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【繁體】數學大歷史

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KingStone

【繁體】數學大歷史

Name: 【繁體】數學大歷史
Brand: KingStone
SKU: 3136021091
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「在我看來，數學與科學、人文的各個分支一樣，都是人類大腦進化和智力發展進程的反映。它們在特定的歷史時期必然相互影響，並呈現出某種相通的特性。在按時間順序講述不同地域文明的同時，我們先後探討了數學與各式各樣文明之間的關係。例如，埃及和巴比倫的數學來源於人們生存的需要，希臘數學與哲學密切相關，中國數學的活力來自曆法改革，印度數學的源泉始於宗教，而波斯或阿拉伯的數學與天文學互不分離。」～蔡天新

數學源於人類生存的需要，觸角幾乎遍及人類歷史、社會和生命的每一個瞬間。

數學也是人類對生活和世界的觀察，以及對現實事物和問題的思考。

本書試圖跨越不同的地域和種族，依次探討數學與不同文明之間的關係，除了各有側重的古文明，文藝復興時期的藝術推動了幾何學的發展，十七世紀微積分的出現解決了一系列工業革命遇到的問題；十八世紀法國大革命的數學涉及力學、軍事和工程技術；十九世紀前半葉，數學和詩歌幾乎同時從古典進入現代；進入二十世紀以後，抽象化又成為數學和人文學科的共同性質。

從人類文明的角度來介紹數學是如此充滿新意與樂趣，數學是毫無疑問的人類智慧結晶，瞭解數學的歷史，就能瞭解人類發展的歷史！

繁體版前言
前言

第一章　中東，或數學的起源
‧數學的起源
計數的開始
數基和進制
阿拉伯數系
形而幾何學
‧尼羅河文明
奇特的地形
萊茵德紙草書
埃及分數
‧在河流之間
巴比倫尼亞
泥板書上的根
普林頓322號
‧結語

第二章　希臘的那些先哲們
‧數學家的誕生
希臘人的出場
論證的開端
畢達哥拉斯
‧柏拉圖學院
芝諾的烏龜
柏拉圖學院
亞里斯多德
‧亞歷山大學派
《幾何原本》
阿基米德
其他數學家
‧結語

第三章　中世紀的中國
‧引子
先秦時代
《周髀算經》
《九章算術》
‧從割圓術到孫子定理
劉徽的割圓術
祖氏父子
孫子定理
‧宋元六大家
沈括和賈憲
楊輝和秦九韶
李冶和朱世傑
‧結語

第四章　印度人和波斯人
‧從印度河到恆河
雅利安人的宗教
《繩法經》和佛經
零和印度數字
‧從北印度到南印度
阿耶波多
婆羅摩笈多
馬哈威拉
婆什迦羅
‧神賜的土地
阿拉伯帝國
巴格達的智慧宮
花拉子密的《代數學》
‧波斯的智者
伊斯法罕的奧瑪珈音
大不里士的納西爾丁
撒馬爾罕的阿爾•卡西
‧結語

第五章　從文藝復興到微積分的誕生
‧歐洲的文藝復興
中世紀的歐洲
斐波那契的兔子
阿伯提的透視學
達文西和丟勒
‧微積分的創立
近代數學的興起
解析幾何的誕生
微積分學的先驅
牛頓和萊布尼茲
‧結語

第六章　分析時代與法國大革命
‧分析時代
業餘數學家之王
微積分學的發展
微積分學的影響
白努利家族
‧法國大革命
拿破崙‧波拿巴
高聳的金字塔
法蘭西的牛頓
皇帝的密友
‧結語

第七章　現代數學與現代藝術
‧代數學的新生
分析的嚴格化
阿貝爾和伽羅瓦
哈密頓的四元數
‧幾何學的變革
幾何學的家醜
非歐幾何學的誕生
黎曼幾何學
‧藝術的新紀元
愛倫‧坡
波特萊爾
從模仿到機智
‧結語

第八章　抽象化：二十世紀以來
‧走向抽象化
集合論和公理化
數學的抽象化
繪畫中的抽象
‧數學的應用
理論物理學
生物學和經濟學
電腦和混沌理論
‧數學與邏輯學
羅素的悖論
維根斯坦
哥德爾定理
‧結語

