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Arabic Mathematics: Forgotten Brilliance? (1999) (st-andrews.ac.uk)
135 points by lioeters 76 days ago | hide | past | web | favorite | 96 comments

Title is slightly misleading! Most of them are Islamic but not Arabic. Khawrazmi [1], Karaji [2], Khayyam [3], and Tusi [4] were all Persian. Ibn Haytham wrote only in Arabic though.

[1] https://en.wikipedia.org/wiki/Muhammad_ibn_Musa_al-Khwarizmi

[2] https://en.wikipedia.org/wiki/Al-Karaji

[3] https://en.wikipedia.org/wiki/Omar_Khayyam

[4] https://en.wikipedia.org/wiki/Sharaf_al-D%C4%ABn_al-%E1%B9%A...

It’s a shorthand; “Arabic” or “Islamic” mathematicians were from a wide range of religions, ethnic groups, regions, etc.

It’s similar to the way we call all of the mathematicians of ~ 500 BCE – 500 CE “Greek”, even though most of the later ones were Roman citizens living in Egypt or elsewhere.

Or the way we call Mesopotamian mathematics generically “Babylonian”, even though most of it was from other cities, and some of the relevant developments lumped in are from before Babylon per se existed, done by people of a different ethnic group who spoke a different language.

Or the way Soviet scientists are often called “Russian”.

The Greeks living in Egypt were actually Greeks, even during the existence of the Roman Empire.

The Persian mathematicians living in Persia in the times after the Islamic conquest simply weren't Arabs, exactly like the Greeks weren't Romans after the Roman conquest.

One doesn't get the new ethnicity by being occupied.

Some of them were ethnically Hellene. But folks of any ethnicity throughout the Roman empire (or earlier the Alexandrian empire etc.) of the time who wanted to do mathematical work would have probably traveled to Alexandria or Athens to study and would have written mathematical results in Greek, which was the language of science/mathematics/philosophy of the day.

We unfortunately don’t have too many biographical details about most of the famous “Greek” mathematicians, so it’s generally not precisely known what their background was.

This is not true. They were likely ethnically Egyptian or Phoenician or Libyan but had Hellenic names. In the same way the Iranian mathematicians in the article had Arabic names. Culture and language often cross ethnic boundaries and it's up to historians to piece it all together.

> Iranian mathematicians

In the middle ages, there was greater Persia and two Iraqs (Iraq al-Arab to the west and Iraq al-Ajman to the east which is today's western and central Iran).

If we are being pedantic, either the polymaths in question were Persian (which they are) or Iraqi Arabs, not Iranians. In fact, Persian empire also encompassed parts of modern day Uzbekistan, Kyrgyzstan, Turkmenistan, Afghanistan, Pakistan, and Kazakhstan, until they came under the Turcko-Mongol rule.




dingoegret: your sibling comment here is dead.

Anyway, “Persia” (Persis) comes from the Greek version of “Pars”. Persians call their language “Farsi”, from the Arabic version, “Fars”. These all have the same origin, and date back millennia.

I think the point was that the mathematics being described is bound by geography rather than by ethnicity. Arabia is used both to refer to an ethnicity and a geographic area. So the usage is sound, as is namirez' subtle clarification due to the history of the area.

The article talks about that:

>Nor were all these mathematicians Arabs, but for convenience we will call our topic "Arab mathematics".

>The regions from which the "Arab mathematicians" came was centred on Iran/Iraq but varied with military conquest during the period. At its greatest extent it stretched to the west through Turkey and North Africa to include most of Spain, and to the east as far as the borders of China.

But is it really a convenience, or is it just a way of ratifying our own ignorance after it has been caught out. "Iranian" mathematicians would be just as convenient, and less in inaccurate.

"Arabic Mathematicians" has some justification as (I suppose) most of these guys were publishing in the Arabic language. But to then switch to ethnic designator Arab is plain wrong.

