Life Évariste Galois

1 life

1.1 life
1.2 budding mathematician
1.3 political firebrand
1.4 final days

life
early life

galois born on 25 october 1811 nicolas-gabriel galois , adélaïde-marie (born demante). father republican , head of bourg-la-reine s liberal party. father became mayor of village after louis xviii returned throne in 1814. mother, daughter of jurist, fluent reader of latin , classical literature , responsible son s education first twelve years. @ age of 10, galois offered place @ college of reims, mother preferred keep him @ home.

the cour d honneur of lycée louis-le-grand, galois attended boy.

in october 1823, entered lycée louis-le-grand, , despite turmoil in school @ beginning of term (when hundred students expelled), galois managed perform first 2 years, obtaining first prize in latin. became bored studies and, @ age of 14, began take serious interest in mathematics.

he found copy of adrien marie legendre s Éléments de géométrie, which, said, read novel , mastered @ first reading. @ 15, reading original papers of joseph louis lagrange, such réflexions sur la résolution algébrique des équations motivated later work on equation theory, , leçons sur le calcul des fonctions, work intended professional mathematicians, yet classwork remained uninspired, , teachers accused him of affecting ambition , originality in negative way.

budding mathematician

in 1828, attempted entrance examination École polytechnique, prestigious institution mathematics in france @ time, without usual preparation in mathematics, , failed lack of explanations on oral examination. in same year, entered École normale (then known l École préparatoire), far inferior institution mathematical studies @ time, found professors sympathetic him.

augustin-louis cauchy reviewed galois mathematical papers.

in following year galois first paper, on continued fractions, published. @ around same time began making fundamental discoveries in theory of polynomial equations. submitted 2 papers on topic academy of sciences. augustin-louis cauchy refereed these papers, refused accept them publication reasons still remain unclear. however, in spite of many claims contrary, held cauchy recognized importance of galois work, , merely suggested combining 2 papers 1 in order enter in competition academy s grand prize in mathematics. cauchy, eminent mathematician of time, though political views @ opposite end galois , considered galois work winner.

on 28 july 1829 galois father committed suicide after bitter political dispute village priest. couple of days later, galois made second , last attempt enter polytechnique, , failed yet again. undisputed galois more qualified; however, accounts differ on why failed. more plausible accounts state galois made many logical leaps , baffled incompetent examiner, enraged galois. recent death of father may have influenced behavior.

having been denied admission polytechnique, galois took baccalaureate examinations in order enter École normale. passed, receiving degree on 29 december 1829. examiner in mathematics reported, pupil obscure in expressing ideas, intelligent , shows remarkable spirit of research.

he submitted memoir on equation theory several times, never published in lifetime due various events. noted before, first attempt refused cauchy, in february 1830 following cauchy s suggestion submitted academy s secretary joseph fourier, considered grand prix of academy. unfortunately, fourier died after, , memoir lost. prize awarded year niels henrik abel posthumously , carl gustav jacob jacobi. despite lost memoir, galois published 3 papers year, 1 of laid foundations galois theory. second 1 numerical resolution of equations (root finding in modern terminology). third important 1 in number theory, in concept of finite field first articulated.

political firebrand

galois, staunch republican, have wanted participate in july revolution of 1830 prevented director of École normale.

galois lived during time of political turmoil in france. charles x had succeeded louis xviii in 1824, in 1827 party suffered major electoral setback , 1830 opposition liberal party became majority. charles, faced abdication, staged coup d état, , issued notorious july ordinances, touching off july revolution ended louis-philippe becoming king. while counterparts @ polytechnique making history in streets during les trois glorieuses, galois , other students @ École normale locked in school s director. galois incensed , wrote blistering letter criticizing director, submitted gazette des Écoles, signing letter full name. although gazette s editor omitted signature publication, galois expelled.

although expulsion have formally taken effect on 4 january 1831, galois quit school , joined staunchly republican artillery unit of national guard. divided time between mathematical work , political affiliations. due controversy surrounding unit, after galois became member, on 31 december 1830, artillery of national guard disbanded out of fear might destabilize government. @ around same time, nineteen officers of galois former unit arrested , charged conspiracy overthrow government.

in april 1831, officers acquitted of charges, , on 9 may 1831, banquet held in honor, many illustrious people present, such alexandre dumas. proceedings grew riotous, , galois proposed toast king louis philippe dagger above cup, interpreted threat against king s life. arrested following day acquitted on 15 june 1831.

on following bastille day (14 july 1831), galois @ head of protest, wearing uniform of disbanded artillery, , came heavily armed several pistols, rifle, , dagger. again arrested. on 23 october sentenced 6 months in prison illegally wearing uniform. released on 29 april 1832. during imprisonment, continued developing mathematical ideas.

