Home About us Products Services Contact us Bookmark
:: wikimiki.org ::
Hermann Günther Grassmann

Hermann Günther Grassmann

Hermann Günther Grassmann (April 15, 1809 – September 26, 1877) was a German mathematician, physicist, linguist, scholar, and neohumanist. Hermann Grassmann was born in Stettin (by chance, on the birthday of Leonhard Euler) and died there in 1877. His father was Justus Günther Grassmann and his mother was Johanne Luise Friederike Grassmann (maiden name: Medenwald). Hermann Grassmann was the son of the school teacher Justus Grassmann, Gymnasial-Professor, who wrote several influential books on physics and mathematics and various notes (Schulprogramme) which influenced his son Hermann. According to a biographical sketch by H. Grassmann himself, he was slow in school, and his father pointed him to a career as gardener. However, he finished the Gymnasium with a high grade and went on to Berlin together with his brother studying theology. During that time his interest in mathematics arose and he wrote a treatise on the theory of the tides (Theorie der Ebbe und Flut, Prüfungsarbeit 1840, published by Justus Grassmann) to grade for a mathematics teacher position. His Geometrische Analyse was submitted to the Fürstliche Jablonowski'schen Gesellschaft, as the only candidate, to reestablish or to newly invent a coordinate-free geometric calculus in the spirit of Gottfried Wilhelm Leibniz. The award was given on July 1, 1846. The main mathematical works of Grassmann are found in his two books on the theory of extensive magnitudes (Die lineale Ausdehnunglehre, ein neuer Zweig der Mathematik, 1844 and Die Ausdehnunglehre: Vollständig und in strenger Form bearbeitet, Berlin 1862, cited and known widely as A1 and A2). Unfortunately these works did not receive the attention they deserved [http://www.maths.utas.edu.au/People/dfs/Papers/GrassmannLinAlgpaper/GrassmannLinAlgpaper.html]. The A1 was submitted as a Ph. D. thesis, but Ferdinand Möbius felt unable to evaluate the work and forwarded it to Ernst Kummer; who rejected it without having studied it carefully. H. Grassmann was awarded the title of Gymnasial-Professor and had to stay as school teacher in Stettin. Not only was Grassmann a great mathematician, he was doing research in physics (crystallography, electromagnetism, mechanics etc.) and physiology (theory of colours, theory of vocals). His colour theory and the three Grassmann laws are still widely known and taught by practitioners. His book on arithmetics could still be printed having an astonishing modern style. After the complete failure of reception of his mathematical works, Grassmann turned to linguistics. He wrote books on German grammar, collected folk songs, and started to study Sanskrit. His dictionary to the Ayurveda and the translation of this holy book (still in print in Germany) were well recognized among philologists and he received a honorary doctorate from the University of Tübingen in 1876.

Works on mathematics

Theory of extensive magnitudes

Following an idea of his father, as Grassmann himself quotes in the A1, he invented a new type of product, the exterior product which he calls also combinatorial product (In German: äußeres Produkt or kombinatorisches Produkt). Since his aim in the A1 was to provide a new foundation of all of mathematics, he started with philosophical and quite general definitions. For more details, see the historical section at exterior power.

Works on linguistics

Grassmann is best known to linguists for his work on an important sound law of Indo-European, today called Grassmann's Law in his honor.

Children

His son Hermann Ernst Grassmann (1857-1922), also called Hermann Grassmann der jungere (the younger), was also a mathematician.

References


- Hermann Grassmanns gesammelte mathematische und physikalische Werke, Friedrich Engel ed., B.G. Teubner, Leipzig 1911, Band 3 II.
- Hermann Grassmann, Sein Leben und seine Werke, Victor Schlege, F.A. Brockhaus, Leipzig, 1878

External links


- Biography at The MacTutor History of Mathematics archive [http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Grassmann.html]
- Hermann Grassmann and the Creation of Linear Algebra [http://www.maths.utas.edu.au/People/dfs/Papers/GrassmannLinAlgpaper/GrassmannLinAlgpaper.html] Grassmann, Hermann Günther Grassmann, Hermann Günther Grassmann, Hermann Grassmann, Hermann Grassmann, Hermann Grassmann, Hermann ja:ヘルマン・グラスマン

April 15

April 15 is the 105th day of the year in the Gregorian calendar (106th in leap years). There are 260 days remaining.

Events


- 1450 - Battle of Formigny; Toward the end of the Hundred Years' War, the French attack and nearly annihilate English forces, ending English domination in northern France.
- 1632 - Battle of Rain; Swedes under Gustavus Adolphus defeat the Holy Roman Empire during the Thirty Years' War.
- 1738 - Premiere in London of Serse, an Italian opera by George Frideric Handel.
- 1755 - Samuel Johnson's A Dictionary of the English Language published in London.
- 1783 - Preliminary articles of peace ending Revolutionary War ratified.
- 1802 - William Wordsworth and his sister, Dorothy come across a "long belt" of daffodils, inspiring the former to pen I Wandered Lonely as a Cloud.
- 1865 - Abraham Lincoln dies after being shot the previous evening by John Wilkes Booth.
- 1865 - Andrew Johnson becomes the 17th President of the United States.
- 1892 - The General Electric Company is formed through the merger of the Edison General Electric Company and the Thomson-Houston Company.
- 1912 - The British passenger liner RMS Titanic sinks at about 2:20 a.m. after hitting an iceberg in the North Atlantic almost three hours earlier.
- 1915 - The Armenian Genocide began when the Ottoman Empire undertook the systematic annihilation of Armenian intellectuals and entrepreneurs within the city of Constantinople and later the entire Armenian population of the Empire.
- 1920 - Anarchists Sacco and Vanzetti allegedly murder two security guards while robbing a shoe store.
- 1923 - Insulin first became generally available for use by diabetics.
- 1924 - Rand McNally publishes its first road atlas.
- 1927 - Douglas Fairbanks, Mary Pickford and Norma and Constance Talmadge become the first celebrities to leave their footprints in cement at Grauman's Chinese Theater in Hollywood.
- 1940 - The Allies start their attack on the Norwegian town of Narvik which was occupied by Nazi Germany.
- 1942 - George Cross awarded to "to the island fortress of Malta - its people and defenders" by King George VI.
- 1945 - The Bergen-Belsen concentration camp is liberated.
- 1947 - Jackie Robinson debuts for the Brooklyn Dodgers baseball team, breaking that sport's color line.
- 1955 - The first McDonald's restaurant opens in Des Plaines, Illinois.
- 1983 - Tokyo Disneyland opens.
- 1985 - Marvin Hagler defeats Thomas Hearns by a knockout in round three to retain boxing's world Middleweight championship in a fight nicknamed The War.
- 1989 - Hillsborough disaster: A human stampede occurs at Hillsborough, a football stadium in Sheffield, England, resulting in the loss of 96 lives.
- 1989 - Upon Hu Yaobang's death, the Tiananmen Square protests of 1989 begin in the People's Republic of China.
- 1994 - Representatives of 124 countries and the European Communities sign the Marrakesh Agreements revising the General Agreement on Tariffs and Trade and setting up the World Trade Organization (effective January 1 1995).
- 1997 - Fire sweeps through a campsite of Muslims making the Hajj pilgrimage; the official death toll is 343.
- 2001 - Easter day (not again until 2063).
- 2002 - An Air China Boeing 767-200, flight CA129 crashes into hillside during heavy rain and fog near Pusan, South Korea killing 128.

