41. The Four Colour Theorem On 17 July 1879 alfred Bray kempe announced in Nature that he had a proof of theFour Colour Conjecture. kempe was a London barrister who had studied http://physics.rug.ac.be/Fysica/Geschiedenis/HistTopics/The_four_colour_theorem.

The four colour theorem Previous topic Next topic History Topics Index The Four Colour Conjecture first seems to have been made by Francis Guthrie . He was a student at University College London where he studied under De Morgan . After graduating from London he studied law but by this time his brother Frederick Guthrie had become a student of De Morgan . Francis Guthrie showed his brother some results he had been trying to prove about the colouring of maps and asked Frederick to ask De Morgan about them. De Morgan was unable to give an answer but, on 23 October 1852, the same day he was asked the question, he wrote to Hamilton in Dublin. De Morgan wrote:- A student of mine asked me today to give him a reason for a fact which I did not know was a fact - and do not yet. He says that if a figure be anyhow divided and the compartments differently coloured so that figures with any portion of common boundary line are differently coloured - four colours may be wanted, but not more - the following is the case in which four colours are wanted. Query cannot a necessity for five or more be invented. ...... If you retort with some very simple case which makes me out a stupid animal, I think I must do as the Sphynx did.... Hamilton replied on 26 October 1852 (showing the efficiency of both himself and the postal service):- I am not likely to attempt your quaternion of colour very soon.

42. Noteworthy Families By Francis Galton And Edgar Schuster : Image 129 History of the, 38 kempe, alfred Bray, 37, 82. alfred John, 37. Edward, 38.Harry Robert, 38 John Arrow, 38. John E., 37, 82. Kelvin, Lord, 68 http://www.mugu.com/browse/galton/search/books/noteworthy-families/pages/notewor

Recognized HTML document INDEX Jevons, W. Stanley, 57 Jerusalem, archaeology of, 76 Johnstone, Professor Robert, 10 Joly, Henry Edward, 36 Jasper Robert, 37 John, 36 Rev. John P., 36 Mary, 37 "Journal of Hygiene," 13, 28 Kashmir, 26, 27 "Kempe and Kemp Families, A History of the,' 38 Kempe, Alfred Bray, 37, 82 Alfred John, 37 Edward, 38 Harry Robert, 38 John Arrow, 38 John E., 37, 82 Kelvin, Lord, 68 Khartoum, Battle of, 46 Kilmore, Bishop of, 43 " King Alfred," 57 King, George, 69 KINSFOLK, NOTEWORTHY, NUMBER OF IN EACH DEGREE, xxxiii NUMBER OF IN EACH DEGREE, XxViii NUMBER OF IN 100 FAMILIES, WHO SURVIVED CHILDHOOD, XXX of each person, difficulty of obtaining number of, x ; reasons for difficulty, x KINSMEN, NUMBER OF NOTEWORTHY, RECORDED IN 207 RETURNS, xl KINSHIP, NOMENCLATURE OF, xxvi Kirkpatrick, Lieutenant-General, 64 Knossos, Palace of, 20 Koptos, prehistoric Egyptian at 53 Kynaston, Professor Herbert, 67 Labouchere, Henry, 4 Lamarck, 17 Lancaster, Joseph, 24 Lankester, Edwin, 38, 81 E. Forbes, J9 Professor E. Ray, 38, 81 Fay, 39 Nina, 39

43. Noteworthy Families By Francis Galton And Edgar Schuster : Image 75 alfred Bray kempe (b. 1849), FRS, Chancellor of the Dioceses of fa, alfredJohn kempe (17841846), distinguished antiquary ; published works on Holwood http://www.mugu.com/browse/galton/search/books/noteworthy-families/pages/notewor

Recognized HTML document NOTEWORTHY FAMILIES me bro, Frederick, Comte de Lusi, soldier ; distinguished himself in the German-Danish War of 1848 ; decorated for valour in saving the life of General H alkett. me fa fa, Spiridion, Comte de Us!, the founder of the de Lusi family, ennobled by Frederick the Great for statesmanship.-[" Percy Anecdotes."] Kelvin, Lord.-See WILLIAM THOMPSON. Alfred Bray Kempe (b. 1849), F.R.S., Chancellor of the Dioceses of Newcastle, Southwell, and St. Albans ; Treasurer and Vice-President of the Royal Society from 1899 ; has published works on mathematics.-[" Who's Who."] fa, John Edward Kempe (b. I8 io), late Rector of St. James's, Piccadilly ; Hon. Chaplain to the King since I9oi.[" Who's Who."]

