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Romans aren't the outlier here. Most ancient civilizations had a similar level of accomplishment; a one or two outstanding mathematicians every century, a few p

Romans aren't the outlier here. Most ancient civilizations had a similar level of accomplishment; a one or two outstanding mathematicians every century, a few practical applications, some new rules of thumb. We did have a dark age, after the Romans after all, which likewise produced little (not none) new math. The question should rather be, what made the Greeks (and, later, others who adopted their deductive, axiomatic method) so exceptionally productive at mathematics? Or to paraphrase Wigner, why is Hellenistic mathematics so unreasonably effective?

crooked-v 7y ago
> We did have a dark age, after the Romans after all, which likewise produced little (not none) new math. Use of the term "dark age" is both dramatically inaccurate in many ways [1] and totally elides everything that happened outside of Europe, such as the establishment of algebra as an independent field of mathematical study (AD 800 in Baghdad), the creation of algebraic geometry (AD 1070 in Persia), and the discovery of ways to solve high-order polynomial equations (approximately AD 1200 in India and China). [1]: https://slate.com/human-interest/2015/01/medieval-history-why-are-the-middle-ages-often-characterized-as-dark-or-less-civilized.html https://slate.com/human-interest/2015/01/medieval-history-wh... Edit: Fixed a location.
- notinpersia 7y ago
  Wrong on Algebra’s origin. Often people will say Persia but it was in Ancient Greece and Baghdad. And the latter is not Persia and was certainly not under Persian occupation during the time of Alkhawarizmi (who is also credited for the invention of the algorithm or at least it was named after him.) The original title of his book that coined the term Algebra is Al Jabr wal Muqabala (casting and equation) Just Google it: where was algebra invented? https://www.google.com/search?q=who.invented+algebra&ie=UTF-8&oe=UTF-8&hl=en-us&client=safari https://www.google.com/search?q=who.invented+algebra&ie=UTF-...
  - deleted 7y ago
    [deleted]
  - shademaan 7y ago
    I mean the first result of that search for me says it was created in Baghdad, but by a Persian mathematician
    - notinpersia 7y ago
      A Muslim Persian, and Baghdad was the melting pot of the world at that time. It’s like saying a German physicist in Princeton, NJ, which is to say that America not Germany was the place where the work was valued and promoted. Likewise, Alkhawarizmi was educated in Baghdad (not in Persia) and wrote his book on Algebra in Arabic. He was not educated in Persia and he did not write his book in Farsi. If we put ethnicity ahead of national origin America can’t claim anything to its name. Period.
      - BalinKing 7y ago
        > If we put ethnicity ahead of national origin America can’t claim anything to its name. Period. It's silly to put ethnicity ahead of national origin, though, since one of America's biggest qualities it that it is a melting pot. This feels like saying "If we put learning curve ahead of type safety Haskell can't claim anything to its name. Period." It's true, but kinda vacuous.
        asveikau 7y ago
        But that particular super-famous German who lived in Princeton, NJ is also recognized as a German physicist. To say he was already quite accomplished when he left Europe would be an understatement. Personally, I think if an immigrant of descendant of immigrants invents something prominent, it is fair for both countries to be proud of the accomplishment, and share that enthusiasm. It doesn't, or shouldn't hurt anyone. If anything, you are affirming accomplishment, not putting other people down.
- steve19 7y ago
  Yes but the Dark Age specifically refers to Western Europe, in much the same way the disastrous impact of the Mongol Empire on Islamic scholarship, for example the burning of libraries during or after the Siege of Baghdad, barely touched Western Europe. Chances are the Mongols destroyed some advanced mathematics that took centuries to rediscover.
  - kennywinker 7y ago
    The dark ages simply refers to the loss of texts. There are few surviving texts from that period, so it is “dark”. Later the term was re-branded to mean “bad time when no new science was done” but that’s a viewpoint that doesn’t fit the facts. Source (a very enjoyable read at that!): https://going-medieval.com/2017/05/26/theres-no-such-thing-as-the-dark-ages-but-ok/ https://going-medieval.com/2017/05/26/theres-no-such-thing-a...
    - Chathamization 7y ago
