Decline of the Greek Mathematics
Decline of the Greek Mathematics Historically, the Greek Mathematics had reached a high level in Greece and its colonies during the Hellenic era, beginning in the sixth century B. C. E. and ending in 476 C. E. when the barbarians invaded Rome. Although there were achievements made during the Roman Empire, the Greeks have had their best productive times before the Roman Empire – the end of third century B. C. E.
Although there might be many reasons why the Greek mathematics decline, I think that the changes in the political and social climate – especially during the Roman Empire – was not sufficient enough for the Greeks to continue their culture – including mathematics. Moreover, the lack of stability and security disrupted Greek schools that were very well known with their mathematical education. Lastly, I also believe that there were fundamental limitations, such as lack of algebra, to the Greek way of mathematics.
First of all, it is very logical to claim that the peace times were very beneficial for the Greek mathematics as they had leisure time and energy to spend on developing mathematics. Greeks used the axiomatic method (axiom, theorem, proof) that can also be called as doing the mathematics just because it is mathematics (not aiming to use it anywhere or using it when applicable. ) On the other hand, Romans – whom invaded the Greeks – considered mathematics only as a way to solve practical problems as opposed to the Greek view.
One of the great examples is that how Romans had to solve problems with geometric methods over trigonometric methods, and they were calling mathematicians as geometers because the term mathematician was considered derogatory. In addition to degradation of mathematicians and their way of work, Romans looked down on to the Greek schools teaching math to students. They have never supported them – those schools were usually state funded – and actually harassed them.
That forced the whole mathematical education system to deteriorate; therefore causing a huge background gap for future Greek mathematicians. Lastly, the Greeks had a very formal way of doing mathematics as I have mentioned above. As everything needed to be precise and needed to have a proof, their mathematical abilities were limited. For example, concepts based on intuition were rejected and their implications were not pursued – which we can see from Zeno’s paradox (famous limit problem. They have avoided using irrationals, ignored algebra, only made finite calculations and overemphasized geometry. Therefore, their ability to move forward from the point there were was very limited. In conclusion, both the Roman invasion (war time) and the lack of mathematical methods had played important roles in the decline of the Greek mathematics. Thus, we can see that the leisure time to be able to spend for development of mathematics and being able to relate it with the real world (practice) is very important in our field.