CRITICS TO THE CLASSICAL APPROACH TO THE HISTORY OF MATHEMATICS
As in the many branches of history, history of mathematics invites us to a discussion about a paradigm for the approach to the past. For many centuries, after the huge heritage of the “Enlightment” and the ancient idealism, historians had been dealt with the past with a dialectic approach mixed with an idealistic determinism; both of which implicitly lead to discussions about the origins of mathematics concerning practical needs versus artistic/artificial/religious origin.
Struik discusses the failures of the Euro-centric approaches to the history of mathematics with some concrete examples. Although he disagrees with some certain approaches, he could not avoid repeating the same paradigm: Struik refuses the deterministic approaches, but he keeps arguing with same kind of deterministic approach. He asks about the “reasons” why Babylon people used so advanced mathematics. Answer is quite expected. Struik replaces the old argument with his “art-for-art” argument. In my opinion, what Struik did is just repeating the same deterministic paradigm, which certainly leads us to an absurd path like digging into the reasons of doing mathematics. As the “End of History” [due to F.Fukuyama], approached; historians of science still keep searching the reasons of some certain events. My claim is straightforward: How can you ensure the validity and truthness of your arguments when it comes to the history? While considering a special topic as the history of mathematics, presented argument of my own seems clear and reasonable.
As Struik indicated in his article, 20th century witnessed some revolutionary changes in history and archeology. However, the comments and conclusions derived from those researches were more or less following the same paradigm. Excavations in Indo-China, Egypt, Lebanon and Mesopotamia displayed a huge civilization including a strong mathematical tradition. Following them, historians concluded that, mathematical inventions were communal and communities were influenced from any other via trade, wars etc. This is the main point that I wish to discuss largely. Skipping the individuality in (even ancient) mathematics, is killing the individuals just for the benefit of society –which composes of the individuals. I am certainly aware of the lack of archeological findings concerning the individual efforts spent on mathematics. But at that point, I give credit to the individualism, leaving the communal approach behind me.
Since I had met first time, I have not been able to comprehend the Aristotle’s approach about the origin of philosophy (and maybe mathematics): leisure. At that point, Adorno and Horkheimer claimed that deductive approach of the science reflects oppression and hierarchy. As a whole, its logical order, (…), unity of its principles were based on division of labor. After remembering the tragic and expected collapse of dialectic materialism, previously presented arguments may be seen more clear. Since the philosophy of Renaissance and the period of enlightment forces us to dominate and rule the nature as the master, mentioned deductive and deterministic approaches gain much more meaning.
As appeared in the texts of Struik and Bernal, historians of science, attempted to explain the ancient periods in a way that, those times should certainly lead to the renaissance way of thinking. This is a simple and primitive (in ordinary meaning) application of the deductive approach. Unfortunately, it appears that, many historians made the same mistakes many times. Bernal discusses and gives some concrete examples about those arguments. Ideas put forward about the ancient Egypt civilization ranges between the ‘spirituality of the priests’ and ‘technical positivism’. Both approaches deduct from different point, but still they skip too many points. My aim is not to appoint a ‘reason’ to be deducted, but rather to claim (without a proof) that looking for a reason certainly leads to a deductive methodology, which should certainly be avoided.
Throughout my article, I disagreed with some certain approaches, which may easily found in our texts, and attempted to explain my ideas on this topic. What I still cannot comprehend is why people still keep searching for the reason to be deducted and appoint some certain and definite reasons to believe in. I found it absurd in the area of history.
Although this article may be seem a bit longer; I should frankly confess that, it is just a summary of my brainstorming about the philosophy of mathematics in the area of history of mathematics. Therefore reader is expected to have a bit tolerance to the writer about the length of the text.
 I used the Turkish edition of J.Zerzan’s masterpiece Future Primitive published by Kaos Yayınları. Quotation of Adorno and Horkheimer appears there. Translation is due to me.