      I mean, there definitely seems to have been a large decline in population, economic output, political cohesion, urbanization, record keeping, trade, etc., in much of the former Roman world following the fifth/sixth century. I suppose it's a value judgement on whether one considers that a "bad time."
      - breck 7y ago
        Curious if you have any sources? I've never seen a data driven case that such a thing as the "dark ages" ever happened.
        atroche 7y ago
        This is an excellent read: https://slatestarcodex.com/2017/10/15/were-there-dark-ages/ https://slatestarcodex.com/2017/10/15/were-there-dark-ages/
        FranzFerdiNaN 7y ago
- deleted 7y ago
  [deleted]
- caiocaiocaio 7y ago
  That's like saying the Tang or Song eras didn't exist because they don't apply to Western Europe.
- ominous 7y ago
  In what way does the characterization of an European period dismiss historical periods elsewhere?
  - theworld572 7y ago
    It doesn't, some people just like to get offended by things.
    - mort96 7y ago
      I find that assuming people who find something to be objectionable just do it because the "like to get offended by things" is a bit unproductive. At least hear them out and decide whether the explanation makes sense or not.
- ralfd 7y ago
  Slatestarcodex has a good roundup of different arguments and metrics (world lead production): https://slatestarcodex.com/2017/10/15/were-there-dark-ages/ https://slatestarcodex.com/2017/10/15/were-there-dark-ages/ > Although I sympathize with the feelings behind both positions, I say the Dark Ages happened. I think the best evidence we have suggests the fall of Rome (and the period just before) was associated with several centuries of economic and demographic decline, only reaching back to their classical level around 1000 AD. I think it was also associated with a broader intellectual and infrastructure decline, which in some specific ways and some specific fields didn’t reach back up to its Roman level until the Renaissance. I think that common sense – the sense you get when you treat the question of the Dark Age the same as any other question, and try to avoid isolated demands for rigor – says that qualifies for the phrase “Dark Age”.
KON_Air 7y ago
I "belivie" it is effect of cumulative knowledge from all their trade partners, who when put together is pretty much everyone on the planet at the time, since they were physically at the center of trade routes.
sumitviii 7y ago
Or maybe its far too soon for us to say if the West (or the Greeks who you guys almost worship as a culture) has produced more than 1 or 2 great mathematicians? Maybe the peoples of the future will only consider one particular mathematician as the relevant one? Maybe like Turing, because most likely computers will become a greater part of the world at large? Maybe we see programmers the way people used to see scribes some time back?
- Godel_unicode 7y ago
  Hard to believe that, if you were to do the absurd reductionist exercise of crediting math to one person, it would be anyone but Gauss.
novaRom 7y ago
> We did have a dark age ... which likewise produced little (not none) new math. Wrong! If you mean times between 500 and 1200: how about arabs, iranians, indians, chinese? Algebra, Negative numbers, 0123456789 system of writing?
gingabriska 7y ago
>Romans after all, which likewise produced little (not none) new math. They had Archimedes of Syracuse
- gingabriska 7y ago
  I'd love to know why I got downvoted.
- emiliobumachar 7y ago
  Archimedes was Greek, the Romans killed him. https://en.m.wikipedia.org/wiki/Archimedes https://en.m.wikipedia.org/wiki/Archimedes
  - gingabriska 7y ago
    He was killed in an error tho but lived in Roman Empire. Many Greeks were part of Roman empire, what difference does it make?
    - nwallin 7y ago
      The Roman empire was, as you say, an empire. Archimedes spoke, read, wrote, and taught in Greek. He wore a beard, which was unfashionable in Rome. His neighbors, friends, and family all considered themselves Greek. There was a myriad of other cultures within Rome's borders with completely different societies. If a Puerto Rican living in Puerto Rico invented something, we'd call it a Puerto Rican invention. If a European immigrated to the US, integrated themselves into the culture by learning English, adopting American cultural norms, and taking the oath of citizenship, we'd call that an American invention, despite the fact that both of them carry a passport that says "United States of America" on it.
metastew 7y ago
Pythagoras could be the reason why. He founded a school(?) and many famous philosophers and mathematicians of that time period were offshoots from that school, but that's based on a hazy recollection of my teenage interests in ancient Greek history.

