[olooney]

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]

> 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-wh...

Edit: Fixed a location.

[steve19]

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]

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-a...

[Chathamization]

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."

[roboys]

The dark ages also saw a huge disparity in education between the East and the West.

Until the 15th century less than 5 people in Europe could do long division. For comparison, Aryabhatta discovered calculus in 5th century India and Madhava made large contributions in the 13th century (Newton/Leibniz were wrongly credited for similar work many years later).

[leereeves]

The way I heard it, Aryabhatta and those who followed discovered some of the ideas behind calculus and a few useful results, but not calculus itself, neither the basic ideas like derivatives and integrals nor the vast conclusions that followed from those.

[Retric]

> Until the 15th century less than 5 people in Europe could do long division.

That’s wildly inaccurate. Arithmetic was very much a subject at several schools with the addition, subtraction, multiplication, and division all being taught. https://en.m.wikipedia.org/wiki/Quadrivium

Long division being difficult in Roman numerals is one of the reasons for the switch.

[breck]

Curious if you have any sources? I've never seen a data driven case that such a thing as the "dark ages" ever happened.

[Keysh]

There's an excellent book on the subject called The Fall of Rome and the End of Civilization, by Bryan Ward-Perkins. It includes a detailed overview of the archeological evidence, which shows a very clear and dramatic decline in the economy and living standards -- and some areas of technology -- between circa 350 and 600 in the Western Empire. (And the recovery afterwards took centuries.) The Eastern Empire, interestingly, doesn't show any signs of a similar decline until the 7th Century.

For example, peasant households in Italy at the height of the empire had a wide variety of well-made pottery, some of it originating from production centers hundreds of miles away, along with tiled roofs; after the collapse, the variety and quality of pottery was greatly reduced, and tiled roofs disappear. (Tiled roofs provide better protection against rain, are less flammable, and require less maintenance and rebuilding than wooden shingles or thatch; but they also require large kilns, lots of clay and fuel, and a good transportation network.)

And ice cores from Greenland show extensive metalworking going on in Western Europe (in the form of copper and lead pollution carried through the air) during the Roman Empire; after the collapse of the Western Empire, the pollution levels don't return to Roman-era values until the 16th Century.

[ghaff]

Another source, in addition to the one cited by Keysh, is Social Development by Ian Morris which goes into some more depth on the data he used in Why the West Rules--for Now.

http://pzacad.pitzer.edu/~lyamane/ianmorris.pdf

Across a wide set of measures, there was a significant decline of the West after the fall of the Roman Empire.

[atroche]

This is an excellent read: https://slatestarcodex.com/2017/10/15/were-there-dark-ages/

[goto11]

It is actually the other way around. The original meaning by Petrarch was not about the lack of historical source material. He did mean "bad/ignorant times".

[wolfgke]

> 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.

Relevant (even though considered as pseudoscience):

> https://en.wikipedia.org/w/index.php?title=New_Chronology_(F...

[cptskippy]

His point is that most Western history lessons completely ignore everything but Western Europe during that time frame and present a view of history that nothing was happening globally of any importance.

That really was my experience growing up in Western education. My understanding was that history focused on the important things and it wasn't until much later in life that I learned there was a lot happening globally after the fall of the Roman empire before the European renaissance.

After the USA was established, US history lessons completely ignore the rest of the globe until the early 20th century. I only learned yesterday that Italy wasn't a country until 1861 and I am almost 40.

[aisofteng]

>most Western history lessons completely ignore everything but Western Europe

That’s because they’re Western history lessons. I had world history as a separate class in high school.

[cptskippy]

I had History, American History and World History but never Western History.

[novacole]

Yes, but Rome isn’t Western Europe. So western Europe’s entire history is a “dark age” before the Age of Enlightenment.

(Edit: incorrectly said renaissance instead of Age of Enlightenment... the renaissance wasn’t Western European either)

[fsloth]

I don't know what you mean, but:

1. Roman empire dominion included, but did not limit to what we now refer to as Western Europe...

2... of whose languages are either mostly descended from, or heavily influenced by Latin...

3. ... And where the dominant religion is still the Roman state religion. Which was lorded over by the Roman state church for a thousand years before an angry German monk suggested that this was really weird and could we keep the book and get rid of the pope.

So, when you say Western Europe is not Rome, you need to say how it isn't, since there are quite a few things that link this geographic area culturally very strongly to that ancient empire.

[jonnybgood]

> when you say Western Europe is not Rome

To be fair, they said Rome is not Western Europe, which is true. Rome didn’t have cultural affinity with Western Europeans. Rome’s cultural affinity flowed to the east with the Greeks et al.

[gingabriska]

Romans culturally ate less meat and frowned upon their Northern Germanic Tribes who almost always ate meat. They were more frugal in their way of life.

The Germanic Tribes were also taller and were acknowledged by Romans as formidable warrior.

Culturally tho, Romans were South Europeans and assimilated what we call South Italy and Greece now.