44. The Four Color Problem And Its Connection To South African Flora solved in the affirmative by the British barrister alfred Bray kempe. kempe presented refinements of his proof, and PG Tait of the University of http://io.uwinnipeg.ca/~ooellerm/guthrie/FourColor.html

The Four Color Problem and its connection to South African Flora In the 1850's Francis Guthrie was the first mathematician to formulate the Four Color Problem . He asked whether it is possible to color any map with four or fewer colors so that adjacent regions (those that share a common boundary) are colored differently. At the time when he posed the problem, he was a student at University College in London. He attempted to prove that the counties of any map could be colored in this map with four colors. However, he was not entirely satisfied with his proof, so he mentioned his problem to his brother Frederick, who, in turn, mentioned it to his instructor, the famous Augustus De Morgan (after whom De Morgan's Laws of set theory are named). In a letter dated October 23, 1852, De Morgan mentioned the problem to Sir William Rowan Hamilton (for whom hamiltonian graphs are named). In his response, Hamilton, perhaps displaying his insight into the difficulty of mathematical problems, replied to De Morgan that he did not plan to consider this problem in the near future. Evidently, De Morgan spoke often of this problem with other mathematicians. Indeed, De Morgan is credited with writing an anonymous article in the April 14, 1860, issue of the journal Athenaeum in which he discusses the Four Colour Problem. This is the first known published reference to the problem.

45. Untitled Document London barrister and amateur mathematician alfred Bray kempe ran with thisapproach, devising an elegant method that claimed to cleanly dispatch with all http://www.jaschahoffman.com/articles/globescience/ittakesfour.html

IT TAKES FOUR The Strange Career of a Cartographic Conjecture math why not five? by Jascha Hoffman Boston Globe SCIENCE / May 13, 2003 Here's a problem Lewis Carroll enjoyed posing to kids like Alice: how many colors do you need to fill in any map so that neighboring countries are always colored differently? It sounds simple enough. But when a Victorian law student first posed the question, guessing that it could be done with a mere four colors, logician Augustus De Morgan was stumped. While no one could devise a map that required more, a proof that every map requires only four colors proved remarkably elusive. Mapmakers didn't care, but problem-solvers were obsessed for decades, including the Bishop of London, a Kentucky colonel, and a California traffic cop. The question's very intractability has inspired innovations in computing and network theory, but some say it still has no satisfying solution. Oxford professor Robin Wilson's Four Colors Suffice: How the Map Problem was Solved (Princeton: 2003) presents the colorful history of this conjecture, with an unassuming lucidity that will appeal to the mathematical novice. It's thrilling to see great mathematicians fall for seductively simple proofs, then stumble on equally simple counter-examples. Or swallow their pride: after telling his class that the problem had been wasted on third-rate minds, the great number-theorist Herman Minkowski took weeks at the blackboard trying to solve it, finally admitting, "Heaven is angered by my arrogance; my proof is also defective."

46. Colorful Mathematics: Part I Portrait of alfred kempe. kempe s argument was so convincing that it was quitea few years before Percy Heawood noticed that it was incorrect. http://www.ams.org/featurecolumn/archive/coloring5.html

Colorful Mathematics: Part I Feature Column Archive 5. Some history Having noticed that it appears that any plane map can be colored with four or fewer colors, attempts were made to prove this result. One person who responded to the challenge of trying to prove the four-color conjecture was Alfred Bray Kempe . Kempe (1849-1922) had studied with the distinguished British mathematician Arthur Cayley when he was a student at Cambridge University. Although Kempe earned his living as a lawyer (barrister), he made significant contributions to mathematics in several different areas. He presented an ingenious argument in attempting to prove the four-color conjecture. His ideas have proved to be very important to the future of coloring problems even though the way he used his ideas in attempting to prove the four-color problem were not fully correct. Kempe's argument was so convincing that it was quite a few years before Percy Heawood noticed that it was incorrect. Kempe's approach reduced the problem to coloring the faces of 3-valent plane maps. The key idea of the proof involved is what are known today as Kempe chains . Suppose that one is coloring a map and one has a 4-sided region R which has faces which have been already colored with the four colors available. Kempe wanted to be able to recolor the map so that the coloring rule was met but that R could be colored. Suppose the colors ( a b c , and d ) around the region R are as represented in the diagram below: Now consider all the regions that are colored

