誰創造數學

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數學(Mathematics)是研究數量、結構、變化以及空間模型等概念的一門學科。透過抽象化和邏輯推理的使用，由計數、計算、量度和對物體形狀及運動的觀察中產生。數學家們拓展這些概念，為了公式化新的猜想以及從合適選定的公理及定義中建立起嚴謹推導出的真理。

其基本概念的精煉早在古埃及、美索不達米亞及古印度內的古代數學文本內便可觀見。從那時開始，其發展便持續不斷地有小幅的進展，直至16世紀的文藝復興時期，因著和新科學發現相作用而生成的數學革新導致了知識的加速，直至今日。

創立於二十世紀三十年代的法國的布爾巴基學派認為：數學，至少純粹數學，是研究抽象結構的理論。結構，就是以初始概念和公理出發的演繹系統。布學派認為，有三種基本的抽象結構：代數結構（群，環，域……），序結構（偏序，全序……），拓撲結構（鄰域，極限，連通性，維數……）。

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數學(mathematics, 希臘語：μαθηματικά)這一詞在西方源自於古希臘語的μάθημα (máthēma)，其有學習、學問、科學，以及另外還有個較狹意且技術性的意義－「數學研究」，即使在其語源內。其形容詞μαθηματικός (mathēmatikós)，意義為和學習有關的或用功的，亦會被用來指數學的。其在英語中表面上的複數形式，及在法語中的表面複數形式les mathématiques，可溯至拉丁文的中性複數mathematica，由西塞羅譯自希臘文複數τα μαθηματικά (ta mathēmatiká)，此一希臘語被亞里士多德拿來指「萬物皆數」的概念。

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數學，起源於人類早期的生產活動，為中國古代六藝之一，亦被古希臘學者視為哲學之起點。數學的希臘語μαθηματικός (mathematikós)意思是「學問的基礎」，源於μάθημα (máthema)（「科學，知識，學問」）。

數學的演進大約可以看成是抽象化的持續發展，或是題材的延展。第一個被抽象化的概念大概是數字，其對兩個蘋果及兩個橘子之間有某樣相同事物的認知是人類思想的一大突破。 除了認知到如何去數實際物質的數量，史前的人類亦了解瞭如何去數抽象物質的數量，如時間－日、季節和年。算術(加減乘除)
也自然而然地產生了。古代的石碑亦證實了當時已有幾何的知識。

http://zh.wikipedia.org/w/index.php?title=%E6%95%B8%E5%AD%B8&variant=zh-tw

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HISTORICAL BACKGROUND

The evolution of mathematics might be seen as an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction was probably that of numbers. The realization that two apples and two oranges have something in common was a breakthrough in human thought. In addition to recognizing how to count physical objects, prehistoric peoples also recognized how to count abstract quantities, like time — days, seasons, years. Arithmetic (addition, subtraction, multiplication and division), naturally followed. Monolithic monuments testify to knowledge of geometry.

Further steps need writing or some other system for recording numbers such as tallies or the knotted strings called quipu used by the Inca empire to store numerical data. Numeral systems have been many and diverse.

From the beginnings of recorded history, the major disciplines within mathematics arose out of the need to do calculations relating to taxation and commerce, to understand the relationships among numbers, to measure land, and to predict astronomical events. These needs can be roughly related to the broad subdivision of mathematics, into the studies of quantity, structure, space, and change.

Mathematics has since been greatly extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries have been made throughout history and continue to be made today. According to Mikhail B. Sevryuk, in the January 2006 issue of the Bulletin of the American Mathematical Society, "The number of papers and books included in the Mathematical Reviews database since 1940 (the first year of operation of MR) is now more than 1.9 million, and more than 75 thousand items are added to the database each year. The overwhelming majority of works in this ocean contain new mathematical theorems and their proofs."

http://en.wikipedia.org/wiki/Mathematics




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數學起源於人類早期的生產活動，為古中國六藝之一，亦被古希臘學者視為哲學之起點。數學的希臘語μαθηματικός (mathematikós)意思是「爱好學問」，源於μάθημα (máthema)（「科學，知識，學問」）。數學最早是研究量、结构、变化以及空间模型的学科。在现代，数学又是利用逻辑形式研究现实世界的空间形式和数量关系的学科。