>"Arabic Mathematicians" has some justification as (I suppose) most of these guys were publishing in the Arabic language. But to then switch to ethnic designator Arab is plain wrong

Perhaps so, and "Persian math" doesn't take much to say.

But then, the distinction between Arabic and Arab is subtle enough that I wouldn't notice at a glance. (Other ethnicities don't even get a different adjective for language, e.g. Russian, French, etc)

It's hard to change language around things like that. For instance, Igor Sikorsky (of the Pan-Am Clipper, and later helicopter fame) is know as a Russian-American inventor, even though he was born, educated, and flourished as an aviator in Kiev, Ukraine (then a part of Russian Empire). Sikorsky's father was a Russian Nationalist. Should we call him a Ukrainian-American given all that? I would, but's a subject of contention over a hundred years after his Ilya Muromets (first 4-engine bomber in production) took flight.

For better or worse, though, we use language to get a point across. "Russian aviation" and "Russian rocketry" gets a certain notion across very fast, even though many key contributors to that notion, like Sikorsky and Korolev (of Sputnik and first-man-in-space fame, among other things) were born, raised, and educated in Ukraine[2].

Perhaps it's the same with "Arab math".



This is the reason its called Islamic Civilization. Most of its scientist weren't Arab. Arabic dictionary wasn't even written by an Arab.

But as I have noticed many people don't feel comfortable to reference a religion, so they go with race.

But find it interesting that we label these scientist based on their origin, not the place that gave them all the reasons to become all they were capable of becoming..

This is like saying Sergey Brin is a Russian entrepreneur.

If Brin lived in Russia, spoke Russian, and wrote books in Russian we wouldn't call him American just because he wrote a few books in English too.

Perhaps you're not familiar with the history of that part of the world, but the individuals that I named were Persian speakers, who lived in a region that is called the Greater Iran today, and wrote most of their work in Persian. But in all fairness, Arabic was the lingua-franca at the time so they wrote books in Arabic too.

A better example would be to call Grigori Perelman an American mathematician because he published his work on arXiv [1].

[1] https://arxiv.org/abs/math/0303109

> If Brin lived in Russia, spoke Russian, and wrote books in Russian we wouldn't call him American just because he wrote a few books in English too.

But if he spoke Enlgish, had an English name, lived his professional life in America. and most of his major works were in Enlgish.

I'd supposed you'd call him an "Anglophone" academic, which is the sense that Arab is used in.

>the individuals that I named were Persian speakers, who lived in a region that is called the Greater Iran today, and wrote most of their work in Persian

And yet they are called Arab mathematicians.

you named al khawarizmi, which is the only one that I'm really familiar with.

he spoke arabic. Most of his major works were in arabic, in Baghdad. and he has an arabic name.

Arab refers to the people living in the Arabic world. If you were to bind it by an ethnicity, most of the people living in the Arab world "Today" would not be Arabs.

From Wikipedia: Arabs are a population inhabiting the Arab world.

> From Wikipedia: Arabs are a population inhabiting the Arab world.

Also from Wikipedia: Persia, present day Iran, is not part of the Arab world.


This is the Arab world today, not at that time.

namirez's point is that the historical people mentioned are Persians being called Arabs. And there are Persians that would take offense to this association.

> And there are Persians that would take offense to this association.

Believe me, it's the same here in North-Africa and Arabs are really loathed. But again, it's a nomination that's often mistaken for an ethnicity.

Much of North Africa is considered part of the Arab world today, as it often refers to places where a dialect of Arabic is spoken and the culture has been affected in parallel. This is a key difference as Persian isn't even considered to be in the same language family as Arabic, unlike the dialects of Arabic that are predominant in the region approximately spanning Morocco to Egypt.

Dialects like French? Ha!

No, not like French. Around 85% of Moroccans are fluent in Moroccan Arabic and about 72% of Algerians speak Algerian Arabic, more than any other language (particularly Berber and French) in their respective countries as far as I can tell. A similar story exists in Tunisia, despite a majority of the country also apparently speaking French.