附錄
‧常用數學符號來歷一覽
‧數學年表
‧參考文獻
‧中外對照
‧索引

各界推薦／推薦序

專文推薦--
賴以威（「數感實驗室」共同創辦人、數學作家）　

具名推薦—
于靖（中央研究院院士、國立臺灣大學數學系教授）
林福來（國立臺灣師範大學數學系名譽教授）

<從小樹苗到通天神木>
文／賴以威　

我第一次「真正開始瞭解數學的本質」，是前幾年教小學生的時候。對方是一位認為數學沒用，不喜歡數學的小朋友。我擺了兩堆蘋果，一堆有三顆，另一堆四顆，請他數完後，把兩堆蘋果合在一起，要他再數一次。

「不用數啦，我知道是七個。」
「為什麼是七個？」
小朋友露出數學老師常有的那種無奈表情，老成地嘆口氣回答：「3+4=7」。
「你覺得數學沒用，但你這不是在用數學了嗎？你覺得數學很討厭，但這時候，數學可是幫了你很大的忙，讓你省去了『數』的功夫。」

我不知道小朋友有沒有完全理解我想表達的，可至少當下的我，真切地感受到加法的意義與重要性。我希望透過這個例子，小朋友能發現，數學不僅僅是抽象的智力鍛鍊、人類智慧的結晶，更是人類從生活中觀察，進而提煉出來的工具，幫助我們過得更便利，完成更多困難的任務。

我有時候會想，許多人不喜歡數學，或許不是懂得太少，而是懂得太多。他們認為必須要有個未知數x，最好搭配一些看不懂的希臘符號，旁邊再擺上個不相關的座標軸，才算得上是數學。「使用加法就可以少數很多次。」對他們來說，不太算是數學。

但其實，這不僅僅是數學，還是數學的起點。

數學的誕生或許要晚一點，是在人類從「二顆雞蛋加三顆雞蛋等於五顆雞蛋」、「二枚箭矢加三枚箭矢等於五枚箭矢」之中抽象出「2 + 3 = 5」時。

你可以想像，遠古的祖先只會數物品，後來「發現一對雛雞和兩天之間有某種共同的東西（數字2）」的抽象化數數。

領悟加法的那一剎那，數學在人類的心智中開始發芽。

經過幾千年演進，數學成長茁壯為通天神木，枝幹深入到各行各業的專業技能，躲在日常生活中無法一眼就看出來的地方：手機裡的晶片，街上紅綠燈的控制，電玩遊戲各個角色的參數設定。最上面的枝枒是數學家展現智力與想像力之處，它們不斷生長，來到目前生活無法觸及的地方，可能得再過幾十年、幾百年，才會有某項科技運用得上這些數學知識。

《數學大歷史》中，蔡天新教授旁徵博引，將文字化為紀錄片，記載了數學從小樹苗一路茁壯的過程。其中我特別喜歡第三章〈中世紀的中國〉，從名家惠施「一尺之棰，日取其半，萬世不竭」的無窮難題開始，劉徽、祖沖之父子、李淳風、沈括、到宋元四大家楊輝、秦九韶、李冶和朱世杰，蔡教授不僅介紹了中國數學的發展，比較中西方的差異，還進一步從社會文化的結構中找尋原因，以中國學者的身分探討「為什麼」中國數學的發展和西方如此不同，這是西方數學史書比較難深入的。蔡教授本身「允文允理」的跨領域背景更讓本書不僅止於一本數學史書，還涉及到藝術、社會文化領域（另一個例子是在書中登場的愛倫•坡，但他不是因為《金甲蟲》裡的密碼學，純粹是以文學家的身分被介紹）。

你絕對能從這本書裡學到更多的數學發展歷史；但你同樣可以抱著輕鬆的心情閱讀，有環繞著數學的故事，有不同時期除了數學外的文化藝術史點綴，還有更多有趣的數學家生平軼事，例如大數學家拉普拉斯擔任過拿破崙的面試官，拿破崙又如何在帶領法國大軍攻城掠地的同時，領導法國數學家奠定一整個時代的數學發展。

請隨意往後翻吧，不論從哪一頁開始讀起，你都可以感受到閱讀的樂趣。

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