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In the West the numerals we use are known as "Arabic numerals" because it came from the middle east. But in the middle east the same numerals are known as "Indi

In the West the numerals we use are known as "Arabic numerals" because it came from the middle east. But in the middle east the same numerals are known as "Indian numerals" because that's where they got it from. Similarly, algebra came from the middle east where it was called "al-Jabr" [1], but they in turn got it from India [2]. The invention of calculus is traditionally attributed to Isaac Newton and Gottfried Leibniz. But this book [3] says calculus was brought into being in India in the 14th century by a mathematician named Madhava. [1] https://en.wikipedia.org/wiki/Al-Jabr https://en.wikipedia.org/wiki/Al-Jabr [2] https://www.theguardian.com/world/article/2024/sep/01/hidden-story-ancient-india-west-maths-astronomy-historians?CMP=oth_b-aplnews_d-1 https://www.theguardian.com/world/article/2024/sep/01/hidden... [3] https://www.nytimes.com/2024/07/24/books/review/the-secret-lives-of-numbers-kate-kitagawa-timothy-revell.html https://www.nytimes.com/2024/07/24/books/review/the-secret-l...

acdha 2y ago
The Arabic-Indic numerals are especially neat because you can see how they evolved as they spread: https://persianlanguageonline.com/wp-content/uploads/2023/07/The_Brahmi_numeral_system_and_its_descendants-1.png https://persianlanguageonline.com/wp-content/uploads/2023/07... Years ago I worked on a site which was translated into Arabic. Some of the early partners were adamant that we needed to use the Indic numerals everywhere, so I had localized all of our UI, including some JavaScript widgets and worked with a third-party to localize their embed. A few years later, they had a larger conference with a wider swath of the Arabic-fluent world represented and pretty much everyone said we should use what the English-speaking world calls Arabic numerals because most people were more familiar with them than the Indic numeral variants they didn’t use, and computers were making that even more pronounced.
csomar 2y ago
The Arabic numerals are called Arabic because the Europeans got them from North African Arabs. They are different to the Indian numerals.
- srean 2y ago
  > They are different to the Indian numerals. Not in any mathematically significant way, except for the big endian little endian swap. In Indian system the units is specified first, then the 10s then the hundreds and so on. Arabs took the same system but they wrote right to left. That's why we write the numbers the way we do.
Dx5IQ 2y ago
It's difficult to call Madhava's work calculus as we know it. He and his school certainly made huge contributions to analysis of infinite series, but they did not develop that into a unifying framework. It's important to note that no mathematics is done in a vacuum, if Newton/Leibniz "invented" Calculus, it's by building on top of hundreds of years of work done throughout the world.
d13 2y ago
Fibonacci himself, who popularised their use, explicitly mentioned that they were from India. Somehow this was muddied in later secondary sources.
canfakt 2y ago
I encountered this topic a while, back and had a deep look into it, I will be sharing my insights and formed opinion based on the facts that I encountered. @Dx51Q I appreciate your perspective, but I'd like to clarify a few points regarding Madhava's contributions to calculus. While it's true that Madhava and his school may not have created a unifying framework like Newton and Leibniz did, their work laid crucial groundwork for what we now consider calculus. Madhava is credited with developing infinite series for trigonometric functions such as sine and cosine, which are equivalent to the Taylor series we use today. For example, his series for sin(x) and cos(x) predate those discovered in Europe by over 200 years[1][2]. His followers, like Jyeṣṭhadeva, further elaborated on these concepts in texts like the Yuktibhāṣā, providing proofs and demonstrating their applications[3][5]. Moreover, Madhava's methods for approximating pi were remarkably accurate, achieving values correct to 11 decimal places, showcasing his advanced understanding of numerical analysis[2][4]. This indicates that he was indeed engaging with concepts foundational to calculus, such as limits and convergence. Thus, while Madhava's work may not fit neatly into the modern definition of calculus, it represents a significant and sophisticated mathematical tradition that deserves recognition as a precursor to later developments in the field. While we are on this topic, we can stop for a second and ponder on why the ancient Indians needed these mathematical formulation. The answer is astronomy, and thus needing a language/framework to understand the cosmos, i.e. mathematics. Additionally, I wanted to share some interesting insights about the Jesuit transmission of both calculus and the Gregorian calendar from Kerala to Europe. The Jesuit missionaries were not only spreading Christianity through their work, but they were scholars in their own right and could see the value of the advance mathematics they encountered by the Kerala (India) school of mathematics by madhava and the advanced calendar, more accurate than the julian calendar used in Europe at the time. Jesuit missionaries, especially Matteo Ricci, were really fascinated by the advanced mathematical knowledge coming from the Kerala school. They connected with local scholars, like Brahmins and Kshatriyas, to learn about their mathematical concepts, including those found in texts like the Yuktibhāṣā and Tantrasangraha [5]. This collaboration was part of the Jesuits' efforts to understand local cultures and improve their missionary work. It’s fascinating to think that this exchange not only contributed to the Gregorian calendar reform in 1582 but also helped introduce key calculus concepts into European mathematics. As to why this is not common knowledge, it’s partly the British colonial policies that muddied the waters and/or suppressed the source of information. But If one looks at it with time, the evidence is there Citations: [1] https://www.linkedin.com/pulse/madhava-man-who-taught-trigonometry-world-sunila-jha https://www.linkedin.com/pulse/madhava-man-who-taught-trigon... [2] https://en.wikipedia.org/wiki/Madhava_of_Sangamagrama https://en.wikipedia.org/wiki/Madhava_of_Sangamagrama [3] https://mathshistory.st-andrews.ac.uk/Biographies/Madhava/ https://mathshistory.st-andrews.ac.uk/Biographies/Madhava/ [4] https://en.wikipedia.org/wiki/Madhava_series https://en.wikipedia.org/wiki/Madhava_series [5] https://indicmandala.com/the-kerala-school-european-mathematics/ https://indicmandala.com/the-kerala-school-european-mathemat...