I think it's pretty fair to call these dialects of Arabic the predominant languages.

Did they write their mathematics books in Persian, or Arabic? If they wrote their books in Arabic, living in Arabic land They are Arabic scientist

If a Russian, scientist, lived and studied in USA, to which country would you attribute his work or achievements, Russia or USA

Slightly? The title is completely wrong!

you mean Iranian right? "Persian" is a colonial term

While you are correct in that it is an exonym, it's not exactly what I, and I assume many others today, would think of when you say "colonial." The origin of the word dates back to thousands of years ago when no present government or society existed.

For those who would like to read a little more: https://en.wikipedia.org/wiki/Name_of_Iran

Absolutely its normally used to refer to the Persian "empires" which you know colonised other lands and where a lot larger that Iran is today.

from your link: "In the Western world, Persia (or one of its cognates) was historically the common name for Iran"

so I will stick to saying colonial as it accurately points to the western world as opposed to Africa or Asia for example

I don't disagree about the name that should be used, as I said. I just think calling it colonial needs a little more context for people who would not unreasonably assume it's something more similar to Western colonialism of India or something.

On that note, "India"/Hindustan/Hindu/etc. are somewhat similarly colonial-rooted names, ironically popularized by the Iranians.

"western colonialism" is redundant. "colonialism" will suffice :)

It's out of date, but that's OK when talking historically. And it was no more colonial than saying "Germany" instead of "Deutschland". Personally I prefer the term "Iran" even for historical usage because it is both older and (usually) more accurate.

But "Persian" is not something that foreigners imposed. It was originally the name of a particular Iranian nation that took over the empire thousands and of years ago. Their name then stuck around in some contexts long after that dynasty was gone, which is why the language is called "Farsi" (anglicised to "Persian").

arab is not used as an ethnicity but refers to someone who speaks arabic as a mother tongue. In the same way, that North africans refer to themselves as Arabs although genetically they are less than 50% Arab.

> In the same way, that North africans refer to themselves as Arabs although genetically they are less than 50% Arab.

Not sure where you got this from, here in Morocco, calling a Berber an Arab is a pretty sure way to piss him/her off.

Tunisia, Lybia. 99% of Tunisians self identify as Arabs

A whopping ~2% of Iranians have Arabic as their native language. That means, if you're going based on language, you're mislabeling 98% of the population.

I hold it to be obvious that I'm talking about the scientists (That lived in the Islamic Golden age) not about modern day Iran.

Plus Most of them were not born in Iran proper.

Many Islamic (not just Arab. Also Persian and others) scholars were on the right track about identifying evolution, and far from the evolution denying general populace today.

See the short "history" section in this article: https://en.m.wikipedia.org/wiki/Islamic_views_on_evolution

Wow, I had no idea! "[they] were on the right track" is an understatement.

... on what he referred to as the "gradual process of creation." He stated that the Earth began with abiotic components such as "minerals." Slowly, primitive stages of plants such as "herbs and seedless plants" developed and eventually "palms and vines." Khaldun connects the later stages of plant development to the first stages of animal development. Finally, he claims that the greater thought capabilities of human beings was "reached from the world of the monkeys."

I wonder, though, to which extent that was somewhat idle speculation, similar to Democritus stating that the world consists of atoms 400 BCE, without really any evidence for it (let alone a fully formed theory).

A bit more from this fascinating topic:


It seems like he had a fully formed theory which is pretty accurate.

A bit late now, but FWIW I don't think from the cited quotes one can deduce that he had anything approaching a fully formed theory; in fact I'd say it's very similar to Democritus idle musings.

Yes. The quotes didn't have any indication of a full theory. However, I find it difficult to believe that they reached so many accurate conclusions without a proper base theory.

