14 ms·

Arabic Mathematics: Forgotten Brilliance? (1999)

135 points by lioeters 7y ago

lioeters 7y ago
> 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.
User23 7y ago
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.
jgalt212 7y ago
At least it's not Muslim Math! /s https://www.youtube.com/watch?v=embMAtagQiU https://www.youtube.com/watch?v=embMAtagQiU
droithomme 7y ago
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.
- mda 7y ago
  Arabic, Turkic, Persian, Moors.
austincheney 7y ago
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.
zwaps 7y ago
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!
- Symmetry 7y ago
  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.
thepete2 7y ago
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 :)
- kragen 7y ago
  He was Kazakh, not Arab, wasn't he?
  - kragen 7y ago
    Geographically Uzbek, ethnically Persian apparently.
- yters 7y ago
  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.
  - csomar 7y ago
    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.
    - dragandj 7y ago
      They seem to be wrong about that “last” prophet thing, since everybody knows about Joseph Smith, who came after Monammed.
      - yters 7y ago
        Hey, what about Sun Moon? And there is a new Dalai Llama each generation!
  - thaumasiotes 7y ago
alpha0mega 7y ago
Most of it was based on translated works from Indian, Europeans conveniently (or out of ignorance) forget that.
- kragen 7y ago
  Much of it was, yes, but there were also translated works from Greek.
- lappet 7y ago
  The same author has a pretty detailed page on Indian mathematics: http://www-history.mcs.st-andrews.ac.uk/Indexes/Indians.html http://www-history.mcs.st-andrews.ac.uk/Indexes/Indians.html
  - lappet 7y ago
    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/index.html http://www-history.mcs.st-andrews.ac.uk/Projects/Pearce/inde...
- wozniacki 7y ago
  I've heard of this before. Could you elaborate on those translated works? Perhaps cite some works that were of well known Indian origin?
  - kragen 7y ago
    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 https://en.m.wikipedia.org/wiki/Indian_mathematics
- newyankee 7y ago
  Indeed, at this point i feel it is willful ignorance in many cases. https://en.wikipedia.org/wiki/Indian_mathematics#Vedic_period https://en.wikipedia.org/wiki/Indian_mathematics#Vedic_perio...
namirez 7y ago
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 https://en.wikipedia.org/wiki/Muhammad_ibn_Musa_al-Khwarizmi [2] https://en.wikipedia.org/wiki/Al-Karaji https://en.wikipedia.org/wiki/Al-Karaji [3] https://en.wikipedia.org/wiki/Omar_Khayyam https://en.wikipedia.org/wiki/Omar_Khayyam [4] https://en.wikipedia.org/wiki/Sharaf_al-D%C4%ABn_al-%E1%B9%AC%C5%ABs%C4%AB https://en.wikipedia.org/wiki/Sharaf_al-D%C4%ABn_al-%E1%B9%A...
- csomar 7y ago
  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.
  - et-al 7y ago
    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.
    - csomar 7y ago
      > 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.
      - vinay427 7y ago
        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.
nobrains 7y ago
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 https://en.m.wikipedia.org/wiki/Islamic_views_on_evolution
- emilsedgh 7y ago
  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."
  - FabHK 7y ago
    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).
    - emilsedgh 7y ago
      A bit more from this fascinating topic: https://en.wikipedia.org/wiki/Muqaddimah#Biology https://en.wikipedia.org/wiki/Muqaddimah#Biology It seems like he had a fully formed theory which is pretty accurate.
      - FabHK 7y ago
        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.
booboolayla 7y ago
Let's not forget that "Islamic Golden Age" is a misnomer that became current in recent decades after Ummah's push to normalize Islam in the West. Islam was never conducive to science and never progressive, despite some Muslims contributing to science and progress. Also, Islam is not to be praised for "preserving our scientific and cultural knowledge" - Islam never preserved any previous cultural or scientific knowledge, wherever it went it destroyed any mention of previous religions and cultures.
rohitupadhyay 7y ago
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
- mda 7y ago
  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.
  - wornohaulus 7y ago
    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..
    - mda 7y ago
      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.
- sabas123 7y ago
  Do you have any source for this?
Hitton 7y ago
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.
deleted 7y ago
[deleted]
La-ang 7y ago
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
GSHF2J32nBpb 7y ago
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 THEREFORE: ::: 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.