Births


- 1452 - Leonardo da Vinci, Italian artist (d. 1519)
- 1489 - Sinan, Ottoman architect (d. 1588)
- 1552 - Pietro Cataldi, Italian mathematician (d. 1626)
- 1580 - George Calvert, 1st Baron Baltimore, English politician and colonizer
- 1588 - Claudius Salmasius, French classical scholar (d. 1653)
- 1641 - Robert Sibbald, Scottish physician and antiquarian (d. 1722)
- 1642 - Suleiman II, Ottoman Sultan (d. 1691)
- 1646 - King Christian V of Denmark (d. 1699)
- 1684 - Catherine I of Russia (d. 1727)
- 1688 - Johann Friedrich Fasch, German composer (d. 1758)
- 1707 - Leonhard Euler, Swiss mathematician (d. 1783)
- 1710 - William Cullen, Scottish physician and chemist (d. 1790)
- 1721 - Prince William Augustus, Duke of Cumberland, English military leader (d. 1765)
- 1772 - Étienne Geoffroy Saint-Hilaire, French naturalist (d. 1844)
- 1793 - Friedrich Georg Wilhelm von Struve, German astronomer (d. 1864)
- 1794 - Jean Pierre Flourens, French physiologist (d. 1867)
- 1800 - James Clark Ross, English explorer (d. 1862)
- 1809 - Hermann Grassmann, German mathematician and physicist (d. 1877)
- 1832 - Wilhelm Busch, German poet and artist (d. 1908)
- 1843 - Henry James, American author (d. 1916)
- 1858 - Émile Durkheim, French sociologist (d. 1917)
- 1861 - Bliss Carman, Canadian poet (d. 1929)
- 1874 - Johannes Stark, German physicist, Nobel Prize laureate (d. 1957)
- 1878 - Robert Walser, Swiss writer (d. 1956)
- 1879 - Melville Henry Cane, American lawyer and poet (d. 1980)
- 1883 - Stanley Bruce, eighth Prime Minister of Australia (d. 1967)
- 1886 - Nikolay Gumilyov, Russian poet (d. 1921)
- 1889 - Thomas Hart Benton, American muralist (d. 1975)
- 1889 - A. Philip Randolph, American activist (d. 1979)
- 1894 - Bessie Smith, American blues singer (d. 1937)
- 1895 - Clark McConachy, New Zealand billiards and snooker player (d. 1980)
- 1896 - Nikolay Nikolayevich Semyonov, Russian chemist, Nobel Prize laureate (d. 1986)
- 1901 - Joe Davis, English snooker player (d. 1978)
- 1902 - Fernando Pessa, Portuguese journalist (d. 2002)
- 1907 - Nikolaas Tinbergen, Dutch ornithologist, recipient of the Nobel Prize in Physiology or Medicine (d. 1988)
- 1912 - Kim Il Sung, President of North Korea (d. 1994)
- 1916 - Alfred S. Bloomingdale, American businessman (d. 1982)
- 1917 - Hans Conried, American actor (d. 1982)
- 1920 - Richard von Weizäcker, President of Germany
- 1921 - Georgi Beregovoi, cosmonaut (d. 1995)
- 1922 - Michael Ansara, Syrian-American actor
- 1922 - Harold Washington, Mayor of Chicago (d. 1987)
- 1924 - Sir Neville Marriner, English conductor and violinist
- 1927 - Robert Mills, American physicist (d. 1999)
- 1930 - Vigdís Finnbogadóttir, President of Iceland
- 1933 - Roy Clark, American musician
- 1933 - Elizabeth Montgomery, American actress (d. 1995)
- 1933 - Boris Strugatsky, Russian author
- 1938 - Claudia Cardinale, Tunisian-born actress
- 1940 - Jeffrey Archer, British author and Member of Parliament
- 1940 - Robert Walker Jr., American actor
- 1942 - Francis X. DiLorenzo, American Catholic prelate
- 1942 - Walt Hazzard, American basketball player
- 1944 - Dzhokhar Dudaev, Chechen leader (d. 1996)
- 1944 - Dave Edmunds, Welsh musician
- 1947 - Lois Chiles, American actress
- 1948 - Michael Kamen, American composer (d. 2003)
- 1950 - Amy Wright, American actress
- 1951 - Heloise, American newspaper columnist
- 1954 - Seka, American actress
- 1955 - Dodi Al-Fayed, Egyptian businessman (d. 1997)
- 1957 - Evelyn Ashford, American athlete
- 1958 - Benjamin Zephaniah, British writer and musician
- 1959 - Emma Thompson, English actress
- 1959 - Thomas F. Wilson, American actor
- 1960 - Tony Jones, English snooker player
- 1962 - Nawal El Moutawakel, Morrocan hurdler
- 1963 - Bobby Pepper, American journalist
- 1965 - Linda Perry, American musician
- 1966 - Samantha Fox, English singer and model
- 1967 - Frankie Poullain, British bassist (The Darkness)
- 1967 - Dara Torres, American swimmer
- 1968 - Ed O'Brien, British musician (Radiohead)
- 1968 - Stacey Williams, American model
- 1970 - Flex Alexander, American actor
- 1972 - Arturo Gatti, Canadian boxer
- 1974 - Danny Pino, American actor
- 1974 - Josh Todd, musician and singer (Buckcherry)
- 1976 - Richard H. Reuling III, American businessman
- 1977 - Chandra Levy, American Congressional intern (d. 2001)
- 1980 - Raúl López, Spanish basketball player
- 1983 - Ilya Kovalchuk, Russian hockey player
- 1986 - Quincy Owusu-Abeyie, Dutch footballer
- 1987 - Samuel Jay Berner, Coolest person ever to live
- 1988 - Leonard Miller, From The Irish Band Breeze [http://www.breezeworld.tk BREEZE THE IRISH BAND]
- 1988 - Uriel Salgado, future filmaker
- 1990 - Emma Watson, English actress
- 1991 - Jacob Muller, Canadian Gamer
- Unknown - Sister Marie Leahy, SSJ and St. Genevieve teacher
- 1992 - Amy Diamond, Swedish pop singer