The word Algorithm comes from a mathematician named al-Khwarizmi. Many words that begin with Al (Arabic definite article) are of Arabic origin. Alcohol is another one :)

I was told of Algebra coming from Al-Jabr meaning "number games". I was surprised I didn't see this mentioned in the article, until I found the book mentioned in Al-Khwarizmi's biography [1]. The book's title is "Hisab al-jabr w'al-muqabala" but no translation is given and Google's translation "Al Jaber account and interview" is not helpful. Can anyone confirm or deny the explanation I was given?

[1] http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Al-Kh...

The translation you're looking for is: "Calculation by Completion and Balancing"

The book's name in English is: "The Compendious Book on Calculation by Completion and Balancing"

So Al-jabr meaning is very close to "calculation by Completion" in that context.

جبر, in transliteration, jabr, is the root of the word and the closest meaning is to bring (with a possible connotation of doing so against the entities natural inclination or state) back together parts (in healing).

To my mind, mathematically it would be closest to the literal concept of integration, but that is calculus and not what is generally considered to be algebra.

I associated al-jabr as classification. The 'back'ness felt more like bring back order by arranging same kinds on same sides.

iirc the title translates to something like "the Study|Art|Practice of balancing and restoring." I recall "al jabr" means "of/relating to balancing"

This source[1] states it as

>the science of restoring what is missing and equating like with like

[1] https://www.lexico.com/en/definition/algebra

Alhambra is another example.

This is also the origin of some definite articles in romance languages - el in Spanish and l' in French. So Alhambra in Spain might have been called Al Hambra or similar instead.

Interestingly, in Persian (which uses Arabic script and shares some loanwords) which is a totally different language, the definite article is assumed, and it instead has an explicit indefinite article (-i or -yi) added to a noun/adjective.

There's a ton of them in Spanish, due to the fact that Spain was partially occupied for centuries (which also has left some amazing architecture like the Alhambra in Granada, or the Alcazar in Seville). Alcohol as in English, but also almohada (pillow), alcalde (mayor), algodón (cotton),... and many more that don't start with "al".

I've also heard that Allah is a variant of Elohim, and was used by Christians in the region before being conquered by the Muslims.

Arabic and Hebrew are both Semitic languages. Elohim is the Hebrew word for "gods", the plural form of el, "god", as seen most commonly today in Hebrew names like Michael, Samuel, Raphael, Emmanuel, Elijah, Eliezer, etc. etc. etc.

Allah is just the Arabic cognate, plus the definiteness marker. So yes, anyone speaking Arabic will use that word to refer to any god, and anyone speaking Arabic in the past would have used that word to refer to any god. Similarly, a German today wouldn't hesitate to apply the word "Gott" ("god") to Thor, because Thor is a god. Whether the hypothetical German is Christian isn't really relevant, and neither is the fact that the Christian god is nameless, being usually referred to by a title such as "God", "Lord", "Father", etc.

> the Christian god is nameles

Inherited from what developed as a norm in Judaism, where the name existed but then stopped being read (the most famous "one who must not be named"), but the original name of the deity is preserved in the given names used around the world:


For the theophoric names, I have a question you probably can't answer.

I've read that the form "Jehovah" results from reading YHWH as if it had the vowel points of the word adonai, "lord". But I can't help noticing that the prefix form of YHWH in names, for which the vowels are known, is yeho-. That really adds some credibility to "Jehovah", except that "Jehovah" supposedly comes from a completely unrelated convention.

How much do we know about the original vowels? How true is the adonai story?

"How true" of course depends on the faith of the one who discusses it -- the faiths are exactly made based on the different "stories" about the same topics, which the believers have to believe. It appears to me that the relevant research behind "1906 Jewish Encyclopedia":


is good and that it gives the sources to its claims. I'm not aware that the later scholars refuted the relevant points for this topic:

"At least as early as the third century B.C. the name seems to have been regarded by the Jews as a "nomen ineffabile," on the basis of a somewhat extreme interpretation of Ex. xx. 7 and Lev. xxiv. 11 (see Philo, "De Vita Mosis," iii. 519, 529). Written only in consonants, the true pronunciation was forgotten by them. The Septuagint, and after it the New Testament, invariably render δκύριος ("the Lord")."

