
Why didn't the Romans contribute much to mathematics? - curtis
https://old.reddit.com/r/AskHistorians/comments/cuu8rc/why_didnt_the_romans_contribute_much_to/
======
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...](https://slate.com/human-interest/2015/01/medieval-history-why-are-the-
middle-ages-often-characterized-as-dark-or-less-civilized.html)

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...](https://going-
medieval.com/2017/05/26/theres-no-such-thing-as-the-dark-ages-but-ok/)

~~~
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."

~~~
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.

~~~
atroche
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
Well, someone has a bone to pick with the early Middle Ages. What an angry
rant to prove that the dark ages really existed. He sometimes has a point but
in total it really is a non-historian making some weird arguments to prove
that 800AD was terrible (look at the difference in these maps! Just completely
ignore any cultural and artistic context that matter why they look the way
they do!). I’m surprised he didn’t compare Greek statues with medieval
paintings to prove his point.

------
riazrizvi
> "There was once a workman who made a glass cup that was unbreakable. So he
> was given an audience of the Emperor with his invention; he made Caesar give
> it back to him and then threw it on the floor. Caesar was as frightened as
> could be. But the man picked up his cup from the ground: it was dented like
> a bronze bowl; then he took a little hammer out of his pocket and made the
> cup quite sound again without any trouble. After doing this he thought he
> had himself seated on the throne of Jupiter, especially when Caesar said to
> him: 'Does anyone else know how to blow glass like this?' Just see what
> happened. He said not, and then Caesar had him beheaded. Why? Because if his
> invention were generally known we should treat gold like dirt. " (Satyricon
> 51)

This apocryphal story on economic incentives vs progressive incentives is as
relevant today as it was 2000 years ago.

~~~
ZhuanXia
The rise of technology was not so much the birth of new capacities, but the
removal of old constraints.

China, despite a much larger and more educated population, did not spark the
industrial revolution. Their feedback loops were too stable, their elites too
competent.

From the perspective of the old power hierarchy, the industrial revolution was
a disaster.

The nobility floated on that great cruel ocean first charted by Malthus, an
ocean which began to boil.

~~~
toasterlovin
How much of the Chinese/Japanese vs Western Europe dichotomy in term of
technological development do you think is due to geography (Europe has been
fractured, politically, for all of history, mostly due to geography, I think,
whereas China and Japan have both been comparatively unified and stable for
thousands of years). My thinking is that this has a lot to do with how
European elites were not able to prevent accumulation of new technology and
ideas, whereas Chinese and Japanese elites were (and did).

And then I guess a follow up question would be: do you have an opinion on why
the scientific revolution happened in Western Europe and not in the
Mediterranean, which is similarly fractured, but also better situated for
exchange of technology and ideas (being connected to Asia and Western Europe).

~~~
dredmorbius
The general form of this question, or at least one version of it ("why did the
Industrial Revolution occur in England and not in China, which had developed a
vastly larger set of technologies far earlier") is known as the _Needham
Question_ , after sinologist Joseph Needham, author of _Science and
Civilisation in China_ , an epic 30+ volume work covering Chinese invention
and technology, begun in 1954 _and still in process_. (Needham himself died in
the 1990s.) There's a fascinating Wikipedia article on the topic, and if you
can find a copy of the completed volumes (many college/university libraries
have it), it's a treat.

The general question of the how, why, and when of the Industrial Revolution
has fascinated historians, technologists, and economists for ages. Karl
Polanyi's _The Great Transformation_ , Gregory Clark's _A Farewell to Alms_
,[1] and numerous other works address this.

Geographic determinism has become tremendously unpopular among historians,
though elements of it carry weight with me. Of China and Japan vs. Europe and
Britain, there are several factors:

\- Political unity vs. disunity, as you note.

\- Crops. Wheat is suitable to individual, independent farming. Rice requires
community coordination.

\- Hydrology. The Chinese empire effectively started as a large civil water
works management bureaucracy. Outside Egypt and Rome's aqueducts, there was no
similarly-scoped coordination in the West.

\- Watersheds. Europe's rivers diverge from the interior, China's flow in
parallel to relatively proximate mouths. Political boundaries in Europe have
typically conformed reasonably well to watersheds, though allied / opposed
alignments have changed with time. Even today, many county-level jurisdictions
correspond to local watersheds. And in both China and Europe, virtually all
heavy transport until modern times was along rivers or canals, if not sea or
lakes.

