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William Dalrymple is one of the finest historians and authors who has previously brought to life the story of East India Company and how it led to British India.
In this book, he focuses on, among other things, how Buddhism spread all over.
It's a fascinating topic. He also has a very successful podcast [1][2] -- with his co-host Anita Anand -- The Empire Podcast, which chronicles the rise and fall of empires. Highly educational, not to mention entertaining.
Recommended!!
[1] Empire Podcast - Apple - https://podcasts.apple.com/gb/podcast/empire/id1639561921 [2] On Spotify - https://open.spotify.com/show/0sBh58hSTReUQiK4axYUVx?si=45f5...
I second the podcast recommendation. Empire pod has been truly worth every bit of the time. I am currently on the episode about History of coffee - ethiopia, ottoman turks etc.
I'm guessing that Anita Anand is not the one that was the Canadian Minister of Defense...
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
[2] https://www.theguardian.com/world/article/2024/sep/01/hidden...
[3] https://www.nytimes.com/2024/07/24/books/review/the-secret-l...
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...
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.
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.
Fibonacci himself, who popularised their use, explicitly mentioned that they were from India. Somehow this was muddied in later secondary sources.
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-trigon... [2] https://en.wikipedia.org/wiki/Madhava_of_Sangamagrama [3] https://mathshistory.st-andrews.ac.uk/Biographies/Madhava/ [4] https://en.wikipedia.org/wiki/Madhava_series [5] https://indicmandala.com/the-kerala-school-european-mathemat...
The Arabic numerals are called Arabic because the Europeans got them from North African Arabs. They are different to the Indian numerals.
Anyone interested in Indian history and its interaction with the world should check out the Odd Compass channel on YouTube (https://www.youtube.com/@OddCompass) - it's really well done, entertaining and just makes you appreciate the world a little more - especially how interconnected we've all been, especially through trade.
I love this channel! The videos are well made narratively while still preseving the facts and citing sources. Almost the ideal combo of being academic and entertaining
> The great mathematician Aryabhata (476-550), in his masterwork composed when he was only 23, covers square and cube roots, the properties of circles and triangles, algebra, quadratic equations and sines, and contains a decent approximation of the value of pi at 3.1416.
TIL...
The man was certified genius, here are some more of his contributions to the world
- Invention of Zero - Decimal Place-Value System - Astronomical Calculations - Understanding of Negative Numbers
here is a good YouTube video on this subject https://www.youtube.com/watch?v=jgjcy04PDRM
While we praise Aryabhatta man, i would like to shed some lights on Madhava of Sangamagrama c. 1340 - c. 1425 CE from India who less well known
Key Contributions
Infinite Series and Trigonometry Discovered power series expansions for trigonometric functions: Madhava's Sine Series: Infinite series representation for the sine function. Madhava's Cosine Series: Infinite series representation for the cosine function. Madhava–Gregory Series: Series for the arctangent function, predating James Gregory by over 200 years.
Calculus and Mathematical Analysis Laid early foundations of calculus through: 200 years before Newton or leibniz Methods of term-by-term integration and iterative techniques for solving transcendental equations. Concepts related to the area under curves, similar to integral calculus. Introduction of convergence tests for infinite series. Creation of trigonometric tables with accurate sine and cosine values.
The Jesuit missionaries in India played a crucial role in the transmission of advanced Indian mathematical and astronomical knowledge to Europe by learning local languages, collaborating with local scholars, and documenting key works, thereby significantly influencing the development of mathematics in the West.
The same kind of math found on Babylonian clay tablets from 2,000 years earlier then?
https://en.wikipedia.org/wiki/Babylonian_mathematics
Which suggests a long oral and|or easily destroyed "document" tradition of teachings being passed down which came to Aryabhata who compiled such things in a manner that survived.
>contains a decent approximation of the value of pi at 3.1416.
I read this somewhere earlier, in some article about the history of mathematics, maybe Indian, Chinese, or both:
Take the number 113355 (easy to remember). Split it down the middle to get 113 and 355. Divide the latter by the former. E.g. in the Python shell:
> print (355/113)
Result:
3.1415929203539825
which is a slightly closer approximation to pi than 3.1416.
Did not expect to see this here. But I have been looking forward to this book for a while. I’m a big fan of William Darlymple. The Anarchy is my favorite of his.