Note: the Septuagint, the translation of the Hebrew bible to Greek is effectively what was since the development of Christianity called by the Christians "the Old Testament" and the Christian bible textual analysis proves that the authors of the New Testament almost exclusively used only the Greek translation and also wrote the New Testament as Greek native speakers in Greek, having even misunderstandings from interpreting the Greek words differently than the original Hebrew, even if Hebrew could also be misinterpreted during reading, but not in the same way. Anyway, that's how other languages got the "Lord" and equivalents in their translations from what was originally written: from the Septuagint and https://en.wiktionary.org/wiki/%CE%BA%CF%8D%CF%81%CE%B9%CE%B... (note the difference from the 1906 Jewish quote).

Anyway, there is also the article about Jehovah, "mispronunciation (introduced by Christian theologians, but almost entirely disregarded by the Jews) of the Hebrew "Yhwh"":


And this is where the faith of these involved in the discussion can influence their interpretation even more.

Still I believe this statement is true:


"Gesenius's proposal to read YHWH as יַהְוֶה is accepted as the best scholarly reconstructed vocalised Hebrew spelling of the Tetragrammaton" (i.e. transliterated into English as Yahweh)"

> Written only in consonants, the true pronunciation was forgotten by them.

So the theophoric names use vowels unrelated to the original pronunciation? Those names all postdate the loss of the vowels?

I would be pretty surprised if that were true. Are the vowels in theophoric names fixed by some consideration other than the vowels in the word from which the names derive?

> the theophoric names use vowels unrelated to the original pronunciation?

It’s not about all names, I guess you ask about YHWH. If you follow the links from previous messages you can see that we have information how the Greeks pronounced it and also the linguistic hints known to the language experts. Based on both it is quite accepted that it’s pronounced approximately yahweh with probably silent h and the ending e sounding like English a in an article like in “a house”. So the alternative maybe simpler spelling would be yaaw. But then people would ask where both h went.

Also note that English pronouncing of J from the German transcriptions like in “Jar” is always wrong, it should always be Y.

Muslims people believe in the Christian/Hebrew single God indeed. They just think that the right way to do it is through Mohammed (The muslim prophet) teaching. The argument is that Mohammed is the last prophet that god sent and thus should be the one to follow.

They seem to be wrong about that “last” prophet thing, since everybody knows about Joseph Smith, who came after Monammed.

Hey, what about Sun Moon? And there is a new Dalai Llama each generation!

Chemistry is derived from alchemy, which is also Arabic in origin.

Yes, Arab alchemists preceded European alchemists.

Pseudo-Geber was a European alchemist who pretended to be an earlier Arabic-speaking alchemist, perhaps in order to give his works more reputation.

He was Kazakh, not Arab, wasn't he?

Geographically Uzbek, ethnically Persian apparently.

I am not sure why this is a surprise. The early Islamic period was a cultural golden age while Europeans were lost in a dark age. Many contributions from that period resulted in advancements for mathematics, exploration, literature, astronomy, and other ares that are still felt today.

1- Everyone who writes in the same language is from the same country and ethnic group.

2- Everyone who wrote in Latin is Italian

3- Newton and Descartes wrote in Latin


::: Newton and Descartes are Italian.

Impeccable logic !

Another gem of flawless argumentation is to say "who cares about ethnicity?! and let's just move on". Well it's been almost two millennia of misunderstanding and misrepresentation. Why don't we just get this very simple fact correct and apply the same intellectual scrutiny that we apply to other areas here as well?

IMHO This is just inexcusable sloppiness and to be honest beneath any human being with a modicum of culture.

> Algebra was a unifying theory which allowed rational numbers, irrational numbers, geometrical magnitudes, etc., to all be treated as "algebraic objects".

> It gave mathematics a whole new development path so much broader in concept to that which had existed before, and provided a vehicle for future development of the subject.

