CARL FRIEDICH GAUSS - 1796

Kenneth Appel and of Wolfgang Haken- Four Problem of Colour [is] famous and unsolved during through years.

Kenneth Appel
Appel, borne [by] Brooklyn, Metropolis of New York, he [is] educated [by] [in] University of Michigan, he finish title of Phd its [in] university of Michigan in the year 1959. After working for two year [in] Institute Analyse Defence of Princeton, he joint forces with faculty of pancaindera [in] University of Illinois, Urbana, where he act as mathematics professor from 1991 until 1993. He later;then take hold of as departmental chief [of] mathematics [in] University of Hampshire new.
In the year 1976,ia working along with Wolfgang Haken ( 1928--Sp;-Sp;), Appel announce one of [the] solution of mathematics which [is] its long standing problems and not yet four-color theorema terbongkar,yaitu. In the year 1852 Francis Guthrie have also noted that map of manapun, [so that/ to be] anampak [is] by colouring map, assuming nations with frontier of public have been coloured differently, without there [is] more than four colour. Guthrie enough intrigue to developing [him/ it] craftily matematik and ask a[n the anticipation evidence by finding the problem of which do not difficult diduga-duga in the reality, as does succeed to replace generation [all] expert of matematik.
Appel And of Hagen use a[n variation [of] a[n first method [of] times;rill tried by Arthur Kempe in the year 1879. and That depend on the fact that map have to contain certain unavoidable configuration- Appel And of Hagen recognize 1482 colour . and Them later;then use a[n computer to indicate that all this can reduce to configuration 4 colour . They start work [in] year 1972 until 1976, and that them enough with its analysis and also program of mereka.dan that take more than 1200 computer time [hour/clock] to prove the theorem.
Kenneth Appel borne in the year 1932. he [is] expert of matematik which is, [in] soybean cake 1976 with friend work Wolfgang Haken [in] University of Illinois [at] Urbana-Champaign, solving one of the most famous problems [in] theorem four-color dalam)matematika,yaitu. They prove that any two-dimensional map, with certain demarcation, can plow under with four colour without is adjacent " nations" sharing [is] same colour . Children of Appel'S, including Laurel of Appel, Petrus Appel, and Andrew Appel, now a[n professor [at] Princeton, assisted [by] [is] inspection to the 1000 case topological constitutoing this evidence.
Voucher have come to one of the most fond of to debate for modern mathematics because of depended heavy [at] computer " number-crunching" to sort;jenis [pass/through] possibilities. Even Appel have agreed, in many interview, that it lacking of accuration and [do] not present any [of] new insight which have guided mathematical research into future.

Wolfgang Haken
Other Orang)Yang, have showed [him/it] to work as start a[n sea-change in expert attitude of matematik base on computer, they have underestimated as a means of for engineer rather than for teoritius leading to creation from what [is] sometime conceived of " experimental mathematics."
In the year 1976 together with friend of k Kenneth Appel erja [in] University of Illinois [at] Urbana-Champaign, Haken solve one of the most famous problems in mathematics, theorem four-color. They prove that any two-dimensional map, with certain demarcation, can plow under with four colour without is adjacent " nations" sharing [is] same colour.
Haken have introduced some important idea, including manifold Haken, Limited Kneser-Haken, and a[n extension of work of Kneser into a[n theory about normal surface. Many its work have a[n aspect / director of algorithmic, and he [is] one of [the] figure having an effect on in topology of algorithmic. One of the contribution the key [at] this area [is] a[n algorithm to detect if a[n gin / node [is] [do] not be bound.
Which Four Problem of Colour [is] famous and unsolved during through years. [Is] there any which [is] solved?
Story of[is problem of
Since its time mapmakers start to make a map of showing different area ( like state or nations), that have been recognized [by] among them trading, that if you plan well enoughly, you will never need more than four colour to colour map which you make.
Rule basis for colour a[n map [is] that [there] no two area sharing a[n boundary earn [is] same colour ( Map will see rancu from a distance.) acceding to two area which only meeting [at] single dot to be coloured [by] [is] same colour, however. If you pay attention a[n map some or a[n atlas, you earn verification that . this [is] how all coloured familiar map.
Mapmakers is not [all] expert of matematik, so that statement which only four colour will which necessary for all map obtain;get acceptance in society map-making from year to year because not a single person have stumbled above map needing usage five colour. When [all] expert of matematik take the problem of conversation , they start with question like: Is sure you that four colour [is] enough? How do you know that not a single person can draw a[n map needing five colour? Whereof that the way of which [is] area arranged and touched one another in a map to make matter like that correctness?
When question come to Society Mathematics [in] Europe by the end of century which is 19th, matter of I tu have been felt [by] when drawing but earning dipecahkan.,terkemuka And experience of the who is [all] expert of matematik doing that problem, have been surprised by ketidak-mampuan of them to solve that. Take example [of], account / this tg-jawab from Four Colouring Problem: Assault And of Conquesst [ by / with] Saaty And of Kainen:
expert of Matematik big, Herman Minkowski, once when telling [all] its student 4-Color not yet been setled because only [all] expert of matematik lowgrade have related/relevantly [of] their x'self with that " I trust I earn to prove that," he announce. After a[n period of lame, he [ confessing / permit " Heaven made angry by my arrogancy; my evidence [is] also handicap ( Saaty& Kainen, 1986,p.8):
[At] 1976, anticipation [is] seen to be proved by Wolfgang Haken And of Kenneth Appel [in] Which [is] Univeristiy for Illinois constructively a[n computer. Program which they write [is] thousands of form and take over 1200 [hour/clock] to run Since then, a[n collective effort by [all] expert of matematik which interest to have come to on the way to check that program] So far the single mistake which have been found [by] [is] complement and [is] easy to specified. Many [all] expert of matematik accept theorem as something right.
Voucher 4-Color-Theorem [is] a[n door enter / exit to some drawing question about role of human being manage and [count/calculate] machine [in] ( mathematics dalam). Is ( itu) `` fair'' to accept when what correctness a[n computer can verification, even though single nobody? Do experiencing of or jacquards from what human being can find [about/around] their world change with usage of computer when thinking tool sebaai? Computer [is] strength and very sophisticated , but limited will its use idea iperkakas sebaga finally limit? This issue [is] lifted and considered [by] Advertisement of Infinitum: Spectre in Machine of Turing'S by Rotman Brian, and Pi ( 22:7) blue in the sky by Yohanes Barrow.