History Made Of

21st century [ edit ] In 2000, the  Clay Mathematics Institute  announced the seven  Millennium Prize Problems , and in 2003 the  Poincaré conjecture  was solved by  Grigori Perelman  (who declined to accept an award on this point). Most mathematical journals now have online versions as well as print versions, and many online-only journals are launched. There is an increasing drive towards  open access publishing , first popularized by the  arXiv . Future of mathematics [ edit ] Main article:  Future of mathematics There are many observable trends in mathematics, the most notable being that the subject is growing ever larger, computers are ever more important and powerful, the application of mathematics to bioinformatics is rapidly expanding, the volume of data to be analyzed being produced by science and industry, facilitated by computers, is explosively expanding.

Modern mathematics [ edit ] 19th century Throughout the 19th century mathematics became increasingly abstract. In the 19th century lived  Carl Friedrich Gauss  (1777–1855). Leaving aside his many contributions to science, in  pure mathematics  he did revolutionary work on  functions  of  complex variables , in  geometry , and on the convergence of  series . He gave the first satisfactory proofs of the  fundamental theorem of algebra  and of the  quadratic reciprocity law . Behavior of lines with a common perpendicular in each of the three types of geometry This century saw the development of the two forms of  non-Euclidean geometry , where the  parallel postulate  of  Euclidean geometry  no longer holds. The Russian mathematician  Nikolai Ivanovich Lobachevsky  and his rival, the Hungarian mathematician  János Bolyai , independently defined and studied  hyperbolic geometry , where uniqueness of parallels no longer holds. In this geometry the sum of angles in a tr

Renaissance mathematics [ edit ] Portrait of Luca Pacioli , a painting traditionally attributed to  Jacopo de' Barbari , 1495, ( Museo di Capodimonte ). During the  Renaissance , the development of mathematics and of  accounting  were intertwined. [127]  While there is no direct relationship between algebra and accounting, the teaching of the subjects and the books published often intended for the children of merchants who were sent to reckoning schools (in  Flanders  and  Germany ) or  abacus schools  (known as  abbaco  in Italy), where they learned the skills useful for trade and commerce. There is probably no need for algebra in performing  bookkeeping  operations, but for complex bartering operations or the calculation of compound interest , a basic knowledge of arithmetic was mandatory and knowledge of algebra was very useful. Luca Pacioli 's  "Summa de Arithmetica, Geometria, Proportioni et Proportionalità"  (Italian: "Review of  Arithmetic ,