> Another important aspect of the introduction of algebraic ideas was that it allowed mathematics to be applied to itself in a way which had not happened before.

Nearly all of the great "arabic" scholars were not arabic at all, they simply wrote in the arabic language. Most of then were Tajik or Uzbek ethnicity.

Arabic, Turkic, Persian, Moors.

most of it was mathematics they learnt from translated books from Sanskrit , Prakrit ( In India ) and Mandarin(Chinese) . None of it was original Arab work , most of Arab historians who came along with invaders have mentioned in detail how learned people were taken in as slaves to translate works in arabic

What do you mean none of it is original, we are talking about a 400 years of process here, science always takes inspiration from all prior studies, do not discredit thousands of scientists that actually inspired western science. Also they were Muslim scientists different ethnicities, e.g Persian, Turkic and definitely Arabs as well.

He means none of the work is original.. neither the number system.. nor the additive and series based mathematics.. it's just a translation.. based10 numbers have been inuse in India for thousands of years.. it's like Columbus finding America..

It is absolutely not "just a translation", they greatly improved and introduced new concepts over prior work of Greek and other scientists considerably. The volume of novelties of Muslim scientists of the time is huge.

Do you have any source for this?

I don't know if things changed in last twenty years, but I consider at least basic knowledge of Al-Khawrazmi pretty common, hardly what I would call forgotten.

I'm pretty sure 99% of the comments are from Arabs/Persians/Berbers backlashing one another over who is who. can you stop arguing and move on to the next article please xD

Let's not forget that the Islamic world was key (though not alone) in preserving our scientific and cultural knowledge.

At that time, Islamic society was quite modern and tolerant - and even often the destination for persecuted religious groups such as the Jews in Spain.

It is absolutely clear that modern Islam is, in fact, much more "conservative" than it used to be in the beginning. Indeed, the very beginning of Islam was a radically progressive movement in the region. It freed slaves, it gave rights to women, it treated with other religions and it abhorred hereditary and even defacto differences between humans. Many of the things that we now find so backwards were a) not as strict at the time and b) much more advanced than other societies in the region. A good example is the difference between the initial Islamic state and the Persian empire. The Persians didn't even fully understand that they were dealing with a sort of grassroots movement, and were constantly trying to find the equivalent of a high status ruler to talk to. But early leaders in the Islamic world were completely different, living in normal or even poor circumstances and operating in a much more democratic manner than was the norm.

Later, these societal properties were the reason that the Arabic world was able to preserve and advance science and culture. Sadly, this did not last into this century, but the reasons for this are complex and almost surely political.

I say this is important to remember because we need to realize that religion and - further - ethnicity (and of course race) are not ingrained attributes determining who is conservative. We need to remember that there was a time when Islam was the paragon of reason and rationality, while Christianity was the embodiment of fanatic action.

In the end, it is all politics, not the people. We do well to remember these things, because it keeps us from condemning other cultures, as it so often happens!

It's really interesting reading Al-Khwarizmi writing back and forth with Ibn Sina speculating about life on other planets and whether they might have been visited by prophets too.

Much, though not all, of the big scientific work in the Islamic world was in Iran and central Asia. But eventually enlightenment led to counter enlightenment and the rise of Gnosticism and mysticism. Then the Mongols rode in and killed everyone. They were normally good about capturing cities in an economically useful state, especially if they surrendered, but Ala ad-Din Muhammad II really pissed of Genghis Khan who was mostly busy with China at the time and couldn't spare the troops for a conquest, just an invasion. So they killed everyone in the cities except a few hundred they shipped back to Mongolia. Then came back a few weeks later and killed any survivors who had come out of hiding. And central Asia went from a trade nexus with possibly the largest cities in the world to the state we know it in today.

Islam is largely Arabic, but is it the case that things attributed to Arabia are mostly Islamic?

