Algebra: Difference between revisions - Wikipedia

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The earliest printed book on algebra was composed by Lucas de Burgo, a minoritet friar. It was first printed in 1494, and again in 1523. The title is '<nowiki/>''Summa de Arithmetica, Geometria, Proportion, et Proportionality''' .<ref>{{Cite book |last=Black |first=Adam, Charles |title=Encyclopædia Britannica |date=1875 |publisher=Adam, Charles Black |year=1875 |edition=Ninth Edition, Vol. 1 |location=Edinburgh |pages=512 |quote=The earliest printed book on algebra was composed by Lucas de Burgo, a minoritet friar. It was first printed in 1494, and again in 1523. The title is Summa de Arithmetica, Geometria, Proportion, et Proportionality.}}</ref> The Italian mathematician [[Fibonacci]] brought al-Khwarizmi's ideas and techniques to Europe in books like his ''[[Liber Abaci]]''.<ref>{{multiref | {{harvnb|Waerden|2013|pp=32–35}} | {{harvnb|Tanton|2005|p=10}} | {{harvnb|Kvasz|2006|p=293}} }}</ref> In 1545, the Italian polymath [[Gerolamo Cardano]] published his book ''[[Ars Magna (Cardano book)|Ars Magna]]'', which covered many topics in algebra, discussed [[imaginary numbers]], and was the first to present general methods for solving [[Cubic equation|cubic]] and [[Quartic equation|quartic equations]].<ref>{{multiref | {{harvnb|Tanton|2005|p=10}} | {{harvnb|Kvasz|2006|p=293}} | {{harvnb|Corry|2024|loc=§ Cardano and the Solving of Cubic and Quartic Equations}} | {{harvnb|Miyake|2002|p=[https://books.google.com/books?id=G0P2BwAAQBAJ&pg=PA268 268]}} }}</ref> In the 16th and 17th centuries, the French mathematicians [[François Viète]] and [[René Descartes]] introduced letters and symbols to denote variables and operations, making it possible to express equations in an abstract and concise manner. Their predecessors had relied on verbal descriptions of problems and solutions.<ref>{{multiref | {{harvnb|Tanton|2005|p=10}} | {{harvnb|Kvasz|2006|pp=291–292, 297–298, 302}} | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ Historical Survey}} | {{harvnb|Corry|2024|loc=§ Viète and the Formal Equation, § Analytic Geometry}} }}</ref> Some historians see this development as a key turning point in the history of algebra and consider what came before it as the prehistory of algebra because it lacked the abstract nature based on symbolic manipulation.<ref>{{multiref | {{harvnb|Hazewinkel|1994|p=[https://books.google.com/books?id=PE1a-EIG22kC&pg=PA73 73]}} | {{harvnb|Merzlyakov|Shirshov|2020|loc=§ Historical Survey}} }}</ref>

[[File:Garrett Birkhoff.jpeg|thumb|alt=Photo of Garrett Birkhoff|[[Garrett Birkhoff]] developed many of the foundational concepts of universal algebra.|left|upright=0.8]]