\- While Britain and Japan are both large islands near continental empires,
the geology is utterly different: sedimentary with vast coal deposits, and
volcanic with virtually no fossil fuels. While each island was tremendously
politically stable, resistant to invasions, England could fuel growth of iron,
glass, and steam industries, Japan could not. England was generally relatively
wealthy, Japan was one of the poorest countries prior to industrialisation.

\- China has long been politically unified (if subject to occasional
invasions), Europe has long been politically fractured. China could shut down
innovation and foreign trade. No such global policies were possible in Europe.

Within Europe, the distribution of coal is almost wholly in the north: Wales,
England, a tiny patch in northern Spain, some in France, and heavy deposits in
Germany and Poland. Southern Germany is very fuel-poor, excepting petroleum
(not very handy in pre-industrial times) in Silesia, Romania, and Baku
(Russia). Coal fueled metalurgy, glassmaking, and eventually steam power in
England.

England's flat terrain and ready access to the sea (no part of Great Britain
is more than 60 miles from the coast) made transport of the bulky fuel by ship
viable. Overland transport wasn't an option -- firewood fuel locally gathered
was far more attractive. A similar situation existed in the US where coal
didn't overtake wood as a fuel until the 1880s. Rail transport finally made
hauling coal from mountain-based mines in Apallachia possible, but benefited
greatly from advances in steelmaking (Bessemer process, 1860s), allowing
stronger, less fracture-prone rails, and stronger, more powerful locomotives.
Rail is effectively canals-on-land, the first truly viable overland freight
tansport mode.

There are many other factors, there's tremendous dispute over all of this, and
as I've hinted, there's a large literature. I obviously find the geological
argument at least plausible in many regards. Given the lack of testability,
final adjudication of the question is unlikely.

________________________________

Notes:

1\. Clark teaches a course at UC Davis on economic history before the
Industrial Revolution, which touches somewhat on this (the principle focus is
Europe). A corrected playlist for the YouTube lectures, in proper order, is
here: [https://pastebin.com/raw/bgKkGyjt](https://pastebin.com/raw/bgKkGyjt)

~~~
vidarh
To add to your points on both flat terrain and waterways in England: in fact
the current railway that runs a few blocks from my house runs along what used
to be a canal dug from the Thames to enable transport. It was one of the last
ones to open before the railway took over (and the operator went bankrupt and
sold the land to a railway company that drained it and used the conveniently
flattened land for more rails)

A local lake used to be an artificial reservoir to keep the canal filled.

The UK is full of canals that were viable to dig because of that flat terrain.

So large parts of England that were not reachable by river are still reachable
by canal boat, and even more used to be before many of the canals were filled
in or drained when no longer commercially viable for transport.

~~~
dredmorbius
And, researching just now: there are a few canals in Japan, though even a
_modern_ listing is short:

[https://en.wikipedia.org/wiki/Category:Canals_in_Japan](https://en.wikipedia.org/wiki/Category:Canals_in_Japan)

Among the earliest is the Takase River canal, in Kyoto, 9.7 kilometers, dug in
1611. Most of the remainder date to the 19th or 20th centuries.

[https://en.wikipedia.org/wiki/Takase_River](https://en.wikipedia.org/wiki/Takase_River)

The Tatsumi Canal was constructed in 1623, 11 km.

[https://en.wikipedia.org/wiki/Tatsumi_Canal](https://en.wikipedia.org/wiki/Tatsumi_Canal)

Contrast the UK:

[https://en.wikipedia.org/wiki/Canals_of_the_United_Kingdom](https://en.wikipedia.org/wiki/Canals_of_the_United_Kingdom)

[https://en.wikipedia.org/wiki/List_of_canals_of_the_United_K...](https://en.wikipedia.org/wiki/List_of_canals_of_the_United_Kingdom)

------
WalterBright
I suspect the roman numeral system played a bigger role in retarding roman
mathematics than the reddit postings suggest.

