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Mathematics history goes back pretty far: the Greeks were studying it in 600BC, the Babylonians and Egyptians all the way back beyond 2000BC, and there's even some evidence of prehistoric mathematics. Calculus was born in the 17th century, and modern mathematics, in the sense I usually hear that term, seems to have started somewhere in the 19th century. There's a lot of time between those intervals.

Was there ever a gap in history where not much mathematics was discovered?

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    $\begingroup$ Dark Ages was a general human drought. $\endgroup$ – Pedro Tamaroff Mar 30 '14 at 2:47
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    $\begingroup$ @PedroTamaroff The middle ages were pretty ripe for mathematics in the middle east. As far as I'm aware, historians tend not to use the term dark ages any more as it is inaccurate. $\endgroup$ – Dan Rust Mar 30 '14 at 3:48
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    $\begingroup$ The dark ages were pretty dark mostly in Western Europe. $\endgroup$ – DonAntonio Mar 30 '14 at 3:59
  • $\begingroup$ The dark ages refer to the period following 535 when volcanic ash darkened the sky, and the century that followed it. So alos a dark age in greece at 687 bc $\endgroup$ – wendy.krieger Mar 30 '14 at 5:50
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    $\begingroup$ @DonAntonio: And all that was changed when Chuck Norris invented photons and light! $\endgroup$ – Asaf Karagila Mar 30 '14 at 13:21
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The Wikipedia page Timetable of Greek mathematicians has a graph that may be quite useful for identifying the fast and slow periods of ancient Greek mathematics. Assuming that the graph has included a "complete" representative list of mathematicians, the amount of mathematical activity at a given time should be roughly proportional to the steepness of the curve. It's a very fuzzy and subjective judgment call here, but (except for a couple of noteworthy outliers like Ptolemy) I'd say the entire Pax Romana period was a time of relative mathematical drought compared to the Hellenistic and classical Greek periods.

The overlapping lifetimes of the mathematicians listed have only two gaps of time during which no one is alive: between the death of Geminus and the birth of Cleomedes, and between the death of Ptolemy and the birth of Diophantus. Interestingly, the first gap coincides pretty nearly with the founding of the Roman Empire and its first few decades. I suspect the correlation is not entirely coincidental.

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The early dark ages, from 535 to 600 is pretty sparse, because a catasthrophic volcano eruption overturned societies everwhere. You expect that with climate change.

See eg https://en.wikipedia.org/wiki/Climate_changes_of_535%E2%80%93536

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  • $\begingroup$ Varāhamihira was active during that period. $\endgroup$ – MJD Mar 30 '14 at 3:37
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    $\begingroup$ Citation needed. $\endgroup$ – Dan Rust Mar 30 '14 at 12:54
  • $\begingroup$ @DanielRust Try googling for 535 AD. You will find plenty of references $\endgroup$ – wendy.krieger Mar 30 '14 at 13:01
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    $\begingroup$ At least some words of caution might be de rigueur: Reviewing Keys' book, the British archaeologist Ken Dark commented that "much of the apparent evidence presented in the book is highly debatable, based on poor sources or simply incorrect" and that "Nonetheless, both the global scope and the emphasis on the 6th century AD as a time of wide-ranging change are commendable, and the book contains some fascinating and obscure information which will be new to many. ... $\endgroup$ – Did Mar 30 '14 at 13:11
  • $\begingroup$ ... However, it fails to demonstrate its central thesis and does not offer a convincing explanation for the many changes discussed." $\endgroup$ – Did Mar 30 '14 at 13:12
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In the year 146 BC, Rome annexed Greece. In the year 31 BC, Egypt had the same fate (and with that the great Alexandria!). The Platonic Academy was closed in the year 529 AD.

Basically: wars and religious tensions destroyed the environment in which Greece had developed so much knowledge. The Romans wanted only "practical" knowledge, and much of the mathematics of the Greeks had been developed for its own sake...

It was only in the 16th century that people continued from the legacy of the Greeks (only fragments of it had survived). The Arabs had translated some works of the Greeks, that were then translated to Latin... The Renaissance started in Italy, and then it went to Poland, Germany, France and England.

Never again let people discard what is "not practical" or not "used in everyday life" like the Romans did.

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  • $\begingroup$ The Indians, Persians and Arabs achieved much during that period, and some of it returned to Europe: a notable example was Fibonacci in 1202 but there were many others. The flowering of universities, starting in Bologna in 1088, also showed that a lot was happening before the Renaissance. $\endgroup$ – Henry Sep 11 '15 at 16:37

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