Deaths


- 1053 - Godwin, Earl of Wessex
- 1220 - Adolf of Altena, Archbishop of Cologne
- 1415 - Manuel Chrysoloras, Greek humanist
- 1446 - Filippo Brunelleschi, Italian architect (b. 1377)
- 1610 - Robert Parsons, English Jesuit priest (b. 1546)
- 1621 - John Carver, first governor of Plymouth Colony
- 1641 - Domenico Zampieri, Italian painter (b. 1581)
- 1659 - Simon Dach, German poet (b. 1605)
- 1704 - Johann van Waveren Hudde, Dutch mathematician b. [[1628]])
- [[1719 - Françoise d'Aubigné, marquise de Maintenon, second wife of Louis XIV of France (b. 1635)
- 1754 - Jacopo Riccati, Italian mathematician (b. 1676)
- 1761 - Archibald Campbell, 3rd Duke of Argyll, Scottish politician (b. 1682)
- 1761 - William Oldys, English antiquarian and bibliographer (b. 1696)
- 1764 - Madame de Pompadour, mistress of King Louis XIV of France (b. 1721)
- 1765 - Mikhail Lomonosov, Russian scientist and writer (b. 1711)
- 1788 - Giuseppe Bonno, Austrian composer (b. 1711)
- 1793 - Ignacije Szentmartony, Croatian Jesuit missionary and geographer (b. 1718)
- 1804 - Charles Pichegru, French general (strangled in prison) (b. 1761)
- 1843 - Noah Webster, American lexicographer (b. 1758)
- 1854 - Arthur Aikin, English chemist, mineralogist, and scientific writer (b. 1773)
- 1865 - Abraham Lincoln, President of the United States (b. 1809)
- 1888 - Matthew Arnold, English poet (b. 1822)
- 1888 - Father Damien, Belgian missionary (b. 1840)
- 1898 - Kepa Te Rangihiwinui, Maori military leader
- 1912 - Victims of the RMS Titanic
  - Edward Smith, Captain of the Titanic (b. 1850)
  - John Jacob Astor IV, American businessman (b. 1864)
  - Benjamin Guggenheim, American businessman (b. 1865)
- 1942 - Robert Musil, German novelist (b. 1880)
- 1949 - Wallace Beery, American actor (b. 1885)
- 1962 - Clara Blandick, American actress (b. 1881)
- 1964 - Rachel Carson, American biologist and author (b. 1907)
- 1969 - Victoria Eugenie of Battenberg, Queen of Spain (b. 1887)
- 1974 - Giovanni D'Anzi, Italian songwriter (b.1906)
- 1975 - Richard Conte, American actor (b. 1910)
- 1980 - Raymond Bailey, American actor (b. 1904)
- 1980 - Jean-Paul Sartre, French philosopher and writer, Nobel Prize laureate (declined) (b. 1905)
- 1982 - Arthur Lowe, British actor (b. 1915)
- 1984 - Tommy Cooper, Welsh comedy magician (b. 1921)
- 1986 - Jean Genet, French author (b. 1910)
- 1988 - Kenneth Williams, English actor and comedian (b. 1926)
- 1988 - Tony Mann, Australian footballer
- 1989 - Hu Yaobang, leader of China (b. 1915)
- 1990 - Greta Garbo, Swedish actress (b. 1905)
- 1993 - John Tuzo Wilson, Canadian geologist (b. 1908)
- 1993 - Leslie Charteris, Singapore-born author (b. 1907)
- 1994 - John Curry, English figure skater (b. 1949)
- 1998 - Pol Pot, Cambodian dictator (b. 1925)
- 2000 - Edward Gorey, American illustrator (b. 1925)
- 2001 - Joey Ramone, American musician and singer (The Ramones) (b. 1951)
- 2002 - Damon Knight, author (b. 1922)
- 2002 - Byron "Whizzer" White, American football player and U.S. Supreme Court Justice (b. 1917)
- 2003 - Erin Fleming, Canadian actress (b. 1941)

Holidays and observances


- Ancient Latvia — Tipsa Diena was observed
- April 15 or, if it falls on the weekend, the following Monday, is the deadline for Americans to file their tax returns—post offices across the United States stay open until midnight to accommodate procrastinators
- Father Damien Day — celebrated annually in Hawai'i
- Feast day of Saint Paternus
- Roman Empire — the Fordicia was celebrated in honor of Terra
- Major League Baseball celebrates "Jackie Robinson Day" each April 15 in all MLB ballparks

External links


- [http://news.bbc.co.uk/onthisday/hi/dates/stories/april/15 BBC: On This Day]
- [http://www.tnl.net/when/4/15 Today in History: April 15] ---- April 14 - April 16 - March 15 - May 15 -- listing of all days ko:4월 15일 ja:4月15日 simple:April 15 th:15 เมษายน

1809

1809 was a common year starting on Sunday (see link for calendar).