47. The Four Color Problem In 1879, alfred kempe published what he thought was a correct proof; indeed, theerror in the paper eluded the notice of many mathematicians. http://www.ams.org/ams/wilson-jmm2003.html

Robin Wilson: "Four Colors Suffice" - Allyn Jackson, Deputy Editor, Notices of the AMS [This MAA Invited Address was given January 15, 2003.] More highlights of the 2003 Joint Mathematics Meetings Comments: webmaster@ams.org Privacy Statement Search the AMS

48. American Scientist Online - Map Quest click for full image and caption. alfred Bray kempe raised a query about themap problem, thereby attracting its next victim, alfred Bray kempe. http://www.americanscientist.org/template/AssetDetail/assetid/21979

Home Current Issue Archives Bookshelf ... Subscribe In This Section Reviewed in This Issue Book Reviews by Issue New Books Received Publishers' Directory ... Virtual Bookshelf Archive Site Search Advanced Search Visitor Login Username Password Help with login Forgot your password? Change your username see list of all reviews from this issue: July-August 2003 MATHEMATICS Map Quest Daniel S. Silver Four Colors Suffice: How the Map Problem Was Solved . Robin Wilson. xiv + 262 pp. Princeton University Press. First published by Penguin Books in 2002. $24.95 Progress in mathematics is inevitable: Given enough time, even the most fearsome problem surrenders to some new attack. The fall of Fermat's Last Theorem to Andrew Wiles in the mid-1990s, after battles spanning three and a half centuries, is an example. A less well-known instance is Kenneth Appel and Wolfgang Haken's conquest in 1976 of the Four-Color Problem, the subject of this lively and captivating book by mathematician Robin Wilson. "A student of mine asked me today to give him a reason for a fact which I did not know was a fact—and do not yet," wrote the English mathematician Augustus De Morgan in 1852 to his Irish friend and colleague Sir William Rowan Hamilton. The "fact" is that only four colors are required to color any map in such a way that adjacent regions receive different colors. The student was Frederick Guthrie, but it was Frederick's older brother, Francis, who first proposed it. Francis decided that it must be true after coloring a map of the counties in England, and he allowed Frederick to submit the challenge to De Morgan. "What do you say?" continued De Morgan in his letter to Hamilton. "The more I think of it the more evident it seems."

49. No. 1961: The Four-Color Problem One alfred Bray kempe, received great acclaim for it. He was made a Fellow ofthe Royal Society in England and was ultimately knighted. http://www.uh.edu/engines/epi1961.htm

No. 1961: THE FOUR COLOR PROBLEM John H. Lienhard presents guest Andrew Boyd Click here for audio of Episode 1961. Today, guest scientist Andrew Boyd colors maps. The University of Houston presents this series about the machines that make our civilization run, and the people whose ingenuity created them. I n 1852, Francis Guthrie found himself trying to color a map of the counties of England. It's very helpful to have a map where every bordering county is a different color, and Guthrie wondered how few colors he could use and still do this. Three colors wouldn't work, but he found he could make do with four. So he wondered, would four colors be enough for any map? Little did he realize that his question would lay its hold on generations of mathematicians. The seeming simplicity of the four color problem led countless people to try their hand at it over the years, including some of the world's most renowned mathematicians. Hermann Minkowski once told his students the problem remained unsolved because third-rate mathematicians had worked on it, only to admit much later that, "heaven is angered at my arrogance; my proof is also defective." The first would-be proof of the result was published in the American Journal of Mathematics in 1879, almost thirty years after Guthrie first posed the problem. One Alfred Bray Kempe, received great acclaim for it. He was made a Fellow of the Royal Society in England and was ultimately knighted.

50. FOXEARTH CENSUS 1881 Melford Ellen Younger wife 23 Ballingdon alfred kempe head m. 43 ag.lab.Little Yeldham Maria kempe wife 42 Castle Camps John kempe son 13 ag.lab. Fox. http://www.foxearth.org.uk/Census1881Foxearth.html

The Foxearth and District Local History Society FOXEARTH CENSUS 1881 HOUSE NAME AGE OCCUPATION WHERE BORN

51. Kempe - HTML alfred Bray kempe 18491922. This proof uses an argument known as kempe Chainsand proceeds as follows. Suppose we have a map in which every region except http://people.bath.ac.uk/ma2ajc/kempe.html