crooked-v 7y ago

> We did have a dark age, after the Romans after all, which likewise produced little (not none) new math. Use of the term "dark age" is both dramatically inaccurate in many ways [1] and totally elides everything that happened outside of Europe, such as the establishment of algebra as an independent field of mathematical study (AD 800 in Baghdad), the creation of algebraic geometry (AD 1070 in Persia), and the discovery of ways to solve high-order polynomial equations (approximately AD 1200 in India and China). [1]: https://slate.com/human-interest/2015/01/medieval-history-why-are-the-middle-ages-often-characterized-as-dark-or-less-civilized.html https://slate.com/human-interest/2015/01/medieval-history-wh... Edit: Fixed a location.

notinpersia 7y ago
Wrong on Algebra’s origin. Often people will say Persia but it was in Ancient Greece and Baghdad. And the latter is not Persia and was certainly not under Persian occupation during the time of Alkhawarizmi (who is also credited for the invention of the algorithm or at least it was named after him.) The original title of his book that coined the term Algebra is Al Jabr wal Muqabala (casting and equation) Just Google it: where was algebra invented? https://www.google.com/search?q=who.invented+algebra&ie=UTF-8&oe=UTF-8&hl=en-us&client=safari https://www.google.com/search?q=who.invented+algebra&ie=UTF-...
- deleted 7y ago
  [deleted]
- shademaan 7y ago
  I mean the first result of that search for me says it was created in Baghdad, but by a Persian mathematician
  - notinpersia 7y ago
    A Muslim Persian, and Baghdad was the melting pot of the world at that time. It’s like saying a German physicist in Princeton, NJ, which is to say that America not Germany was the place where the work was valued and promoted. Likewise, Alkhawarizmi was educated in Baghdad (not in Persia) and wrote his book on Algebra in Arabic. He was not educated in Persia and he did not write his book in Farsi. If we put ethnicity ahead of national origin America can’t claim anything to its name. Period.
    - BalinKing 7y ago
      > If we put ethnicity ahead of national origin America can’t claim anything to its name. Period. It's silly to put ethnicity ahead of national origin, though, since one of America's biggest qualities it that it is a melting pot. This feels like saying "If we put learning curve ahead of type safety Haskell can't claim anything to its name. Period." It's true, but kinda vacuous.
      - asveikau 7y ago
        But that particular super-famous German who lived in Princeton, NJ is also recognized as a German physicist. To say he was already quite accomplished when he left Europe would be an understatement. Personally, I think if an immigrant of descendant of immigrants invents something prominent, it is fair for both countries to be proud of the accomplishment, and share that enthusiasm. It doesn't, or shouldn't hurt anyone. If anything, you are affirming accomplishment, not putting other people down.
steve19 7y ago
Yes but the Dark Age specifically refers to Western Europe, in much the same way the disastrous impact of the Mongol Empire on Islamic scholarship, for example the burning of libraries during or after the Siege of Baghdad, barely touched Western Europe. Chances are the Mongols destroyed some advanced mathematics that took centuries to rediscover.
- kennywinker 7y ago
  The dark ages simply refers to the loss of texts. There are few surviving texts from that period, so it is “dark”. Later the term was re-branded to mean “bad time when no new science was done” but that’s a viewpoint that doesn’t fit the facts. Source (a very enjoyable read at that!): https://going-medieval.com/2017/05/26/theres-no-such-thing-as-the-dark-ages-but-ok/ https://going-medieval.com/2017/05/26/theres-no-such-thing-a...
  - Chathamization 7y ago
    I mean, there definitely seems to have been a large decline in population, economic output, political cohesion, urbanization, record keeping, trade, etc., in much of the former Roman world following the fifth/sixth century. I suppose it's a value judgement on whether one considers that a "bad time."
    - breck 7y ago
      Curious if you have any sources? I've never seen a data driven case that such a thing as the "dark ages" ever happened.
      - atroche 7y ago
        This is an excellent read: https://slatestarcodex.com/2017/10/15/were-there-dark-ages/ https://slatestarcodex.com/2017/10/15/were-there-dark-ages/
        FranzFerdiNaN 7y ago
deleted 7y ago
[deleted]
caiocaiocaio 7y ago
That's like saying the Tang or Song eras didn't exist because they don't apply to Western Europe.
ominous 7y ago
In what way does the characterization of an European period dismiss historical periods elsewhere?
- theworld572 7y ago
  It doesn't, some people just like to get offended by things.
  - mort96 7y ago
    I find that assuming people who find something to be objectionable just do it because the "like to get offended by things" is a bit unproductive. At least hear them out and decide whether the explanation makes sense or not.
ralfd 7y ago
Slatestarcodex has a good roundup of different arguments and metrics (world lead production): https://slatestarcodex.com/2017/10/15/were-there-dark-ages/ https://slatestarcodex.com/2017/10/15/were-there-dark-ages/ > Although I sympathize with the feelings behind both positions, I say the Dark Ages happened. I think the best evidence we have suggests the fall of Rome (and the period just before) was associated with several centuries of economic and demographic decline, only reaching back to their classical level around 1000 AD. I think it was also associated with a broader intellectual and infrastructure decline, which in some specific ways and some specific fields didn’t reach back up to its Roman level until the Renaissance. I think that common sense – the sense you get when you treat the question of the Dark Age the same as any other question, and try to avoid isolated demands for rigor – says that qualifies for the phrase “Dark Age”.