Events


- January 5 - Treaty of Dardanelles between Britain and France concluded
- January 16 - Peninsular War: The British defeat the French at the Battle of Corunna.
- February 3 - Illinois Territory was created.
- February 8 - Franz I of Austria declares war on France
- February 11 - Robert Fulton patents the steamboat.
- February 20 - A decision by the Supreme Court of the United States states that the power of the federal government is greater than any individual state.
- March 4 - James Madison succeeds Thomas Jefferson as the President of the United States.
- March 13 - Military coup ousts Gustav IV Adolf of Sweden - he is confined in the Gripsholm castle.
- March 29 - At the Diet of Porvoo, Finland's four Estates pledge allegiance to Alexander I of Russia, commencing the secession of the Grand Duchy of Finland from Sweden. King Gustav IV Adolf of Sweden abdicates after a coup d'état and is later exiled.
- April 9 - Tyroleans rise against French and Bavarian occupation - they include militia lead by Andreas Hofer.
- April 14 - Napoleon defeats Austrians in the Battle of Abensberg, Bavaria
- April 19 - Battle of Raszyn between armies of Austria (attackers) and Duchy of Warsaw (defenders) as a part of struggles of the Fifth Coalition (1809). Austrian army was defeated.
- April 22 - Battle at Eckmuhl - French troops beat Austrians under archduke Karl
- May - Napoleon captures Vienna, is excommunicated, imprisons pope Pius VII.
- May 5 - Mary Kies is the first woman to be awarded a patent.
- May 5 - The Swiss canton of Aargau denies Jews citizenship.
- May 17 - Napoleon I of France orders the annexation of the Papal States to the French empire. When he announces Pope's secular power has ended, pope excommunicates him.
- May 21 - Battle at Aspern-Essling: Austrian troops under archduke Karl beat French under Napoleon
- May 24 - Dartmoor Prison opens, first to house French prisoners of war
- June 1 - Allardyce Barclay begins a bet of walking 1 mile every hour for 1,000 hours. Each hour he walked a mile round trip from his home
- June 6 - Sweden promulgates a new Instrument of Government, which restores political power to the Riksdag of the Estates after authoritarian rule since 1772.
- June 7 - Shoja Shah of Afghanistan signs a treaty with the British. Only weeks later, he is succeeded by Mahmud Shah.
- July 5-6 - Battle of Wagram - Napoleon defeats the Austrians
- July 6 - French troops arrest Pope Pius VII and take him to Liguria
- July 30 - British invasion army lands in Walcheren
- August 8 - 70 disciples of Gaon of Vilnus arrive in Palestine
- August 10 - Ecuador declares independence from Spain
- August 11 - Severe earthquakes strike the Azores and sinks the village of São Miguel
- September 17 - Peace of Hamina - Peace between Russia and Sweden in the Finnish War. The territory to become the Grand Duchy of Finland is ceded to Russia by the Treaty of Fredrikshamn.
- September 18 - Royal Opera House opens in London
- October 11 - Along the Natchez Trace in Tennessee, explorer Meriwether Lewis dies under mysterious circumstances at an inn called Grinder's Stand.
- October 14 - Treaty of Schoenbrunn cedes Illyrian provinces to France
- December 26 - British invasion troop leaves Vlissingen
- December 30 - Wearing masks at balls forbidden in Boston, Massachusetts
- USS Constitution (Old Ironsides) is recommissioned as flagship of the North Atlantic Squadron.
- Louis Poinsot describes the two remaining Kepler-Poinsot solids.
- Jean-Baptiste Lamarck publishes Philosophie Zoologique, outlining the concept of evolution.
- First running of the Two Thousand Guineas Stakes horse race in England.
- Miami University (Ohio) established by congressional order by George Washington.

Ongoing events


- Napoleonic Wars (1799-1815)-Peninsular War/Finnish War/Fifth Coalition

Births


- :Category:1809 births
- January 4 - Louis Braille, French teacher of the blind (d. 1852).
- January 15 - Pierre-Joseph Proudhon, French anarchist (d. 1864)
- January 19 - Edgar Allan Poe, American writer and poet (d. 1849)
- February 3 - Felix Mendelssohn, German composer (d. 1847)
- February 12 - Abraham Lincoln, 16th President of the United States (d. 1865)
- February 12 - Charles Darwin, British naturalist (d. 1882)
- February 15 - Cyrus McCormick, American inventor (d. 1884)
- March 31 - Nikolai Gogol, Russian writer (d. 1852)
- April 15 - Hermann Gunter Grassmann, Prussian mathematician (d. 1877)
- June 4 - Columbus Delano, American statesman (d. 1896)
- June 4 - John Henry Pratt, English clergyman and mathematician (d. 1871)
- June 8 - Richard Wigginton Thompson, American politician (d. 1900)
- August 6 - Alfred Lord Tennyson, British poet (d. 1892)
- August 8 - Heinrich Abeken, German theologian (d. 1872)
- August 27 - Hannibal Hamlin, American politician (d. 1891)
- August 29 - Oliver Wendell Holmes, Sr., American physician and writer (d. 1894)
- October 22 - Volney E. Howard, American politician (d. 1889)
- December 24 - Kit Carson, American frontiersman (d. 1868)
- December 29 - William Ewart Gladstone, British politician (d. 1898)

