Latest / Tamerlane: The Conqueror Who Tried to Rebuild the Mongol Legacy — Fexingo History / Tamerlane's Captive Mathematicians: Algebra in Samarkand
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- Lucas: So we've talked a lot about Tamerlane bringing craftsmen and engineers to Samarkand — the papermakers, the goldsmiths, the astronomers. But there's one group we haven't really touched on: the mathematicians. Luna: Mathematicians? I wouldn't have thought of that as a priority for a conqueror. Lucas: Right? But it makes sense when you think about it. Tamerlane needed engineers for siege weapons, surveyors for his roads, astrologers for court predictions — all of that relies on math. And when he sacked Damascus in 1401, among the captives was a man named Ghiyath al-Din Jamshid al-Kashi, one of the finest mathematicians of the medieval Islamic world. Luna: Wait — al-Kashi? I think I've heard that name before. Lucas: Yeah, he's famous for a few things. He wrote a book called Miftah al-Hisab, which is Arabic for 'The Key of Arithmetic.' And he did something that seems obvious to us but was revolutionary then: he developed a system for working with decimal fractions. I mean, the concept of a decimal point — he didn't invent the idea entirely, but he systematised it and showed how to use it for practical calculations like finding square roots or measuring land. Luna: So he was basically doing what we learn in school today, centuries before it caught on in Europe. Lucas: Exactly. He also calculated pi to an incredible degree of precision. In his treatise al-Risala al-Muhitiya — 'The Treatise on the Circumference' — he computed pi to 16 decimal places. That was the most accurate calculation in the world for almost 200 years, until the German mathematician Ludolph van Ceulen beat it in the late 16th century. Luna: Sixteen decimal places — by hand, without modern tools. That's mind-blowing. Lucas: And it wasn't just theoretical. al-Kashi used a method based on Archimedes' approach — inscribing and circumscribing polygons around a circle — but he pushed it way further. He started with a 3x2^28-sided polygon. That's over 800 million sides. The calculations alone must have taken months, maybe years. Luna: So how did he end up in Samarkand? Was he forced, or did he go willingly? Lucas: That's actually a really interesting question. The sources are a bit contradictory. The historian Ibn Arabshah, who was captured by Tamerlane as a child and later wrote a hostile biography — he's the one who gives us that dramatic story of scholars being chained and brought to Samarkand. But other accounts suggest al-Kashi may have come voluntarily, or at least under better conditions. Luna: I remember you saying that Tamerlane's court was genuinely interested in learning. Lucas: Yeah, Tamerlane himself was illiterate, but he understood the value of knowledge for prestige and practical use. His grandson Ulugh Beg — who was a child when Tamerlane was still alive — would later build the famous Samarkand Observatory. And al-Kashi was actually recruited to work on that project. He was one of the key figures in designing the instruments and training the astronomers. Luna: So he wasn't just a mathematician — he was also an astronomer and an instrument maker. Lucas: Right. He wrote about the construction of astrolabes and other observational tools. And his work on decimal fractions was directly motivated by the need to make astronomical calculations easier. The old method was sexagesimal — base-60, like we still use for time and angles — which is clunky for complex multiplication. He showed that by using decimal fractions, you could do the same calculations much faster, with less chance of error. Luna: It's amazing that algebra and arithmetic were advancing right in the middle of all that conquest. Lucas: It really is. And here's another layer: al-Kashi wasn't the only mathematician in Samarkand. He had colleagues like Qadizada al-Rumi, a scholar from what's now Turkey, and al-Kashi's own student, Ali Qushji, who later became the director of the observatory. So it was a real community — a kind of research institute before the term existed. Luna: What happened to al-Kashi? Did he stay in Samarkand for the rest of his life? Lucas: He did. He apparently died around 1429, so he lived into the reign of Ulugh Beg. But there's a tragic story — some sources say he was murdered, or at least that his death was suspicious. The story goes that Ulugh Beg was so impressed with his work that he became jealous, or that al-Kashi offended someone at court. But we don't really know. The details are murky. Luna: That's a familiar pattern — brilliant people at the mercy of powerful patrons. Lucas: Yeah. But his legacy lived on. His book Miftah al-Hisab was used as a textbook in the Islamic world for centuries. And through the work of later scholars like Ali Qushji, some of those ideas filtered into Europe. So in a way, the decimal point we use today has a direct line back to a man who was brought to Samarkand in chains — or at least under duress. Luna: That ties back to something you mentioned earlier — the idea that Tamerlane's empire was a crucible for culture, even if it was built on violence. Lucas: Exactly. And you know, it's a reminder that these episodes we do — they're possible because listeners like you support the show. A handful of people chip in monthly through buy me a coffee dot com slash fexingo, and that literally funds making these deep dives. So if you've been getting something out of these conversations, it's worth checking out. Luna: Yeah — it's a small way to keep this going ad-free. Lucas: So, back to al-Kashi: one of his lesser-known contributions was in solving cubic equations. He developed a method that was essentially iterative — you'd start with a guess and refine it. That's the same idea behind Newton's method, but centuries earlier. Luna: So he was doing numerical analysis before the term existed. Lucas: Exactly. And he applied it to problems like finding the sine of one degree, which required solving a cubic equation. He got it to an accuracy of something like 10^-17. It's incredible. Luna: It makes you wonder what else was lost or forgotten when empires collapsed. Lucas: That's the thing — a lot of al-Kashi's work was preserved, but some manuscripts are still being studied. And there are surely other scholars like him whose names we'll never know. But at least for al-Kashi, we have a pretty clear picture of a man who, whether captive or not, made the most of his situation and left a permanent mark on mathematics. Luna: And his story is another reminder that history isn't just about battles and kings. Lucas: It really isn't. Next time, we'll look at another side of Tamerlane's intellectual world — but for now, I think that's a good place to leave it.