I picked it up from the title alone because I was on a medieval history kick and I unreasonably expected it to be about... "The Anarchy"... you know, the period of history that actually goes by that name... but no. I was surprised and disappointed to find it was about The East India Company which I didn't have much of a hankering after. I still feel cheated!
I’m reading this right now, and it’s excellent. Some amazing stories in there, like that of Wu Zetian, the real life Mother of Dragons:
Wow reading the comments here, there is so much in terms of invention and contribution that I wasn’t taught (in American schools). Given the importance of some of these contributions, I feel a bit shocked at how much is left out of our education in America (and I assume Europe) about what other cultures have provided. India in particular feels like a blind spot - they’re the largest country by population but also conspicuously missing. All you hear about is Gandhi, and even that is not covered well (in terms of the politics of colonization or the partition of India). It feels to me like it is purposeful - how else do you explain skipping out on all these math inventions that are critical to the modern world?
Many things are not taught in school, because basic education is short, and a lot of it happens before people's cognitive abilities have fully developed. The average kid probably spends about a year learning about society and culture, and much of it must be devoted to topics that are relevant to daily life in their own society.
Back in Finland some decades ago, there was pretty decent coverage of India in three topics: world religions and the history of religion; European explorers, colonialism, and imperialism; and "modern" history with Gandhi, Nehru, the partition, and the wars. There were also some passing mentions in other topics. Overall, we probably spent more time on Indian history than American history.
The West hardly knows anything "true" of India; almost everybody looks at it only through a narrow perspective and thus are "incorrect".
The History of India is a multi-branched tree with the main branches being; a) Oral Tradition b) Linguistic Tradition c) Philosophical/Religious Tradition d) Literature/Poetry e) Mythologies f) Historical writings g) Writings by other cultures/civilizations h) Archeology. All of them have to be studied to get an idea of what India was/is.
1) A good book to start with is A.L.Basham's The Wonder That Was India: A Survey of the Culture of the Indian Sub-Continent Before the Coming of the Muslims.
The Book: https://archive.org/details/TheWonderThatWasIndiaByALBasham_...
The Author : https://en.wikipedia.org/wiki/Arthur_Llewellyn_Basham
2) For a modern idiosyncratic and funny take, see Sam Miller's book A Strange Kind of Paradise: India through Foreign Eyes.
Not just that! For many hundreds of years there were over 250 ships a year trading between India and Rome, and tariffs on that trade alone accounted for 25% of the Roman Empire’s tax revenue. Among many other things, India fed the demand for transparent clothing, which was all the rage in the Roman Empire during that period.
I’ve been fascinated with Indian history (mostly for selfish reasons to understand my lineage). My oversimplified summary has been,
India has had 3 major golden ages in its history.
The earliest was during the Mauryan Period. This is the age Dalrymple is talking about, the time of Aryabhatta, the popularization of Buddhism, arguably the time when most of the Indian epics were written (dating them has become notoriously political to the point that discerning the truth is hard now). This is the age Indian nationalists stress on, and the left wing tries to ignore. This age declines because the empire got too big, lost control and slowly disintegrated.
The second age was during the Islamic golden age for India which the right tries to ignore and left stress on. My general sense is that there was a golden age of architecture, poetry and arts and probably not so much in Science. The Taj Mahal for instance was built during this time. This age declined mostly due to wars, the Mughal rulers were never successful in fully unifying India, even to the extent the Mauryans did. They fought consistent wars against pockets of resistance in the South, and towards the end began losing these wildly expensive wars (leading to a brief reign by Shivaji)
The third golden age which no one wants to admit (left or right) is the British Golden age. There really was a renaissance in Indian thought in arts, science during British rule. This was when Indian history was “rediscovered”, first by British orientalists and then by mostly Indian Bengalis. CV Raman won the Nobel prize in science, Tagore won the Nobel prize in literature, Ramanujan etc, the names are numerous. The British rule also was the largest and most stable unification of India till the modern times. After 1850s there were almost no pockets of military resistance against the British rule. The British age declined with WW1 and WW2, and ended with Indian independence.