52. Math Forum - Ask Dr. Math In 1879 a British mathematician, alfred kempe, published a proof that wasaccepted by the mathematics establishment until in 1890 Percy Heawood of Durham http://mathforum.org/library/drmath/view/52466.html

Associated Topics Dr. Math Home Search Dr. Math The Four-Color Map problem Date: 11/11/97 at 23:25:27 From: Lisa Subject: The Four Color Map problem I just need help on what it is and where I can find information on it. I am having trouble finding information on it over the Internet. Thanks a lot. Date: 11/12/97 at 10:00:34 From: Doctor Anthony Subject: Re: The Four Color Map problem You can try Eric Weisstein's World of Mathematics, which will then refer you to a great deal of literature on the subject. http://mathworld.wolfram.com/Four-ColorTheorem.html http://mathforum.org/dr.math/ Associated Topics High School History/Biography Middle School History/Biography Search the Dr. Math Library: Find items containing (put spaces between keywords): Click only once for faster results: [ Choose "whole words" when searching for a word like age. all keywords, in any order at least one, that exact phrase parts of words whole words Submit your own question to Dr. Math Math Forum Home Math Library Quick Reference ... Math Forum Search Ask Dr. Math TM http://mathforum.org/dr.math/

53. Math Forum - Ask Dr. Math In 1879 a British mathematician alfred kempe published a proof that was acceptedby the mathematics establishment until in 1890 Percy Heawood of Durham http://mathforum.org/library/drmath/view/52535.html

Associated Topics Dr. Math Home Search Dr. Math Four-Color Map Problem: Some History Date: 12/10/97 at 19:57:56 From: Inoka Perera Subject: The Four colour Problem I need a description about the above topic. Could you please help me out? Thanks. Inoka http://mathforum.org/dr.math/ Associated Topics High School History/Biography Search the Dr. Math Library: Find items containing (put spaces between keywords): Click only once for faster results: [ Choose "whole words" when searching for a word like age. all keywords, in any order at least one, that exact phrase parts of words whole words Submit your own question to Dr. Math Math Forum Home Math Library Quick Reference ... Math Forum Search Ask Dr. Math TM http://mathforum.org/dr.math/

54. Apr 21 - Author Anniversaries Edmund James MILLS 1922 Sir, alfred Bray kempe 1923 James Booth MILBURN1924 Mary MILLS, Mrs MACKAY (ps Marie CORELLI) 1925 Olga NOVIKOFF, http://www.kingkong.demon.co.uk/aa/apr21.htm

Author Anniversaries for Apr 21 If you find a person's date of birth or death on this page and want to find that person's date of death or birth, or other information, try looking them up in the New General Catalog of Old Books and Authors pages. Born: nee )Jordan PERRY 1895: Prof, Otis Weldon COAN 1896: Henry(-Marie-Joseph-Millon) de MONTHERLANT 1897: Prof, Hul-Cee Marcus ACTON 1899: James Wentworth DAY 1899: Randall THOMPSON 1900: Jessie ( nee nee DODDS 1908: Elizabeth Boatwright COKER 1909: Prof, Rollo (Reece) MAY 1912: Prof, Samuel J KIMURA 1912: Robin RICHMOND 1913: Ronald William Parkinson SMITH (ps: Norman PARKINSON) 1914: Bertrand MATHER 1914: Manfred LACHS 1914: Prof, Abram BURK (ps: Abram BERGSON) 1915: Anthony (Rudolph Oaxaca) QUINN 1915: Prof, Edwin Charles ROZWENC 1915: Prof, Garrett (J) HARDIN 1918: Sir, Lawrence (Burnett) GOWING 1919: Prof, Michael Thomas MANN 1920: Donald POTTER 1921: Preston LOVE 1923: John MORTIMER 1923: Tilda ROSEN, Mrs GLASER (ps: Jane Rosen Glaser) 1924: Prof, Donald Cole FRESHWATER 1927: Peter Humphry GREENWOOD 1927: Prof, John Harold SMITH 1928: Joan WAKELIN 1928: Olivia MILLS 1936: Charles Stuart SMITH 1938: Lawrence (Ray) CLAYTON 1938: Wallace (H) TERRY 1939: Sister(CSJ), Helen PREJEAN 1943: Kole(=Bankole Ajibabi) OMOTOSO 1944: Prof, Lynn M GUNZBERG Died: nee DURONCERAY 1804: Sarah WISTER 1809: Francis GREEN 1866: Jane (Baillie) ( nee )Welsh CARLYLE 1877: Rev, Robert Cotton MATHER 1893: David Alfred DOUDNEY 1893: Edward Henry STANLEY, 15th Earl of DERBY 1909: Henry North HOLROYD, 3rd Earl of SHEFFIELD (ps: A Sussex PEER) 1910: Samuel Langhorn CLEMENS (ps: Mark TWAIN) 1913: Charles Edmund NEWTON-ROBINSON 1914: Samuel Rutherford CROCKETT 1914: Sir, Edwin DURNING-LAWRENCE, 1st Baronet DURNING-LAWRENCE