Not at all, the Koran is written in the context of Arabia at the time. This is not a matter of interpretation, the book itself references local customs and laws. Therefore, our understanding, the practice and everything else in Islam is crucially shaped by the society in Arabia, and the change it brought to it. I think it is best read and understood in terms of the Delta - the change - it meant to convey (but that is my opinion).

On the other hand, however, much of the Arabic language and customs are of course shaped by Islam. For example, one difficulty of interpreting the Islam is that the words that are used now convey the connotation that was coined by centuries of religious practice, and it is difficult to know exactly what they originally meant. In addition, much like the Bible (translations), it coined many terms and semantic concepts.

Overall, the question you pose it not answerable in any way. Interpreting the core - the Koran - does not have a unique solution. And even though Islam has taken great care to preserve the text, traditions and reasons behind them, it is not clear cut. For example, the large majority of Muslisms prescribe to the Hadiths as interpretation and additional norms, but there are also Hadidths stating that you should not do that, and the Koran is enough. But on that basis, many more interpretations would be possible. Paradoxically - and in contrast to Christianity - the Muslisms who rely primarily on the book alone, are much more progressive than the ones also relying on the traditions.

I don't think your question will find a true answer.

> the Muslisms who rely primarily on the book alone, are much more progressive than the ones also relying on the traditions.

As an ex-Muslim, the way I see it is: If you were to rely primarily/only on the Koran, it is because you want to justify and legitimate your own agenda. The Koran is very flexible and can be either very progressive or very conservative, strict and violent.

So you make your pick and then find the particular "bayt" that supports your claims :)

Yes... In the sense that the works discussed here were produced by scholars of Islamic fate. Check the Wikipedia links in another top comment and you'll see the time being referenced as the "Islamic Golden Age".

BUT: this is "islamic" in the sense that western science of the middle ages or Charles Darwin are "christian". These are names of cultures, not religions.

Are you talking back in the day or now? Now Arabs are the minority in the Islamic World[0]

[0]: https://en.wikipedia.org/wiki/Islam_by_country

> It freed slaves

Only if they converted. Otherwise the slavery never stopped to be OK for that religion (those paying the "protection" are also not allowed to be enslaved). See the (currently insulting) word used for slaves in South Africa, where the slaves from the northern African areas were sold by the adherents to the said religion. Also in the other parts of the world:


> gave rights to women


Muslims inherited a great number if slaves from the empires they conquered. The most responsible political course of action was to introduce gradual manumission with incentives that would benefit the people of the Caliphate. So yes, they did free slaves. It wasn't some fairy tale day 1 everyone is free now, let society burn in disorder, do whatever you want, but it was the correct thing to do.


Indeed, at this point i feel it is willful ignorance in many cases.


The same author has a pretty detailed page on Indian mathematics: http://www-history.mcs.st-andrews.ac.uk/Indexes/Indians.html

I stumbled upon an interesting essay on "Indian Mathematics: Redressing the balance" at the same page: http://www-history.mcs.st-andrews.ac.uk/Projects/Pearce/inde...

Much of it was, yes, but there were also translated works from Greek.

I've heard of this before.

Could you elaborate on those translated works? Perhaps cite some works that were of well known Indian origin?

The Aryabhatiya, which contains the first known instance of the algorithm we use today for finding multiplicative inverses in Galois fields, is one well-known example. (Of course Aryabhata didn't know it could be used for that.) The Surya Siddhantha, from which we derive the word "sine", is another example. I recommend reading https://en.m.wikipedia.org/wiki/Indian_mathematics

At least it's not Muslim Math! /s


Interestingly, it was the Arabic conquest of the eastern Mediterranean and North Africa and subsequent control of the sea lanes that cut western Europe off from the east. Intellectual commerce between east and west was greatly curtailed after the Byzantines started losing badly. It wasn't until the Battle of Lepanto that western Europeans started to have more or less free access to the east again.

There is no denying that in western Eurasia the Mediterranean was the seat of high culture and learning until about the 17th century.

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