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I know that Roman Empire built some of the most beautiful things for the epoch and also had an incredible culture (law, poetry, ...).

However, my question is: Why there are there no known Roman mathematicans from the Roman Empire? All the famous roman were emperors, soldiers, lawyers, but not mathematicians.

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Roman empire did not consist of Latin-speaking "Romans" only. It included Greece, North Africa and what we call now Middle East. Probably a majority of the inhabitants of the Roman empire were Greek-speaking. And there were mathematicians among them. Menelaus, Ptolemy and Diophantus were living in the Roman empire. Some of them could be Roman citizens, some not. We know practically nothing about their lives. Most likely all were Roman citizens after the citizenship was granted to all residents of the empire.

So the correct questions would be:

Why Roman mathematicians wrote in Greek?

Why most of them preferred Africa for their residence?

And the answer is that there was a tradition among the Greeks, in Greek language, especially in the Middle East, especially in Alexandria. Tradition means schools, libraries, scientific environment. This environment was created by the Greeks in the Hellenistic times, and partially survived almost to the end of the Roman empire.

By the way, many Roman works in applied sciences and engineering were also written in Greek. See a related discussion here:

Roman engineers

Greek was the language of science in the Roman empire. Like Latin was the language of Science in Europe in 16-18 centuries.

EDIT. We really know nothing about Diophantus, except the books signed with this Greek-sounding name. Where did he live? When did he live? His masterpiece looks completely isolated (nothing remotely similar before or after or around his time). Could he create all this out of nothing? Very improbable.

EDIT2. The question implicitly assumes that science and mathematics (in the modern sense) are necessary (or common, or desirable) activities of a civilization.

Far from it. There was no mathematicians in Rome. But there was also no mathematicians in Parthian empire, India or China at that time. Mathematics (in the modern narrow sense) was invented by the Greeks, flourished in the Hellenistic world, then declined and vanished, as an activity, and very little of it spread elsewhere. Why should one expect it in Rome, or in Londinium or in the Parthian empire? This was just some marginal activity of the Greek culture.

It is only recently (since 17th century) that mathematics became important and mathematical research spread widely.

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  • $\begingroup$ I like your answer, and I found it interesting, but I think it misses the meat of the question. Rome the city had a million citizens and more wealth and free time available to them then any other place. They made great strides in many areas, but few to almost none in pure mathematics. A big part of this, I think, was they considered applied math to be important and theoretical math, less so. It's the theoretical mathematicians and their discoveries that history remembers. Applied math was useful in maintaining the empire but not interesting to the history of mathematics. $\endgroup$ – userLTK Dec 9 '16 at 15:47
  • $\begingroup$ Before I address this, can you tell me what are examples of "great studies" in ANY area of science/engineering, pure or applied which are made in the CITY of Rome. $\endgroup$ – Alexandre Eremenko Dec 9 '16 at 18:10
  • $\begingroup$ I was just going off general info, not a high degree of knowledge. The aqueducts come to mind and roman engineering, which you did mention. I can delete my comment if you think it's unfair. $\endgroup$ – userLTK Dec 9 '16 at 19:43
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    $\begingroup$ In the link to my answer I made a conjecture that most "Roman engineers" were in fact Greeks. This is only a conjecture, but nobody disproved it. $\endgroup$ – Alexandre Eremenko Dec 9 '16 at 21:15
  • $\begingroup$ India had a lot of mathematicians who were called Rishis. The subject was not unknown to India.VoL7,No.4,pp.ll-13;No.IO,p.6,2002. Mathematics in Ancient India by Amartya Kumar Dutta ias.ac.in/article/fulltext/reso/007/04/0004-0019 This is a comment on "But there was also no mathematicians in Parthian empire, India or China at that time. Mathematics (in the modern narrow sense)..." in the first answer. $\endgroup$ – Partha Shakkottai May 4 at 17:12
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In ancient Rome doing calculations with Roman numerals was a very cumbersome procedure which impeded the development of mathematics. Interestingly, ancient Rome also had no prominent scientists or philosophers as compared to ancient Greece. Probably science, mathematics and philosophy were not highly regarded in Roman society similarly to ancient China. These activities were left to Greek (slaves), who were also frequently used as teachers.

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