KON_Air 7y ago

I "belivie" it is effect of cumulative knowledge from all their trade partners, who when put together is pretty much everyone on the planet at the time, since they were physically at the center of trade routes.

sumitviii 7y ago

Or maybe its far too soon for us to say if the West (or the Greeks who you guys almost worship as a culture) has produced more than 1 or 2 great mathematicians? Maybe the peoples of the future will only consider one particular mathematician as the relevant one? Maybe like Turing, because most likely computers will become a greater part of the world at large? Maybe we see programmers the way people used to see scribes some time back?

Godel_unicode 7y ago
Hard to believe that, if you were to do the absurd reductionist exercise of crediting math to one person, it would be anyone but Gauss.

novaRom 7y ago

> We did have a dark age ... which likewise produced little (not none) new math. Wrong! If you mean times between 500 and 1200: how about arabs, iranians, indians, chinese? Algebra, Negative numbers, 0123456789 system of writing?

gingabriska 7y ago

>Romans after all, which likewise produced little (not none) new math. They had Archimedes of Syracuse

gingabriska 7y ago
I'd love to know why I got downvoted.
emiliobumachar 7y ago
Archimedes was Greek, the Romans killed him. https://en.m.wikipedia.org/wiki/Archimedes https://en.m.wikipedia.org/wiki/Archimedes
- gingabriska 7y ago
  He was killed in an error tho but lived in Roman Empire. Many Greeks were part of Roman empire, what difference does it make?
  - nwallin 7y ago
    The Roman empire was, as you say, an empire. Archimedes spoke, read, wrote, and taught in Greek. He wore a beard, which was unfashionable in Rome. His neighbors, friends, and family all considered themselves Greek. There was a myriad of other cultures within Rome's borders with completely different societies. If a Puerto Rican living in Puerto Rico invented something, we'd call it a Puerto Rican invention. If a European immigrated to the US, integrated themselves into the culture by learning English, adopting American cultural norms, and taking the oath of citizenship, we'd call that an American invention, despite the fact that both of them carry a passport that says "United States of America" on it.

metastew 7y ago

Pythagoras could be the reason why. He founded a school(?) and many famous philosophers and mathematicians of that time period were offshoots from that school, but that's based on a hazy recollection of my teenage interests in ancient Greek history.