After all, it's fairly well known that the characteristics of a particular
programming language have a strong influence on the way the language is used.
(For instance, people don't do OOP or FP using C.)

~~~
jacobolus
Roman numerals are profoundly misunderstood by most people today, whose main
knowledge about them is that various authority figures use them as an example
of an awkward and cumbersome precursor to Hindu–Arabic numerals, backed up by
a slight bit of personal experience learning to encode/decode Roman numerals,
which is difficult because nobody today has any substantial amount of practice
at it.

Roman numerals are a recording tool, not a calculating tool. Romans did
calculations using pebbles or other counters on a counting board. Roman
numerals are just a way of recording the state of a counting board
before/after performing some algorithm. The goal of them is to be as direct
and faithful a record of the counting board state as possible.

~~~
WalterBright
> Romans did calculations using pebbles or other counters on a counting board.

I think you just made my point :-)

Have fun doing long division that way.

~~~
jacobolus
You can do long division just fine on a counting board, though it is unclear
if people had developed something like the modern elementary school division
algorithm 2000+ years ago.

We don’t really know much about people’s calculation algorithms, because they
were an oral tradition not written down, and only a very small number of
counting boards (e.g. made of marble) survived; others were presumably made of
leather, wood, cloth, lines scratched in the dirt, ....

Japanese soroban experts handily beat westerners at doing division, in both
speed and accuracy. There is no reason to believe that calculation experts of
the ancient world would not have been comparably competent.

~~~
WalterBright
> You can do long division just fine on a counting board

I searched around a bit, and didn't find much of anything you could do with a
counting board beyond division.

~~~
mlyle
Counting boards / the abacus are about as good as you get for calculating
methods until mechanical calculators and logarithmic slide rules. So it's not
really fair to say the Romans had a disadvantage here when no one had anything
better. (Granted, the wire abacus was faster than counting boards / jetons).

------
w8rbt
I was under the impression that the Romans were more applied/practical and
less theoretical, but I may be wrong. I got that notion from a professor I had
years ago who was fond of saying, "The Romans built roads. The Greeks talked
about building roads." Has anyone else ever heard that saying?

~~~
riffraff
I've heard "Greeks were mathematicians, Romans were engineers", which conveys
the same concept.

------
mjfl
They probably innovated in math, in some form of risk modeling or something,
but no single fancy intellectual wrote it all down:

[https://priceonomics.com/how-maritime-insurance-built-
ancien...](https://priceonomics.com/how-maritime-insurance-built-ancient-
rome/)

------
boomboomsubban
I'm not an expert here, but wasn't the development of "zero" a rather
monumental leap that was required before you could advance past Greek math?
The spread into the Islamic world certainly enabled them to finally push past
the Greeks.

------
dwheeler
In general the ancient Romans were more interested in mathematical
application, instead of abstraction. I think that's true for many other
ancient civilizations as well. It's not true that the Romans didn't understand
mathematics, they were spectacular engineers. They just focused on something
different.

The Romans invented Roman numerals, and it's important to acknowledge that
this was a mathematical achievement even though we don't use them as much any
more. By putting smaller numbers in front of larger ones, they created a
number writing system where you did not have to learn a large number of
symbols yet any particular number was short and easy to write. Greek numbers
had separate symbols not only for one through nine, but for each of the
symbols 10 through 90, which meant you had to learn a lot more symbols for
just one through 99.

It's true that doing calculations with Roman numerals is a pain, especially
division, but I don't think the Romans thought this was a big deal.
Calculations were typically done using an abacus anyway, so you simply needed
a simple way to record results.

------
known
The Arabic countries led by the Muslims were the most advanced
scientists/engineers in the world, until they let the religious crazies take
over. J
[https://en.wikipedia.org/wiki/Timeline_of_science_and_engine...](https://en.wikipedia.org/wiki/Timeline_of_science_and_engineering_in_the_Islamic_world)

~~~
Sag0Sag0
I just have to object.

Early science throughout the world came about because of religion, not despite
it. Early Muslim proto scientists like Ibn Sina and Ibn Khaldun explicitly did
their science through religion and were heavily involved the religious
politics of the day. This was also true also of early scientists in europe
like Issac Newton.

Also that statement implicitly kinda carries the idea that europeans took over
role of the "advancers of science" due to their tolerance and secularism. That
was certainly not the case, european christianity in the 16th and 17th
centuries was not in any way tolerant/moderate.

Similarly even if we agree that a decline occurred there are a myriad of other
factors that could potentially cause a drop in scientific output such as the
various consequences of war, the policies of the Ottoman empire, a lack of the
urbanisation that occurred in China and Europe etc.

~~~
empath75
The Pythagoreans were also a religious group, as well as the platonists who
followed them.

