How did the mountain ranges in the northern and western regions india remain independent for thousands of years

The study of mathematics as a "demonstrative discipline" begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from the ancient Greek μάθημα (mathema), meaning "subject of instruction".[4] Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning and mathematical rigor in proofs) and expanded the subject matter of mathematics.[5] Although they made virtually no contributions to theoretical mathematics, the ancient Romans used applied mathematics in surveying, structural engineering, mechanical engineering, bookkeeping, creation of lunar and solar calendars, and even arts and crafts

Explanation:

i believe it is capitalists.  

early greek culture has had an important impact on government and education. first of all, they established the democratic political systems and procedures we have today. consequently, we inherited trial by jury for example. considering education, greek philosphers, mathematicians set he intellectual basis of different areas of studies. in addition, the alphabet originated from the phoenician alphabet into the one we have today and the first library was built in egypt. moreover, greek culture has an impact in current art, architecture and sports disciplines.