135 points by lioeters 7y ago

> 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.

User23 7y ago

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.

jgalt212 7y ago

At least it's not Muslim Math! /s https://www.youtube.com/watch?v=embMAtagQiU https://www.youtube.com/watch?v=embMAtagQiU

droithomme 7y ago

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.

mda 7y ago
Arabic, Turkic, Persian, Moors.

austincheney 7y ago

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.

zwaps 7y ago

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!

Symmetry 7y ago
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.

thepete2 7y ago

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 :)

kragen 7y ago
He was Kazakh, not Arab, wasn't he?
- kragen 7y ago
  Geographically Uzbek, ethnically Persian apparently.
yters 7y ago
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.
- csomar 7y ago
  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.
  - dragandj 7y ago
    They seem to be wrong about that “last” prophet thing, since everybody knows about Joseph Smith, who came after Monammed.
    - yters 7y ago
      Hey, what about Sun Moon? And there is a new Dalai Llama each generation!
- thaumasiotes 7y ago

alpha0mega 7y ago

Most of it was based on translated works from Indian, Europeans conveniently (or out of ignorance) forget that.

kragen 7y ago
Much of it was, yes, but there were also translated works from Greek.
lappet 7y ago
The same author has a pretty detailed page on Indian mathematics: http://www-history.mcs.st-andrews.ac.uk/Indexes/Indians.html http://www-history.mcs.st-andrews.ac.uk/Indexes/Indians.html
- lappet 7y ago
  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/index.html http://www-history.mcs.st-andrews.ac.uk/Projects/Pearce/inde...
wozniacki 7y ago
I've heard of this before. Could you elaborate on those translated works? Perhaps cite some works that were of well known Indian origin?
- kragen 7y ago
  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 https://en.m.wikipedia.org/wiki/Indian_mathematics
newyankee 7y ago
Indeed, at this point i feel it is willful ignorance in many cases. https://en.wikipedia.org/wiki/Indian_mathematics#Vedic_period https://en.wikipedia.org/wiki/Indian_mathematics#Vedic_perio...

namirez 7y ago

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 https://en.wikipedia.org/wiki/Muhammad_ibn_Musa_al-Khwarizmi [2] https://en.wikipedia.org/wiki/Al-Karaji https://en.wikipedia.org/wiki/Al-Karaji [3] https://en.wikipedia.org/wiki/Omar_Khayyam https://en.wikipedia.org/wiki/Omar_Khayyam [4] https://en.wikipedia.org/wiki/Sharaf_al-D%C4%ABn_al-%E1%B9%AC%C5%ABs%C4%AB https://en.wikipedia.org/wiki/Sharaf_al-D%C4%ABn_al-%E1%B9%A...

csomar 7y ago
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.
- et-al 7y ago
  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.
  - csomar 7y ago
    > 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.
    - vinay427 7y ago
      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.

nobrains 7y ago

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 https://en.m.wikipedia.org/wiki/Islamic_views_on_evolution

emilsedgh 7y ago
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."
- FabHK 7y ago
  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).
  - emilsedgh 7y ago
    A bit more from this fascinating topic: https://en.wikipedia.org/wiki/Muqaddimah#Biology https://en.wikipedia.org/wiki/Muqaddimah#Biology It seems like he had a fully formed theory which is pretty accurate.
    - FabHK 7y ago
      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.

booboolayla 7y ago

Let's not forget that "Islamic Golden Age" is a misnomer that became current in recent decades after Ummah's push to normalize Islam in the West. Islam was never conducive to science and never progressive, despite some Muslims contributing to science and progress. Also, Islam is not to be praised for "preserving our scientific and cultural knowledge" - Islam never preserved any previous cultural or scientific knowledge, wherever it went it destroyed any mention of previous religions and cultures.

rohitupadhyay 7y ago

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

mda 7y ago
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.
- wornohaulus 7y ago
  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..
  - mda 7y ago
    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.
sabas123 7y ago
Do you have any source for this?

Hitton 7y ago

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.

deleted 7y ago

[deleted]

La-ang 7y ago

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

GSHF2J32nBpb 7y ago

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 THEREFORE: ::: 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.