Deaths


- January 16 - John Moore, British general (killed in battle) (b. 1761)
- March 7 - Johann Georg Albrechtsberger, Austrian composer (b. 1736)
- March 25 - Anna Seward, English writer (b. 1747)
- March 27 - Joseph-Marie Vien, French painter (b. 1716)
- May 13 - Beilby Porteus, English bishop and abolitionist (b. 1731)
- May 17 - Leopold Auenbrugger, Austrian physician (b. 1722)
- May 31 - Joseph Haydn, Austrian composer (b. 1732)
- May 31 - Jean Lannes, French marshal (mortally wounded in battle (b. 1769)
- June 4 - Nikolaj Abraham Abildgaard, Danish painter (b. 1743)
- June 8 - Thomas Paine, American revolutionary writer (b. 1737)
- August 18 - Matthew Boulton, English manufacturer and engineer (b. 1728)
- October 8 - James Elphinston, Scottish philologist (b. 1721)
- October 11 - Meriwether Lewis, American explorer (suicide) (b. 1774)
- November 9 - Paul Sandby, English cartographer and painter (b. 1725) Category:1809 ko:1809년 ms:1809 simple:1809

September 26

September 26 is the 269th day of the year (270th in leap years) in the Gregorian Calendar, with 96 days remaining.

Events


- 46 BC - Julius Caesar dedicates a temple to his mythical ancestor Venus Genetrix in fulfilment of a vow he made at the battle of Pharsalus.
- 1580 - Sir Francis Drake circumnavigates the globe.
- 1687 - The Parthenon in Athens is partially destroyed after an explosion caused by the bombing from Venetian forces led by Morosini who were besieging the Ottoman Turks stationed in Athens.
- 1777 - British troops occupy Philadelphia, Pennsylvania during the American Revolution.
- 1789 - Thomas Jefferson is appointed the first United States Secretary of State, John Jay is appointed the first Chief Justice of the United States, Samuel Osgood is appointed the first United States Postmaster General, and Edmund Randolph is appointed the first United States Attorney General.
- 1810 - A new Act of Succession is adopted by the Riksdag of the Estates and Jean Baptiste Bernadotte becomes heir to the Swedish throne.
- 1907 - New Zealand and Newfoundland each becomes a dominion of the British Empire.
- 1914 - The US Federal Trade Commission (FTC) is established by the Federal Trade Commission Act.
- 1918 - World War I: Battle of Meuse.
- 1934 - Steamship RMS Queen Mary is launched.
- 1944 - World War II: Operation Market Garden fails.
- 1950 - United Nations troops recapture Seoul from the North Koreans.
- 1954 - Japanese rail ferry Toya Maru sinks during a typhoon in the Tsugaru Strait, Japan killing 1,172.
- 1957 - Leonard Bernstein's West Side Story opens on Broadway
- 1960 - In Chicago, Illinois, the first televised debate takes place between presidential candidates Richard M. Nixon and John F. Kennedy.
- 1961 - Bob Dylan makes his public debut.
- 1962 - Yemen Arab Republic is proclaimed
- 1962 - Premiere of The Beverly Hillbillies on CBS.
- 1969 - The Chicago Seven trial begins.
- 1969 - The Beatles album Abbey Road is released in the UK.
- 1973 - Concorde makes its first non-stop crossing of the Atlantic in record-breaking time.
- 1970 - The Laguna Fire starts in San Diego County, California, burning 175,425 acres (710 km²).
- 1981 - Baseball: Nolan Ryan sets a Major League record by throwing his fifth no-hitter.
- 1983 - Soviet military officer Stanislav Petrov averts a worldwide nuclear war.
- 1983 - Australia II, the first non-American winner, wins the Americas Cup.
- 1984 - United Kingdom agrees handover of Hong Kong.
- 1988 - Ben Johnson is stripped of his gold medal in the 100 m sprint at the Seoul Olympics for failing a drug test.
- 1991 - Biosphere 2 opens.
- 1996 - Nintendo 64 went on sale in the United States.
- 1997 - A Garuda Indonesia Airbus A-300 crashes near Medan, Indonesia, airport, killing 234
- 1997 - An earthquake strikes the Italian regions of Umbria and the Marche, causing part of the Basilica of St. Francis at Assisi to collapse.
- 2001 - Anti-globalization protests in Prague (some 20,000 protesters) police turned violent during the IMF and World Bank summits.
- 2001 - Star Trek: Enterprise begins airing in the US.
- 2002 - The overcrowded Senegalese ferry Joola capsizes off the coast of Gambia killing 1,836 people.
- 2002 - Thirty people are killed in a gun attack at a temple in Gandhinagar, India
- 2002 - Five people are shot dead in a botched bank robbery in Norfolk, Nebraska, United States.
- 2005 - The shock elimination of favoured to win, Teresa Bergman, on New Zealand Idol.