55. Alfred University : Course Descriptions : Women Studies alfred, NY 14802 Ph 607.871.2137 Fx 607.871.2339 Interim Provost Margery kempe, Julian of Norwich, and Christine de Pizan presented to orthodox http://www.alfred.edu/courses/women.html

contact news events sitemap Contact Us: Alfred University Academic Affairs Carnegie Hall 1 Saxon Drive Alfred, NY 14802 Ph: 607.871.2137 Fx: 607.871.2339 Interim Provost: William Hall, Ph.D. Email Course Descriptions Undergraduate : Women Studies Click here for details about the department and faculty who teach these courses. WST 105 - Women in Society WST 120 - Nonviolent Crisis Intervention WST 204 - Art of the Personal Essay WST 205 - Women in American Theatre ... WST 490 - Internship WST 105 - Women in Society 4 hours. Top WST 120 - Nonviolent Crisis Intervention 1 hour. Nonviolent crisis intervention is a behavior management system. We demonstrate techniques useful for prevention of acting out behavior, personal safety techniques which avoid staff or client injury during confrontation, and nonviolent physical control and restraint techniques for crisis management. Prerequisite: PSY 100 and permission of instructor. (Cross-listed as PSY 120) Top WST 204 - Art of the Personal Essay 2 hours.

56. English 205 On-Line English Literature I Links The Life of King alfred This fascinating site has an etext of The Life of For links to information on Margery kempe and The Book of Margery kempe, http://www.grammardoc.com/eng205/links.htm

Links The following are links to literature pages on the Web. Book Lovers : This site contains an abundance of links to every imaginable book-related site. Fabulous! WebLit : This site contains lots of links to other good sites, but its real claim to fame is its alphabetical list of authors and poets, with biographical and bibliographical information on each, from Dante to Pynchon. An extremely useful resource. Bookwire : This site also has good links to other sites; more important, it links you to lists of the Nobel, Pulitzer, Pen-Faulkner, and other award winners. And not least, it takes you to The Boston Review of Books and The Hungry Mind Review , among others. The Internet Book Information Center : This site contains book reviews, articles, author biographies, and also information on book-related Usenet groups. The Word : This site contains a list of links to other book sites, especially on-line journals and reference sources. A very inclusive list. Voice of the Shuttle is an excellent resource for information on just about anything under the sun (and beyond it), including literature. NYBooks, the Reader's Website

57. The National Archives National Register Of Archives Browse The kempe, Sir alfred Bray (18491922) Knight Mathematician and Civil Servant (1).kempe, alfred John (? 1785-1846) Antiquary (3). kempe, JE (fl 1895), http://www.nra.nationalarchives.gov.uk/nra/browser/person/page/person_KE.htm

Contact us Help A to Z index Site search Sorry, your browser can't show the date here. dqmcodebase = "/script/"; //script folder location You are here: Home Search the archives National Register of Archives Search the register by: Browse the Personal Index and Diaries and Papers Index Jump to: A B C D ... Z Select an alphabetical group from the list below to continue browsing. Then to: KA KE KH KI ... KY List of persons with surname beginning "KE" result(s) were found. Kean, Charles John (? 1811-1868) Actor Kean, Edmund (1787-1833) Actor Kean, Ellen (1805-1880) Actress Keane, Henry Edward (1783-1866) Colonel 7th Hussars Keane, Hugh Payne (1807-1891) West India Colonist St Vincent Italy Keane, Hugh Perry (1767-1821) Barrister Keane, John (1781-1844) 1st Baron Keane, Lieutenant General Keane, Michael (d 1796) Attorney General of St Vincent Keane, Susan (b1798) West India Colonist St Vincent Kearley, Gerald Chester (b 1890) 2nd Viscount Devonport Kearley, Hudson Ewbanke (1856-1934) 1st Viscount Devonport Kearney, Hugh Francis (b 1924) Historian Kearney, John (1741-1813) Bishop of Ossory