------
strainer
Consider the title of this famous Great work wrote later : "The Compendious
Book on Calculation by Completion and Balancing"

It has a graceful theme which is perhaps not accidental for mathematical
inspiration. The same symbolic methods, being symbolic could have been painted
as "domination and sacrificing" but that might not temper a mindset as
mathematically conducive as notions of "completion and balancing".

A cultures achievements in different areas could owe substantially to the
spectrum of mindsets which it hosts and celebrates.

~~~
sumitviii
>but that might not temper a mindset as mathematically conducive as notions of
"completion and balancing".

Or maybe what would be considered a mathematically conducive mindset is
determined by whose mathematical tradition we are following? Maybe there
exists a mathematical mindset out there where "domination and sacrificing" are
the requirement for conductivity of ideas?

~~~
strainer
It would seem to be a well kept secret branch if so

~~~
sumitviii
By out there I don't mean in the physical world, I mean in the world of
possibility.

------
29athrowaway
Paper makes you productive. Romans did not have it.

They had papyrus, parchments and wax tablets, none of them were as convenient
or affordable as paper.

The adoption of paper was what really set things in motion in Europe, the
Renaissance.

~~~
yesenadam
Paper - yet another Chinese invention, about 100AD, along with movable type
printing, about 1000AD. With gunpowder and compass, two more Chinese
inventions, Europeans navigated and conquered the world..

~~~
29athrowaway
And technology and animals from the fertile crescent, efficient crops from the
Americas, African slaves and significant military help from local groups.

A lot of merit to share.

------
Gatsky
Makes you wonder what will be said for our era in 500 years time...

~~~
markholmes
Does it? We visited the moon and created the internet in the span of one
generation. We are arguably in the most innovative scientific period in our
history.

~~~
fortran77
Probably the discovery of solid state devices and the invention of the digital
computer is more important than the "Internet"

~~~
dkersten
We will be remembered for our most important achievement: bringing high speed
access to cat pictures to the masses.

~~~
abdullahkhalids
Nope. Our most important achievement has been to create a system where smart
people spend their life trying to get people to click on ads, using morally
dubious dark-patterns.

~~~
cbHXBY1D
If I had to bet, western society will be judged for creating an industrialized
world while knowingly ignoring the effect of greenhouse gases.

~~~
juanbyrge
To be fair I think the severity of climate change has only come into
mainstream focus in the past 5-10 years. Just as one data point, when I was
shopping for a car in 2012, I did not even consider CO2 emissions. Now,
climate change is top of mind for me. I now own an electric car, stopped
eating beef, mostly eliminated travel, etc... I'm not saying this will make a
difference overall, but I imagine others feel similarly, and a lot of young
people will hopefully be in a position to work on solving some of these
problems.

~~~
FranzFerdiNaN
Thanks to fossil fuel companies like Exxon spending billions to confuse the
general public, bribe politicians and do everything else needed to spread lies
so they could keep their profits up. Exxons own research already confirmed
climate change was caused by fossil fuels in the 1970s, yet they sat on it
doing nothing.

The Kyoto Protocol was in 1997, but the US didn’t ratify it because the API
managed to influence US politicians enough to cast doubt on the problem.

------
oneepic
O/T: One real answer, and multiple bot posts, including one about removing
another real person's comment. As a person who doesn't read much Reddit, it
leaves a really strange impression.

Anyway, the top answer was still a cool read.

~~~
umanwizard
This is typical of /r/AskHistorians , not Reddit as a whole.

They have an explicit policy of removing any amateurish or unsourced answers,
in order to keep quality high.

~~~
Judgmentality
Doesn't that imply that the rest of reddit which is less heavily moderated has
more low quality comments?

~~~
umanwizard
Yes, and IMO it really does.

------
LeonB
Yeh, what have the Romans ever done for us?

[https://www.youtube.com/watch?v=Y7tvauOJMHo](https://www.youtube.com/watch?v=Y7tvauOJMHo)

------
williamDafoe
I bet it's a bitch to learn addition or multiplication using Roman numerals!

~~~
ithkuil
You might find this interesting:

[http://www.phy6.org/outreach/edu/roman.htm](http://www.phy6.org/outreach/edu/roman.htm)

------
fortran77
We still use their numbering system today, in prefaces and clocks!

~~~
jackcosgrove
And SuperBowls.