Post independence was not a smooth going party. If you came to India during 1980s, you could argue independence had been a disaster with everything getting worse post independence. But since 1990s economic liberalization India has a new ish golden age with unique characteristics. Who knows how long this will continue and when it will inevitably end
I don't think British India can be described as a Golden Age, when it was arguably the biggest transfer of wealth in history. When the British started colonizing India, its share of the World GDP was approximately between 1/5 and 1/4. So it was a major player. When they left, GDP share was a mere 4/100. Under British rule, India experienced massive de-industrialization. For example, the UK disassembled most of the handloom industry.
You forgot the Gupta Empire from mid 3rd century CE to mid 6th century CE. Aryabhatta - the famous mathematician was a product of this age.
The empire unfortunately promulgated the extensive spread of Buddhism, became pacifist and passive and was easily invaded and looted by invaders from Central Asia. The late Gupta empire's army was a joke - only existed on paper.
The fall of Indian civilization from the 7th century on-wards is very painful to read. No military of any note - Islamic invaders would regularly invade and loot and burn great temples and libraries every few years with little to no trouble. Foundational records and knowledge of ancient India was utterly annihilated. So much critical informational on Aryuveda, astronomy, mathematics and the physical sciences was lost forever. Some libraries were so huge, they burned for days.
Islam was at the height of its military era at the time and easily destroyed and annexed other passive cultures. Lots of journals of invaders from that time that documented their utter contempt for peoples who couldn't defend themselves.
The West had learned this lesson early and well from the Roman era: Si vis pacem, para bellum.
> CV Raman won the Nobel prize in science, Tagore won the Nobel prize in literature, Ramanujan etc, the names are numerous.
So golden age of India was when the country with a seventh of the world's population won 2 nobel prizes over 5 decades ?
> The British rule also was the largest and most stable unification of India till the modern times. After 1850s there were almost no pockets of military resistance against the British rule.
Mughal and Gupta empires lasted over 3 centuries, Mauryan empire a little under 1.5 centuries. By comparison, east india company rule lasted a century and the British crown's rule less than that. So again completely incorrect.
> The third golden age which no one wants to admit (left or right) is the British Golden age.
There's your hint: if people on both sides of the aisle don't "want to admit" something, maybe it doesn't make sense. Not to mention a slap in the face of billions of Indians.
> The British age declined with WW1 and WW2, and ended with Indian independence.
Thank god for that decline, otherwise Indian taxpayers would have been funding Brexit and the crumbling British economy right now.
> My oversimplified summary has been
This is not a summary, it's a lazy opinion backed by little research.
Good summary, even if I disagree with the 3rd piece being called a golden age. But my question is why ignore the cholas, pallavas and pandyas? Only because they didn’t capture the whole subcontinent? Our schools history books were Delhi centric but we don’t have to be going forward. Those 3 empires had a lot of arts and culture too - and in terms of impact, they spread to parts of SE Asia too.
> you could argue independence had been a disaster with everything getting worse post independence
There hasn't been a single famine in india since independence. The last one was the bengal famine of 1943. India became independent in 1947.
And, it should be on track to become the world’s largest economy by 2075 - which historically it and China always have been.
I hear what you’re saying, but this idea of a golden age under rule by some outside force is often the positive take about many historical periods where someone who committed significant crimes (invasions, genocides, etc) is then praised hundreds of years later because of the positive effect they had for the economy or whatever. Julius Caesar is one such example that comes to mind.
But I feel that approach sometimes discounts what the country and its people could have achieved on their own if they were not invaded. For example, the Taj Mahal is just one building in India. There are lots of other structures that exist that were not built under rule from outside invaders, but they never get attention (at least I’ve not heard of them). With Britain - you mentioned that they unified India and brought stability but how true is that if you compare it to the period of India much earlier? India was rocked by Islamic invasions (which led to the Mughal period) and colonized by those Islamic rulers for hundreds of years. That’s what the European colonizers took over. Is that really a fair period to compare against? India basically spent a millennium ruled by one outside genocidal invader or the other. I am guessing the period before that was more peaceful and not in need of some outside unifying force to feel ‘stable’.
What do you think about Gupta india
You missed Gupta.. but I too consider Islamic/Mighal as well as British time too Golden period from world progress perspective.