Births


- 1406 - Thomas de Ros, 9th Baron de Ros, English soldier and politician (d. 1430)
- 1711 - Richard Grenville-Temple, 2nd Earl Temple, English politician (d. 1779)
- 1750 - Cuthbert Collingwood, 1st Baron Collingwood, British admiral (d. 1810)
- 1774 - Johnny Appleseed, American environmentalist (d. 1847)
- 1791 - Théodore Géricault, French painter (d. 1824)
- 1869 - Komitas, Armenian composer (d. 1935)
- 1870 - King Christian X of Denmark (d. 1947)
- 1871 - Winsor McCay, American cartoonist (d. 1934)
- 1873 - Aleksey Shchusev, Russian architect (d. 1949)
- 1874 - Lewis Hine, American photographer and social activist (d. 1940)
- 1875 - Edmund Gwenn, Welsh actor (d. 1959)
- 1876 - Edith Abbott, American social worker, educator, and author (d. 1957)
- 1877 - Ugo Cerletti, Italian neurologist (d. 1963)
- 1877 - Alfred Cortot, Swiss pianist (d. 1962)
- 1886 - Archibald Vivian Hill, English physiologist, Nobel Prize laureate (d. 1977)
- 1887 - Antonio Moreno, Spanish-born actor (d. 1967)
- 1887 - Sir Barnes Neville Wallis, British scientist, engineer and inventor (d. 1979)
- 1888 - J. Frank Dobie, American folklorist and newspaper columnist (d. 1964)
- 1888 - T. S. Eliot, American writer and editor, Nobel Prize laureate (d. 1965)
- 1889 - Martin Heidegger, German philosopher (d. 1976)
- 1891 - Charles Munch, French conductor and violinist (d. 1968)
- 1895 - George Raft, American actor (d. 1980)
- 1897 - Arthur Rhys Davids, English pilot (d. 1917)
- 1897 - Pope Paul VI (d. 1978)
- 1898 - George Gershwin, American composer (d. 1937)
- 1907 - Anthony Blunt, English art historian and Soviet spy (d. 1983)
- 1907 - Bep van Klaveren, Dutch boxer (d. 1992)
- 1909 - Bill France, Sr., American founder of NASCAR (d. 1992)
- 1914 - Jack LaLanne, American fitness advocate
- 1923 - Dev Anand, Indian actor and film producer
- 1925 - Marty Robbins, American singer (d. 1982)
- 1926 - Masatoshi Koshiba, Japanese physicist, Nobel Prize laureate
- 1926 - Julie London, American singer and actress (d. 2000)
- 1930 - Fritz Wunderlich, German tenor (d. 1966)
- 1932 - Richard Herd, American actor
- 1932 - Dr. Manmohan Singh, Prime Minister of India
- 1932 - Vladimir Voinovich, Russian writer and dissident
- 1933 - Donna Douglas, American actress
- 1936 - Winnie Mandela, South African anti-apartheid activist
- 1942 - Kent McCord, American actor
- 1943 - Ian Chappell, Australian test cricket player and broadcaster
- 1944 - Anne Robinson, British television host
- 1945 - Bryan Ferry, British singer
- 1946 - Andrea Dworkin, American feminist (d. 2005)
- 1946 - Christine Todd Whitman, American politician
- 1947 - Lynn Anderson, American singer
- 1948 - Olivia Newton-John, Australian singer
- 1949 - Clodoaldo, Brazilian football player
- 1951 - Stuart Tosh, Scottish musician
- 1954 - Kevin Kennedy, baseball manager and television host
- 1956 - Linda Hamilton, American actress
- 1962 - Melissa Sue Anderson, American actress
- 1963 - Lysette Anthony, British actress
- 1967 - Shannon Hoon, American singer (Blind Melon) (d. 1995)
- 1968 - James Caviezel, American actor
- 1973 - Chris Small, Scottish snooker player
- 1974 - Martin Müürsepp, Estonian basketball player
- 1975 - Emma Härdelin, Swedish singer (Garmarna and Triakel)
- 1976 - Michael Ballack, German footballer
- 1976 - Yoshiko Horie, Japanese singer and voice actor.
- 1981 - Christina Milian, American actress and singer
- 1981 - Serena Williams, American tennis player

Deaths


- 1417 - Francesco Zabarella, Italian jurist (b. 1360)
- 1468 - Juan de Torquemada, Spanish Catholic cardinal (b. 1388)
- 1626 - Wakisaka Yasuharu, Japanese warrior (b. 1554)
- 1763 - John Byrom, English poet (b. 1692)
- 1764 - Benito Jerónimo Feijóo y Montenegro, Spanish scholar (b. 1767)
- 1802 - Baron Jurij Vega, Slovenian mathematician, physicist, and military officer (b. 1754)
- 1820 - Daniel Boone, American frontiersman (b. 1734)
- 1868 - August Ferdinand Möbius, German mathematician and astronomer (b. 1790)
- 1877 - Hermann Grassmann, German mathematician and physicist (b. 1809)
- 1904 - John F. Stairs, Canadian businessman and statesman (b. 1848)
- 1937 - Bessie Smith, American singer (b. 1894)
- 1945 - Béla Bartók, Hungarian composer (b. 1881)
- 1947 - Hugh Lofting, British writer (b. 1886)
- 1952 - George Santayana, Spanish philosopher (b. 1863)
- 1965 - James Fitzmaurice, Irish aviation pioneer (b. 1898)
- 1972 - Charles Correll, American radio actor (b. 1890)
- 1976 - Lavoslav Ružička, Croatian chemist, Nobel Prize laureate (b. 1887)
- 1978 - Manne Siegbahn, Swedish physicist, Nobel Prize laureate (b. 1886)
- 1984 - John Facenda, American broadcaster and sports announcer (b. 1913)
- 1998 - Betty Carter, American singer (b. 1930)
- 2000 - Richard Mulligan, American actor (b. 1932)
- 2003 - Robert Palmer, British singer (b. 1949)

Holidays and observations


- Calendar of Saints - Sts. Cosmas and Damian Also see September 26 (Eastern Orthodox liturgics)
- Discordianism - Bureflux
- [http://www.ecml.at/edl/ European Day of Languages]

External links


- [http://news.bbc.co.uk/onthisday/hi/dates/stories/september/26 BBC: On This Day] ---- September 25 - September 27 - August 26 - October 26 - more historical anniversaries ko:9월 26일 ms:26 September ja:9月26日 simple:September 26 th:26 กันยายน

1877



Mathematics

Mathematics is often defined as the study of topics such as quantity, structure, space, and change. Another view, held by many mathematicians, is that mathematics is the body of knowledge justified by deductive reasoning, starting from axioms and definitions. Practical mathematics, in nearly every society, is used for such purposes as accounting, measuring land, or predicting astronomical events. Mathematical discovery or research often involves discovering and cataloging patterns, without regard for application. The remarkable fact that the "purest" mathematics often turns out to have practical applications is what Eugene Wigner has called "the unreasonable effectiveness of mathematics." Today, the natural sciences, engineering, economics, and medicine depend heavily on new mathematical discoveries. The word "mathematics" comes from the Greek μάθημα (máthema) meaning "science, knowledge, or learning" and μαθηματικός (mathematikós) meaning "fond of learning". It is often abbreviated maths in Commonwealth English and math in North American English.