58. Not Slothful In Business: Macleod, Kempe And The Glass Of Govan Old Parish Churc alfred Tombleson had devoted his whole life to working for kempe, and hiscontribution to the firm s reputation was immense so much so that he alone of http://www.govanold.org.uk/reports/1991_slothful.html

Articles Church Stained Glass Sculpture ... Contact Not Slothful in Business: Macleod, Kempe and the Glass of Govan Old Parish Church By Philip N. H. Collins and Adrian Barlow This dramatic presentation of the Govan correspondence was devised by Philip N. H. Collins and written by Adrian Barlow. It was performed ( with illustrative slides ) at the launch event on Saturday 7th July 1990 within the Steven Chapel. Adrian Barlow took the part of the Narrator, Philip Collins the part of Charles Eamer Kempe, and Gilbert Bell used his Scots tongue to give flavour to the Govan 'voices'. All three speakers are members of the Kempe Society. Our connection with the Kempe Society was established by Mr. William Murray, formerly Organist at Govan Old. The correspondence between Kempe and his studio and Dr. John Macleod and Govan Parish has been published by the Kempe Society as 'The Govan Correspondence'. The original letters and accounts are deposited by Govan Old at the Strathclyde Regional Archive, located in the Mitchell Library, Glasgow. Narrator 'Not Slothful in Business', the title of our talk, is part of the inscription to be found on the East window of this Church. This window was installed as a memorial to Dr. John Macleod; and the full text of the inscription, approved by the Kirk Session in March 1899, reads as follows:

59. Problems From 1998 Colorado Marhematical Olympiad Problem 5(a) comes from the famous 1879 paper by alfred Bray kempe, in which theauthor published his attempted proof of the FourColor Conjecture (a http://www.uccs.edu/~asoifer/prob98.html

Fifteenth Annual Colorado Mathematical Olympiad April 24, 1998 These problems were selected and edited for you by the Problem Committee: Gary Miller and Alexander Soifer. The first four problems were created by Alexander Soifer especially for this year’s Olympiad. Problem 5(a) comes from the famous 1879 paper by Alfred Bray Kempe, in which the author published his attempted proof of the Four-Color Conjecture (a mistake was found 11 years later!). Problem 5(b) is a part of a less known 1880 paper by Peter Guthrie Tait, in which the author attempted to prove the Four-Color Conjecture as well (it was finally settled in 1976 by Kenneth Appel and Wolfgang Haken). Present complete solutions. We will give no credit for answers submitted without supporting work. Conversely, a minor error that leads to an incorrect answer will not substantially reduce your credit. The Great Divide All digits of a 1998-digit number A are 1. Find the greatest common divisor of A and 1111. 2. American Highway The United States has 1998 cities, some pairs of which are connected by highways. Every city is connected to at least 999 other cities. Prove that the highway system allows one to travel from any city to any other city with at most one change of highway. 3. Washington

60. The Origins Of Proof IV: The Philosophy Of Proof but in 1879 an Englishman called alfred kempe announced his proof in both Thus the problem was solved and kempe s proof was accepted far and wide. http://plus.maths.org/issue10/features/proof4/

about Plus support Plus ... Plus search plus with google home latest issue explore the archive ... news Permission is granted to print and copy this page on paper for non-commercial use. For other uses, including electronic redistribution, please contact us. Issue 10 January 2000 Contents Features Self-similar syncopations In space, do all roads lead to home? Codes, trees and the prefix property The origins of proof IV: The philosophy of proof Career interview Career interview: Sales forecasting Regulars Plus puzzle Pluschat Letters Staffroom A good BETT Book reviews News from January 2000 All the latest news ... posters! January 2000 Features The origins of proof IV: The philosophy of proof by Robert Hunt In this final article in our series on Proof, we examine the philosophy of mathematical proof. What precisely is a proof? The answer seems obvious: starting from some axioms , a proof is a series of logical deductions , reaching the desired conclusion. Every step in a proof can be checked for correctness by examining it to ensure that it is logically sound, and you can tell that you've proved a theorem once and for all by making sure that every step is correct. This might sound simple enough, but one problem is that humans (and even computers) are fallible: what if the person checking a proof for correctness makes a mistake and thinks that a step which is logically incorrect is in fact correct? Obviously somebody else will need to check that the person doing the checking didn't make any mistakes; and somebody will need to check

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