If Invasions and colonization were golden age we should continue that tradition throughout the world. /s
I guess the author, a historian, writes about ancient Indian mathematical contributions (a science of which he has no expertise presumably). These historical references I have learnt in various mathematical texts (the story of Fibonacci and al khwarizmi) - the journey across multiple centuries, of these innovations made by Aryabhata or Brahmagupta.
As an Indian, and as a math aficionado (and degree holder) - I wonder, that was about 1500 years ago. In that era, a discovery (as you can read it) took 500 years to move from Arabia to Europe, thanks to Fibonacci's writing. Contrast it to today's instant dissemination of information and breakthroughs. Yes those were the glory days of Indian civilization. We have a Ramanujan every 100 years in India. Breakthrough ideas (earthshaking ones like the concept of 0) emerging out of India are few and far between. Around 1000 years ago, the fountain of (world-changing) creativity and ideas seems to have dried up, as far as India is concerned. Maybe it was the invaders , easy to blame everything on outsiders, though - what is India today was 600 or 400 odd kingdoms, frequently warring each other - so turmoil was always there. And if you were a reclusive monk in a forest with a bunch of students, no Brit or Mughal dude was stopping you from innovating. So, the big question is - can we explain why genius ideas stopped (without blaming British, or Mughals etc) - because thanks to Indian's instincts, the first step is to blame the Brits/Mughals , so problem solved, proved, ostrich is happy in the sand.
I can only indulge in thought exercises , like : Aryabhata and Brahmagupta didn't have computers, didn't even have pencil and paper. They just sat there and thought. For months, or years. Or maybe they were walking. And gazed at the stars and observed and observed. And most likely, and importantly debated orally : endlessly with their teachers (in a monastery type place class sizes were small), peers- I believe this was a time in India's cultural history when debating, and disagreeing were positive things. In modern India, intellectualism has taken a back seat. To disagree is to be unpatriotic even. (Nalanda University comes to mind https://en.wikipedia.org/wiki/Nalanda_mahavihara - not its modernized recreation which is likely going to be hardly attempting to break the mold). WhatsApp - the destroyer of brain cells by atrophy , has a grip on every mind.
We read about the great Greek debates. We see videos of Tibetan buddhist monks practice debating in a monastery. Surely this kind of debating, face-to-face is missing in today's world (without getting angry) - this is the equivalent of the modern cafe in Paris or Vienna, with Godel and co. debating . This debating society , was Nalanda back a thousand years until invaders burnt every manuscript down and slaughtered every monk almost - except the manuscripts the Chinese monks took back to the Emperor in China - they are the only written records of life that remain, that and some arabic ones.
Yet I hope new lotuses will bloom from India - we can never predict where the next genius or breakthrough idea will emerge from - why not Africa?
I think it's just that industrialization, the computer, and the Internet were such massive juice that even if you have a brilliant mind it doesn't matter because the guy with that tool can take anything you think of and make it better. Each of these is a step up so huge that no mind can match it. So you have to match the tool first before the minds start mattering.
>didn't even have pencil and paper.
The oral tradition was certainly strong but there was no dearth as such of writing instruments. What makes their work not easy to access is their poetic symbolism, sun is one, moon is two and so on. These symbolisms were not even one to one, thus always leaving a window a doubt about what they really meant in their verses.
Since you mention Fibonacci, you may know what we call Fibonacci series was worked out around 250 BC by Pingala as an exercise in enumerating meter of verse
The Guardian also published a promotional piece for this book if you can't get past the paywall of TFA.
https://www.theguardian.com/world/article/2024/sep/01/hidden...
Dalrymple has a uniquely addictive style of writing that very few history writers do. I can't recall any other nonfiction book becoming such a page-turner for me as his "Anarchy" did. Terrific writer.
Anyone know why the hardcover isn’t available until April 2025?
I was super excited to read this book but I hate buying kindle books as it’s easier to share real books.
Tangential but interesting - see also Sam Miller's idiosyncratic and funny book A Strange Kind of Paradise: India through Foreign Eyes.
It's a fine surprise that I just ordered the book independently and then discovered the podcast and found the book being discussed on HN all in the same day. Pretty nice coincidence.
Very good writer, but he personally wound me up with his public "Great Escape" from India during the pandemic and laid himself open to the criticism that followed, of being a fairweather friend.