History

:Main article: History of mathematics The evolution of mathematics might be seen to be an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction was probably that of numbers. The realization that two apples and two oranges do have something in common, namely that they fill the hands of exactly one person, was a breakthrough in human thought. In addition to recognizing how to count concrete objects, prehistoric peoples also recognized how to count abstract quantities, like time -- days, seasons, years. Arithmetic (e.g. addition, subtraction, multiplication and division), naturally followed. Monolithic monuments testify to a knowledge of geometry. Further steps need writing or some other system for recording numbers such as tallies or the knotted strings called khipu used by the Inca empire to store numerical data. Numeral systems have been many and diverse. Historically, the major disciplines within mathematics arose, from the start of recorded history, out of the need to do calculations on taxation and commerce, to understand the relationships among numbers, to measure land, and to predict astronomical events. These needs can be roughly related to the broad subdivision of mathematics, into the studies of quantity, structure, space, and change. Mathematics since has been much extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries have been made throughout history and continue to be made today.

Inspiration, pure and applied mathematics, and aesthetics

Mathematics arises wherever there are difficult problems that involve quantity, structure, space, or change. At first these were found in commerce, land measurement and later astronomy; nowadays, all sciences suggest problems studied by mathematicians, and many problems arise within mathematics itself. Newton invented infinitesimal calculus and Feynman his Feynman path integral using a combination of reasoning and physical insight, and today's string theory also inspires new mathematics. Some mathematics is only relevant in the area that inspired it, and is applied to solve further problems in that area. But often mathematics inspired by one area proves useful in many areas, and joins the general stock of mathematical concepts. As in most areas of study, the explosion of knowledge in the scientific age has led to specialization in mathematics. One major distinction is between pure mathematics and applied mathematics. Within applied mathematics, two major areas have split off and become disciplines in their own right, statistics and computer science. Many mathematicians talk about the elegance of mathematics, its intrinsic aesthetics and inner beauty. Simplicity and generality are valued. There is beauty also in a clever proof, such as Euclid's proof that there are infinitely many prime numbers, and in a numerical method that speeds calculation, such as the fast Fourier transform. G. H. Hardy in "A Mathematicians Apology" expressed the belief that these esthetic considerations are, in themselves, sufficient to justify the study of pure mathematics. Main article: Mathematical beauty.

Notation, language, and rigor

Mathematical writing is not easily accessible to the layperson. A Brief History of Time, Stephen Hawking's 1988 bestseller, contained a single mathematical equation. This was the author's compromise with the publisher's advice, that each equation would halve the sales. The reasons for the inaccessibility even of carefully-expressed mathematics can be partially explained. Contemporary mathematicians strive to be as clear as possible in the things they say and especially in the things they write (this they have in common with lawyers). They refer to rigor. To accomplish rigor, mathematicians have extended natural language. There is precisely-defined vocabulary for referring to mathematical objects, and stating certain common relations. There is an accompanying mathematical notation which, like musical notation, has a definite content and also has a strict grammar (under the influence of computer science, more often now called syntax). Some of the terms used in mathematics are also common outside mathematics, such as ring, group and category; but are not such that one can infer the meanings. Some are specific to mathematics, such as homotopy and Hilbert space. It was said that Henri Poincaré was only elected to the Académie Française so that he could tell them how to define automorphe in their dictionary. Rigor is fundamentally a matter of mathematical proof. Mathematicians want their theorems to follow mechanically from axioms by means of formal axiomatic reasoning. This is to avoid mistaken 'theorems', based on fallible intuitions; of which plenty of examples have occurred in the history of the subject (for example, in mathematical analysis). Axioms in traditional thought were 'self-evident truths', but that conception turns out not to be workable in pushing the mathematical boundaries. At a formal level, an axiom is just a string of symbols, which has an intrinsic meaning only in the context of all derivable formulas of an axiomatic system. It was the goal of Hilbert's program to put all of mathematics on a firm axiomatic basis, but according to Gödel's incompleteness theorem every (strong enough) axiom system has undecidable formulas; and so a final axiomatization of mathematics is unavailable. Nonetheless mathematics is often imagined to be (as far as its formal content) nothing but set theory in some axiomatization, in the sense that every mathematical statement or proof could be cast into formulas within set theory.

Is mathematics a science?

Carl Friedrich Gauss referred to mathematics as the Queen of the Sciences. The mathematician-physicist Leon M. Lederman has quipped: "The physicists defer only to mathematicians, and the mathematicians defer only to God (though you may be hard pressed to find a mathematician that modest)." If one considers science to be strictly about the physical world, then mathematics, or at least pure mathematics, is not a science. An alternative view is that certain scientific fields (such as theoretical physics) are mathematics with axioms that are intended to correspond to reality. In fact, the theoretical physicist, J. M. Ziman, proposed that science is public knowledge and thus includes mathematics. [http://info.med.yale.edu/therarad/summers/ziman.htm] In any case, mathematics shares much in common with many fields in the physical sciences, notably the exploration of the logical consequences of assumptions. Intuition and experimentation also play a role in the formulation of conjectures in both mathematics and the (other) sciences.

