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**GEORGE****BOOLE**(1815**-**1864),**English****logician****and****mathematician**,**was****born****in****Lincoln****on****the**2nd**of****November**1815.**Being****especially****interested****in****mathematical****science**,**the****father****gave****his****son****his****first****lessons**;**but****the****extraordinary****mathematical****powers****of****George****Boole****did****not****manifest****themselves****in****early****life**.**Almost****the****only****changes****which****can****be****called****events****are****his****successful****establishment****of****a****school****at****Lincoln**.**To****the****public****Boole****was****known****only****as****the****author****of****numerous****abstruse****papers****on****mathematical****topics**,**and****of****three****or****four****distinct****publications****which****have****become****standard****works**.**To****the****Cambridge****Mathematical****Journal****and****its****successor**,**the****Cambridge****and****Dublin****Mathematical****Journal**,**Boole****contributed****in****all****twenty-two****articles**.**The****works****of****Boole****are****thus****contained****in****about****fifty****scattered****articles****and****a****few****separate****publications**.**Only****two****systematic****treatises****on****mathematical****subjects****were****completed****by****Boole****during****his****lifetime**.**These****treatises****are****valuable****contributions****to****the****important****branches****of****mathematics****in****question**,**and****Boole**,**in****composing****them**,**seems****to****have****combined****elementary****exposition****with****the****profound****investigation****of****the****philosophy****of****the****subject****in****a****manner****hardly****admitting****of****improvement**.**Boole****was****one****of****the****most****eminent****of****those****who****perceived****that****the****symbols****of****operation****could****be****separated****from****those****of****quantity****and****treated****as****distinct****objects****of****calculation**.**During****the****last****few****years****of****his****life****Boole****was****constantly****engaged****in****extending****his****researches****with****the****object****of****producing****a****second****edition****of****his****Differential****Equations****much****more****complete****than****the****first****edition**;**and****part****of****his****last****vacation****was****spent****in****the****libraries****of****the****Royal****Society****and****the****British****Museum**.**With****the****exception****of****Augustus****de****Morgan**,**Boole****was****probably****the****first****English****mathematician****since****the****time****of****John****Wallis****who****had****also****written****upon****logic**.**His****novel****views****of****logical****method****were****due****to****the****same****profound****confidence****in****symbolic****reasoning****to****which****he****had****successfully****trusted****in****mathematical****investigation**.**Thus**,**if****x**=**horned****and****y**=**sheep**,**then****the****successive****acts****of****election****represented****by****x****and****y**,**if****performed****on****unity**,**give****the****whole****of****the****class****horned****sheep**.**Boole****showed****that****elective****symbols****of****this****kind****obey****the****same****primary****laws****of****combination****as****algebraical****symbols**,**whence****it****followed****that****they****could****be****added**,**subtracted**,**multiplied****and****even****divided**,**almost****exactly****in****the****same****manner****as****numbers**.**Given****any****propositions****involving****any****number****of****terms**,**Boole****showed****how**,**by****the****purely****symbolic****treatment****of****the****premises**,**to****draw****any****conclusion****logically****contained****in****those****premises**.**Though****Boole****published****little****except****his****mathematical****and****logical****works**,**his****acquaintance****with****general****literature****was****wide****and****deep**.**Dante****was****his****favourite****poet**,**and****he****preferred****the****Paradiso****to****the****Inferno**.**The****personal****character****of****Boole****inspired****all****his****friends****with****the****deepest****esteem**.**As****far****back****as**1 773**Joseph****Louis****Lagrange**,**and****later****Carl****Friedrich****Gauss**,**had****met****with****simple****cases****of****such****functions**,**George****Boole**,**in**1841 (**Camb**.**Thus****what****have****been****called****seminvariants****are****not****all****of****them****invariants****for****the****general****substitution**,**but****are****invariants****for****the****particular****substitution****xl**= X11 +**J-**s12,**X**2 = 112**Again**,**in****plane****geometry**,**the****most****general****equations****of****substitution****which****change****from****old****axes****inclined****at****w****to****new****axes****inclined****at****w**' =13 -**a**,**and****inclined****at****angles****a**, l3**to****the****old****axis****of****x**,**without****change****of****origin**,**are****x-sin**(**wa**)**X**+**sin**(**w**-/3)**Y****sin****w****sin**' _sin**ax****y****sin****w****a****transformation****of****modulus****sin****w**'**sin****w**'**The****theory****of****invariants****originated****in****the****discussion**,**by****George****Boole**,**of****this****system****so****important****in****geometry**.**Boole**,**Laws****of****Thought**(**London**, 1854);**E**.**Little****is****known****of****the****constitution****of****Paros**,**but****inscriptions****seem****to****show****that****it****was****democratic**,**with****a****senate**(**Boole**)**at****the****head****of****affairs**(**Corpus****inscript**.**In****the****Boole****of****Enoch**"**the****four****great****archangels**"**are****Michael**,**Uriel**,**Suriel****or****Raphael**,**and****Gabriel**,**who****is****set****over**"**all****the****powers**"**and****shares****the****work****of****intercession**.