final days

siméon poisson reviewed galois paper on equation theory , declared incomprehensible .

galois returned mathematics after expulsion École normale, although continued spend time in political activities. after expulsion became official in january 1831, attempted start private class in advanced algebra attracted interest, waned, seemed political activism had priority. siméon poisson asked him submit work on theory of equations, did on 17 january 1831. around 4 july 1831, poisson declared galois work incomprehensible , declaring [galois ] argument neither sufficiently clear nor sufficiently developed allow judge rigor ; however, rejection report ends on encouraging note: suggest author should publish whole of work in order form definitive opinion. while poisson s report made before galois july 14 arrest, took until october reach galois in prison. unsurprising, in light of character , situation @ time, galois reacted violently rejection letter, , decided abandon publishing papers through academy , instead publish them privately through friend auguste chevalier. apparently, however, galois did not ignore poisson s advice, began collecting mathematical manuscripts while still in prison, , continued polishing ideas until release on 29 april 1832.

galois fatal duel took place on 30 may. true motives behind duel obscure. there has been speculation reasons behind it. known 5 days before death, wrote letter chevalier alludes broken love affair.

some archival investigation on original letters suggests woman of romantic interest mademoiselle stéphanie-félicie poterin du motel, daughter of physician @ hostel galois stayed during last months of life. fragments of letters her, copied galois himself (with many portions, such name, either obliterated or deliberately omitted), available. letters hint mlle. du motel had confided of troubles galois, , might have prompted him provoke duel himself on behalf. conjecture supported other letters galois later wrote friends night before died. galois cousin, gabriel demante, when asked if knew cause of duel, mentioned galois found himself in presence of supposed uncle , supposed fiancé, each of whom provoked duel. galois himself famously exclaimed: victim of infamous coquette , 2 dupes.

much more detailed speculation based on these scant historical details has been interpolated many of galois biographers (most notably eric temple bell in men of mathematics), such repeated speculation entire incident stage-managed police , royalist factions eliminate political enemy.

as opponent in duel, alexandre dumas names pescheux d herbinville, 1 of nineteen artillery officers acquittal celebrated @ banquet occasioned galois first arrest. however, dumas alone in assertion, , if correct unclear why d herbinville have been involved. has been speculated might have been du motel s supposed fiancé @ time (she married else), no clear evidence has been found supporting conjecture. on other hand, extant newspaper clippings few days after duel give description of opponent (identified initials l.d. ) appear more accurately apply 1 of galois republican friends, ernest duchatelet, imprisoned galois on same charges. given conflicting information available, true identity of killer may lost history.

whatever reasons behind duel, galois convinced of impending death stayed night writing letters republican friends , composing become mathematical testament, famous letter auguste chevalier outlining ideas, , 3 attached manuscripts. mathematician hermann weyl said of testament, letter, if judged novelty , profundity of ideas contains, perhaps substantial piece of writing in whole literature of mankind. however, legend of galois pouring mathematical thoughts onto paper night before died seems have been exaggerated. in these final papers, outlined rough edges of work had been doing in analysis , annotated copy of manuscript submitted academy , other papers.

the galois memorial in cemetery of bourg-la-reine. Évariste galois buried in common grave , exact location still unknown.

early in morning of 30 may 1832, shot in abdomen, abandoned opponents , seconds, , found passing farmer. died following morning @ ten o clock in hôpital cochin (probably of peritonitis), after refusing offices of priest. there plans initiate uprising during funeral, during same time frame leaders heard of general jean maximilien lamarque s death, , rising postponed without uprising occurring until 5 june. galois younger brother notified of events prior galois death. 20 years old. last words younger brother alfred were:

“ne pleure pas, alfred ! j ai besoin de tout mon courage pour mourir à vingt ans !”

(don t cry, alfred! need courage die @ twenty.)

on 2 june, Évariste galois buried in common grave of montparnasse cemetery exact location unknown. in cemetery of native town – bourg-la-reine – cenotaph in honour erected beside graves of relatives.

galois mathematical contributions published in full in 1843 when liouville reviewed manuscript , declared sound. published in october–november 1846 issue of journal de mathématiques pures et appliquées. famous contribution of manuscript novel proof there no quintic formula – is, fifth , higher degree equations not solvable radicals. although abel had proved impossibility of quintic formula radicals in 1824 , ruffini had published solution in 1799 turned out flawed, galois methods led deeper research in called galois theory. example, 1 can use determine, polynomial equation, whether has solution radicals.