印度数学

古代和中世纪的印度数学作品，都是用梵语写成，通常由称作契经的一部分组成，在其中为了帮助学生记忆，用极少的字词陈述了一些规则和问题。在这之后是第二部分，包括一篇散文评论（有时是来自不同学者的多篇评论），其更详细地解释了问题并为解决方案提供了更多的理由。在散文部分，形式（和记忆）比起其涉及的思想来说并不是很重要。在公元前500年之前，所有的数学作品都是由口头传播，之后同时以口头和手稿的形式传播。现存的印度次大陆上最古老的数学文献是写在桦树皮上的巴赫沙利手稿，它在1881年于巴赫沙利村被发现，靠近白沙瓦（现位于巴基斯坦）并可能来自公元7世纪。

印度数学的后期里程碑是公元15世纪喀拉拉邦学派的数学家对三角函数（正弦，余弦和反正切）的级数展开的发展。 他们的卓越工作，在欧洲发明微积分之前两个世纪完成，提供了现在被称为幂级数的第一个例子（除了等比数列） 。 然而，他们没有制定出系统的微分和积分理论，也没有任何直接证据证明他们的结果是在喀拉拉邦以外传播的。

在摩亨佐-達羅、哈拉帕與其他幾個印度河流域文明的遺址中，都發現了使用"實用數學"的證據。他們使用4:2:1的比例製造磚頭，此作法被認為有利於磚頭結構的穩定性。他們使用了標準化的砝碼，以比例:1/20, 1/10, 1/5, 1/2, 1, 2, 5, 10, 20, 50, 100, 200與500進行製作，其中的一單位的重量約等於28克。他們大量生產有規則形狀的砝碼，有六面體、桶形、錐形與柱形，從而展示出對於基本幾何的理解。

印度文明的居民曾試圖對於長度量測進行高精準度的標準化。他們設計出了摩亨佐達羅尺，尺上的單位長度約為3.4公分，並且再分割成十等分。古代摩亨若達羅的磚頭尺寸通常是此單位長度的整數倍。

在洛沙爾(Lothal,2200 BCE)與卓拉維拉(Dholavira)發現的貝殼製中空柱狀物體上面有8個裂縫，被認為可用來製作羅盤，證明了能在平面上測量角度的能力，並可藉此確定星星的位置進行導航。

吠陀時期的宗教文本提供了使用大數的證據。在《夜柔吠陀》（公元前1200-900年）文本中，包含的數字高達10¹²。

耆那學者認為世界是永恆的，只有形式上的變化，與婆羅門教創造萬物的理論不同。耆那教由筏陀摩那在前6世紀創立，但耆那數學著作大部分是在前6世紀後撰寫的。耆那學者將數字分為三類。

耆那重要數學家包括賢臂（英语：Bhadrabahu）(Bhadrabahu，卒於公元前298年），他是兩部天文著作的作者。

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• Science and Mathematics in India（页面存档备份，存于互联网档案馆）
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• Mathematics in ancient India by R. Sridharan（页面存档备份，存于互联网档案馆）
• Combinatorial methods in ancient India （页面存档备份，存于互联网档案馆）
• Mathematics before S. Ramanujan （页面存档备份，存于互联网档案馆）