Overview of fields of mathematics

As noted above, the major disciplines within mathematics first arose out of the need to do calculations in commerce, to understand the relationships between numbers, to measure land, and to predict astronomical events. These four needs can be roughly related to the broad subdivision of mathematics into the study of quantity, structure, space, and change (i.e. arithmetic, algebra, geometry and analysis). In addition to these main concerns, there are also subdivisions dedicated to exploring links from the heart of mathematics to other fields: to logic, to set theory (foundations) and to the empirical mathematics of the various sciences (applied mathematics). The study of quantity starts with numbers, first the familiar natural numbers and integers and their arithmetical operations, which are characterized in arithmetic. The deeper properties of whole numbers are studied in number theory. The study of structure began with investigations of Pythagorean triples. Neolithic monuments on the British Isles are constructed using Pythagorean triples. Eventually, this led to the invention of more abstract numbers, such as the square root of two. The deeper structural properties of numbers are studied in abstract algebra and the investigation of groups, rings, fields and other abstract number systems. Included is the important concept of vectors, generalized to vector spaces and studied in linear algebra. The study of vectors combines three of the fundamental areas of mathematics, quantity, structure, and space. The study of space originates with geometry, beginning with Euclidean geometry. Trigonometry combines space and number. The modern study of space generalizes these ideas to include higher-dimensional geometry, non-Euclidean geometries (which play a central role in general relativity) and topology. Quantity and space both play a role in analytic geometry, differential geometry, and algebraic geometry. Within differential geometry are the concepts of fiber bundles, calculus on manifolds. Within algebraic geometry is the description of geometric objects as solution sets of polynomal equations, combining the concepts of quantity and space, and also the study of topological groups, which combine structure and space. Lie groups are used to study space, structure, and change. Topology in all its many ramifications may be the greatest growth area in 20th century mathematics. Understanding and describing change is a common theme in the natural sciences, and calculus was developed as a most useful tool. The central concept used to describe a changing quantity is that of a function. Many problems lead quite naturally to relations between a quantity and its rate of change, and the methods of differential equations. The numbers used to represent continuous quantities are the real numbers, and the detailed study of their properties and the properties of real-valued functions is known as real analysis. These have been generalized, with the inclusion of the square root of negative one, to the complex numbers, which are studied in complex analysis. Functional analysis focuses attention on (typically infinite-dimensional) spaces of functions. One of many applications of functional analysis is quantum mechanics. Many phenomena in nature can be described by dynamical systems; chaos theory makes precise the ways in which many of these systems exhibit unpredictable yet still deterministic behavior. Beyond quantity, structure, space, and change are areas of pure mathematics that can be approached only by deductive reasoning. In order to clarify the foundations of mathematics, the fields of mathematical logic and set theory were developed. Mathematical logic, which divides into recursion theory, model theory, and proof theory, is now closely linked to computer science. When electronic computers were first conceived, several essential theoretical concepts in computer science were shaped by mathematicians, leading to the fields of computability theory, computational complexity theory, and information theory. Many of those topics are now investigated in theoretical computer science. Discrete mathematics is the common name for the fields of mathematics most generally useful in computer science. An important field in applied mathematics is statistics, which uses probability theory as a tool and allows the description, analysis, and prediction of phenomena where chance plays a part. It is used in all the sciences. Numerical analysis investigates methods for using computers to efficiently solve a broad range of mathematical problems that are typically beyond human capacity, and taking rounding errors or other sources of error into account to obtain credible answers.

Major themes in mathematics

An alphabetical and subclassified list of mathematical topics is available. The following list of themes and links gives just one possible view. For a fuller treatment, see Areas of mathematics or the list of lists of mathematical topics.

Quantity

This starts from explicit measurements of sizes of numbers or sets, or ways to find such measurements. : :Number – Natural number – Integers – Rational numbers – Real numbers – Complex numbers – Hypercomplex numbers – Quaternions – Octonions – Sedenions – Hyperreal numbers – Surreal numbers – Ordinal numbers – Cardinal numbers – p-adic numbers – Integer sequences – Mathematical constants – Number names – Infinity – Base

Structure

:Pinning down ideas of size, symmetry, and mathematical structure. : :Abstract algebra – Number theory – Algebraic geometry – Group theory – Monoids – Analysis – Topology – Linear algebra – Graph theory – Universal algebra – Category theory – Order theory – Measure theory

Space

:A more visual approach to mathematics. : :Topology – Geometry – Trigonometry – Algebraic geometry – Differential geometry – Differential topology – Algebraic topology – Linear algebra – Fractal geometry

Change

:Ways to express and handle change in mathematical functions, and changes between numbers. : :Arithmetic – Calculus – Vector calculus – Analysis – Differential equations – Dynamical systems – Chaos theory – List of functions

Foundations and methods

:Approaches to understanding the nature of mathematics. :philosophy of mathematics – mathematical intuitionism – mathematical constructivism – foundations of mathematics – set theory – symbolic logic – model theory – category theory – Logic – reverse mathematics – table of mathematical symbols

Discrete mathematics

:Discrete mathematics involves techniques that apply to objects that can only take on specific, separated values. : :Combinatorics – Naive set theory – Theory of computation– Cryptography – Graph theory

Applied mathematics

:Applied mathematics uses the full knowledge of mathematics to solve real-world problems. :Mathematical physics – Mechanics – Fluid mechanics – Numerical analysis – Optimization – Probability – Statistics – Mathematical economics – Financial mathematics – Game theory – Mathematical biology – Cryptography – Information theory

Important theorems

:These theorems have interested mathematicians and non-mathematicians alike. :See list of theorems for more :Pythagorean theorem – Fermat's last theorem – Gödel's incompleteness theorems – Fundamental theorem of arithmetic – Fundamental theorem of algebra – Fundamental theorem of calculus – Cantor's diagonal argument – Four color theorem – Zorn's lemma – Euler's identity – classification theorems of surfaces – Gauss-Bonnet theorem – Quadratic reciprocity – Riemann-Roch theorem.

Important conjectures

See list of conjectures for more :These are some of the major unsolved problems in mathematics. :Goldbach's conjecture – Twin Prime Conjecture – Riemann hypothesis – Poincaré conjecture – Collatz conjecture – P=NP? – open Hilbert problems.

History and the world of mathematicians

See also list of mathematics history topics :History of mathematics – Timeline of mathematics – Mathematicians – Fields medal – Abel Prize – Millennium Prize Problems (Clay Math Prize) – International Mathematical Union – Mathematics competitions – Lateral thinking – Mathematical abilities and gender issues

Mathematics and other fields

:Mathematics and architecture – Mathematics and education – Mathematics of musical scales