Fejér) ( February 9, 1880, Pécs – October 15, 1959, Budapest) was a Hungarian George Pólya (b December 13, 1887 &ndash d September 7, 1985, in Hungarian Pólya György) was a Hungarian Paul (Pál Turán ( ( August 18 1910 &ndash September 26 1976)was a Hungarian Mathematician who worked primarily in
  4. ^ Biography of Alfréd Rényi by J. J. O'Connor and E. F. Robertson
  5. ^ Hill, J. Paul Erdos, Mathematical Genius, Human (In That Order)
  6. ^ Schechter, Bruce. My Brain Is Open: The mathematical journeys of Paul Erdos, New York : Simon & Schuster, 1998, p. 70-71
  7. ^ "Paul Erdős (1913–1996)" . Notices of the American Mathematical Society 45 (1). Notices of the American Mathematical Society is a membership journal of the American Mathematical Society. American Mathematical Society. The American Mathematical Society (AMS is an association of professional Mathematicians dedicated to the interests of mathematical research and scholarship which  
  8. ^ This essay is in Mathematics: Frontiers and Perspectives, Edited by V. I. Arnold, Michael Atiyah, Peter D. Lax and Barry Mazur, American Mathematical Society, 2000.
  9. ^ Joel Spencer, Prove and Conjecture!, a review of Mathematics: Frontiers and Perspectives. American Scientist, Volume 88, No. 6 November-December 2000
  10. ^ Paths to Erdos
  11. ^ From Trails to Erdos, by DeCastro and Grossman, in The Mathematical Intelligencer: vol. 21, no. 3 (Summer 1999), 51–63: A careful reading of Table 3 shows that although Erdos never wrote jointly with any of the 42 [Fields] medalists (a fact perhaps worthy of further contemplation). . . there are many other important international awards for mathematicians. Perhaps the three most renowned. . . are the Rolf Nevanlinna Prize, the Wolf Prize in Mathematics, and the Leroy P. Steele Prizes. . . . Again, one may wonder why KAPLANSKY is the only recipient of any of these prizes who collaborated with PAUL ERDOS. (After this paper was written, collaborator Lovasz received the Wolf prize, making 2 in all).
  12. ^ Wolf Foundation Mathematics Prize Page
  13. ^ Michael Golomb's obituary of Paul Erdős
  14. ^ Goffman, Casper (1969). Michael Golomb ( May 3, 1909 in Munich &ndash April 9, 2008) was an American Mathematician and Educator "And what is your Erdős number?". American Mathematical Monthly 76: 791. doi:10.2307/2317868. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.  

Books about Erdős and references

See also

External links


Persondata
NAME Erdős, Paul
ALTERNATIVE NAMES Erdos, Paul (Anglicization); Erdős Pál (Birth name)
SHORT DESCRIPTION Mathematician
DATE OF BIRTH March 26, 1913
PLACE OF BIRTH Budapest, Hungary
DATE OF DEATH September 20, 1996
PLACE OF DEATH Warsaw, Poland

Events 1026 - Pope John XIX crowns Conrad II as Holy Roman Emperor. Year 1913 ( MCMXIII) was a Common year starting on Wednesday (link will display the full calendar of the Gregorian calendar (or a Common Budapest ( also /ˈbʊ-/) is the capital city of Hungary. As the largest city of Hungary it serves as the country's principal Political, Hungary (Magyarország 'mɔɟɔrorsaːg) officially in English the Republic of Hungary ( Magyar Köztársaság, literally Magyar (Hungarian Republic Events 451 - The Battle of Chalons takes place in North Eastern France. Year 1996 ( MCMXCVI) was a Leap year starting on Monday (link will display full 1996 Gregorian calendar) Warsaw (Warszawa; also known by other names) is the Capital and Largest city of Poland. Poland (Polska officially the Republic of Poland
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