They also captured parts of middle east but culturally they never became Romans.

>3. ... And where the dominant religion is still the Roman state religion. Which was lorded over by the Roman state church for a thousand years before an angry German monk suggested that this was really weird and could we keep the book and get rid of the pope.

There were other Pagan religions at the time and in middle east Jews didn't accept Roman state religion.

But then again, people born in Roman Empire got Roman citizenship on Birth so it didn't matter what you were culturally or religiously or tribe/ethnicity.

[DiogenesKynikos]

> But then again, people born in Roman Empire got Roman citizenship on Birth

That depends on when you're talking about. Until Caracalla made all free subjects citizens in 212 AD (supposedly so that he could tax them more heavily),[1] Roman citizenship was restricted and highly coveted.

> There were other Pagan religions at the time and in middle east Jews didn't accept Roman state religion.

From the late 300s onwards, pagans were persecuted in the Roman Empire. Nicene Christianity was the state religion. Also, Jews lived throughout the empire, not just in the Middle East. From about the 1st century AD onwards, there were more Jews living outside of the land of Israel than within it.

1. https://en.wikipedia.org/wiki/Constitutio_Antoniniana

[tempguy9999]

> people born in Roman Empire got Roman citizenship on Birth

I assume 'people' excluded slaves?

[boomboomsubban]

For the period being described, the Roman Empire did not include Western Europe, they did not speak Latin nor did they view the Papacy as the head of their religion. Yet they were still the Roman Empire. That's why Western Europe is not Rome.

[sk5t]

What's this about "Rome isn’t Western Europe"--have you consulted a map of the Roman empire?

[boomboomsubban]

Have you looked at the population spread of the Roman Empire? Rome had people, the rest of the empire was predominantly to the East/South. Rome was Mediterranean, not Western European.

[kgwgk]

What is your definition of “Western European” precisely?

https://aaron7roberts.files.wordpress.com/2015/04/roman_empi...

https://en.m.wikipedia.org/wiki/Demography_of_the_Roman_Empi... also shows larger populations in the “Latin West” than in the “Greek East”.

[kgwgk]

> renaissance wasn’t Western European

Was it Byzantine?

[caiocaiocaio]

That's like saying the Tang or Song eras didn't exist because they don't apply to Western Europe.

[notinpersia]

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-...

[shademaan]

I mean the first result of that search for me says it was created in Baghdad, but by a Persian mathematician

[notinpersia]

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.

[Keysh]

No, Baghdad was located in the heart of the former Persian (Sassanian) Empire, a mere 35 km from the site of the Sassanian capital (Ctesiphon). Although the whole area gradually became Arabized, at the time it was still significantly Persian.

(Frankly, I doubt we know where Al-Khwarizmi was educated. We know he was originally from what's now Uzbekistan, and that he ended up in Baghdad, but not much more than that.)

[notinpersia]

He wrote his treatise on Algebra in Arabic because he was educated in Arabic and the language of science was Arabic in that area and at that time. AlNassirya in Baghdad was the most advanced educational institution in the world at the time. I don’t know if he was a student or teacher there but it also has an Arabic name and was built by an Islamic caliph. The same with mathematicians from India traveling all the way to Baghdad to tell the caliph about their invention of zero. Persians has many amazing contributions to science and math but Persia itself has none. Like the Romans, they were war mongers and Their culture was toxic to science.

[csomar]

> No, Baghdad was located in the heart of the former Persian (Sassanian) Empire, a mere 35 km from the site of the Sassanian capital (Ctesiphon).

Mesopotamia was conquered by Arabs in 633. Al-Khwarizmi was born in 780. Most the Arabic lands were gained by conquest. Even modern day Yemen and Oman were not under Arabic influence if you go back far enough. The "original" arabs spread from Hijaz and Najd.

edit: from wikipedia

> The Abbasid Caliphate first centred its government in Kufa, modern-day Iraq, but in 762 the caliph Al-Mansur founded the city of Baghdad, near the ancient Sasanian capital city of Ctesiphon.

My guess is that families from the Sassanid have immigrated to the new city and as a result Al-Khwarizmi was born there.

[BalinKing]

> 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]

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.

[empath75]

Why can’t you just include both. We talk about Italian Americans and African Americans or whatever all the time when we talk about accomplishment. He was a Persian who lived in an Arab empire.

[ominous]

In what way does the characterization of an European period dismiss historical periods elsewhere?

[theworld572]

It doesn't, some people just like to get offended by things.

[mort96]

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]

Slatestarcodex has a good roundup of different arguments and metrics (world lead production):

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]

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.

[metastew]

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.

[novaRom]

> 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]

>Romans after all, which likewise produced little (not none) new math.

They had Archimedes of Syracuse

[emiliobumachar]

Archimedes was Greek, the Romans killed him.

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

[gingabriska]

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]

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.

[gingabriska]

I'd love to know why I got downvoted.

[sumitviii]

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]

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.