acdha 2y ago

The Arabic-Indic numerals are especially neat because you can see how they evolved as they spread: https://persianlanguageonline.com/wp-content/uploads/2023/07/The_Brahmi_numeral_system_and_its_descendants-1.png https://persianlanguageonline.com/wp-content/uploads/2023/07... Years ago I worked on a site which was translated into Arabic. Some of the early partners were adamant that we needed to use the Indic numerals everywhere, so I had localized all of our UI, including some JavaScript widgets and worked with a third-party to localize their embed. A few years later, they had a larger conference with a wider swath of the Arabic-fluent world represented and pretty much everyone said we should use what the English-speaking world calls Arabic numerals because most people were more familiar with them than the Indic numeral variants they didn’t use, and computers were making that even more pronounced.

csomar 2y ago

The Arabic numerals are called Arabic because the Europeans got them from North African Arabs. They are different to the Indian numerals.

srean 2y ago
> They are different to the Indian numerals. Not in any mathematically significant way, except for the big endian little endian swap. In Indian system the units is specified first, then the 10s then the hundreds and so on. Arabs took the same system but they wrote right to left. That's why we write the numbers the way we do.

Dx5IQ 2y ago

It's difficult to call Madhava's work calculus as we know it. He and his school certainly made huge contributions to analysis of infinite series, but they did not develop that into a unifying framework. It's important to note that no mathematics is done in a vacuum, if Newton/Leibniz "invented" Calculus, it's by building on top of hundreds of years of work done throughout the world.

d13 2y ago

Fibonacci himself, who popularised their use, explicitly mentioned that they were from India. Somehow this was muddied in later secondary sources.

canfakt 2y ago

I encountered this topic a while, back and had a deep look into it, I will be sharing my insights and formed opinion based on the facts that I encountered. @Dx51Q I appreciate your perspective, but I'd like to clarify a few points regarding Madhava's contributions to calculus. While it's true that Madhava and his school may not have created a unifying framework like Newton and Leibniz did, their work laid crucial groundwork for what we now consider calculus. Madhava is credited with developing infinite series for trigonometric functions such as sine and cosine, which are equivalent to the Taylor series we use today. For example, his series for sin(x) and cos(x) predate those discovered in Europe by over 200 years[1][2]. His followers, like Jyeṣṭhadeva, further elaborated on these concepts in texts like the Yuktibhāṣā, providing proofs and demonstrating their applications[3][5]. Moreover, Madhava's methods for approximating pi were remarkably accurate, achieving values correct to 11 decimal places, showcasing his advanced understanding of numerical analysis[2][4]. This indicates that he was indeed engaging with concepts foundational to calculus, such as limits and convergence. Thus, while Madhava's work may not fit neatly into the modern definition of calculus, it represents a significant and sophisticated mathematical tradition that deserves recognition as a precursor to later developments in the field. While we are on this topic, we can stop for a second and ponder on why the ancient Indians needed these mathematical formulation. The answer is astronomy, and thus needing a language/framework to understand the cosmos, i.e. mathematics. Additionally, I wanted to share some interesting insights about the Jesuit transmission of both calculus and the Gregorian calendar from Kerala to Europe. The Jesuit missionaries were not only spreading Christianity through their work, but they were scholars in their own right and could see the value of the advance mathematics they encountered by the Kerala (India) school of mathematics by madhava and the advanced calendar, more accurate than the julian calendar used in Europe at the time. Jesuit missionaries, especially Matteo Ricci, were really fascinated by the advanced mathematical knowledge coming from the Kerala school. They connected with local scholars, like Brahmins and Kshatriyas, to learn about their mathematical concepts, including those found in texts like the Yuktibhāṣā and Tantrasangraha [5]. This collaboration was part of the Jesuits' efforts to understand local cultures and improve their missionary work. It’s fascinating to think that this exchange not only contributed to the Gregorian calendar reform in 1582 but also helped introduce key calculus concepts into European mathematics. As to why this is not common knowledge, it’s partly the British colonial policies that muddied the waters and/or suppressed the source of information. But If one looks at it with time, the evidence is there Citations: [1] https://www.linkedin.com/pulse/madhava-man-who-taught-trigonometry-world-sunila-jha https://www.linkedin.com/pulse/madhava-man-who-taught-trigon... [2] https://en.wikipedia.org/wiki/Madhava_of_Sangamagrama https://en.wikipedia.org/wiki/Madhava_of_Sangamagrama [3] https://mathshistory.st-andrews.ac.uk/Biographies/Madhava/ https://mathshistory.st-andrews.ac.uk/Biographies/Madhava/ [4] https://en.wikipedia.org/wiki/Madhava_series https://en.wikipedia.org/wiki/Madhava_series [5] https://indicmandala.com/the-kerala-school-european-mathematics/ https://indicmandala.com/the-kerala-school-european-mathemat...