{"id":2758,"date":"2022-07-02T08:52:26","date_gmt":"2022-07-02T12:52:26","guid":{"rendered":"https:\/\/josmfs.net\/?page_id=2758"},"modified":"2024-09-16T16:21:46","modified_gmt":"2024-09-16T20:21:46","slug":"symbolic-algebra-timelines","status":"publish","type":"page","link":"https:\/\/josmfs.net\/wordpress\/symbolic-algebra-timelines\/","title":{"rendered":"Symbolic Algebra Timelines"},"content":{"rendered":"

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As I am sure is common with most mathematicians, I had become interested in the history of the development of mathematical symbols, first for numbers (numerals) and then for algebra (symbolic algebra).\u00a0 Joseph Mazur\u2019s book Enlightening Symbols<\/em> provided an excellent history of this evolution.\u00a0 His focus on the development and significance of symbolic algebra in the Renaissance was especially illuminating.\u00a0 I also augmented Mazur\u2019s information with details from Albrecht Heeffer\u2019s work.<\/p>\n

Such a subject cries out for a timeline to appreciate the order and timing of discoveries, which Mazur provided, concentrating on the Renaissance.\u00a0 I decided to both simplify Mazur\u2019s version and expand it to cover the evolution of numbers and their notation, as well as to set the whole enterprise in the context of historical periods.\u00a0 I relied further on Kline\u2019s 1972 history of math.\u00a0 My designation of historical periods represents the Western bias of my formal education, but I can\u2019t think of a viable alternative at this late stage.\u00a0 The boundaries of these periods are fuzzy, or one might even say fractal in that they often varied geographically.\u00a0 Furthermore the periods are meant to be chunky for ease of recall and to avoid the controversies of multiple experts.<\/p>\n

At the heart of such a presentation is the question of sources and evidence, as well as who influenced whom versus the independence of discoveries.\u00a0 This is a massive scholarly tangle beset on all sides by controversy.\u00a0 Cultural pride and prejudice often cloud objective assessment of the frequently vague and conflicting evidence.\u00a0 For example, for years Western bias assumed that all mathematics basically derived from the Greeks, even if it detoured through the Arabs.\u00a0 There certainly was cross-fertilization between West and East, especially with astronomy, but we now know that pivotal discoveries came from the East, such as the number<\/em> zero and negative numbers.\u00a0 (For my crude purposes I consider the \u201cWest\u201d to refer mainly to Latin, largely Roman Catholic, western Europe, and the \u201cEast\u201d to refer mainly to Greek, Byzantine, Orthodox Christian eastern Europe, followed by the multi-religious Middle East (Syria, Iran\/Persia), South Asia (India), and East Asia (China).)<\/p>\n

Hopefully my timeline reveals some important historical features.<\/p>\n

For more explanation see Symbolic Algebra Timelines<\/a><\/p>\n

Here is another timeline that provides more detail at a critical stage in history.<\/p>\n

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(Update 9\/9\/2024<\/strong>) How Ancient India Shaped The West<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

As I am sure is common with most mathematicians, I had become interested in the history of the development of mathematical symbols, first for numbers (numerals) and then for algebra (symbolic algebra).\u00a0 Joseph Mazur\u2019s book Enlightening Symbols provided an excellent history of this evolution.\u00a0 His focus on the development and significance of symbolic algebra in […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-2758","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/pages\/2758","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=2758"}],"version-history":[{"count":20,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/pages\/2758\/revisions"}],"predecessor-version":[{"id":4098,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/pages\/2758\/revisions\/4098"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2758"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}