History of mathematics since the 9th century BC


By the ninth and eighth centuries BC mathematics was in its infancy in Babylon. The Babylonians and Egyptians already had algebra and geometry, but only enough for their practical needs, not organized science. In Babylon, mathematics was cultivated among the scribes responsible for the royal treasures. For all the algebraic material that the Babylonians and Egyptians had, we can only view mathematics as science in the modern sense of the word from the sixth and fifth centuries BC.

Greek mathematics is distinguished from Babylonian and Egyptian mathematics by the way it is viewed. The Greeks made it a science proper without concern for its practical applications.

From a structural standpoint, Greek mathematics differs from the previous one in that it takes into account problems related to infinite processes, motion and continuity. The various attempts by the Greeks to solve such problems led to the axiomatic-deductive method. This method consists in admitting as certain (more or less obvious) prepositions and from them, through a logical chain, arrive at more general propositions. The difficulties encountered by the Greeks in studying the problems of infinite processes (especially problems about irrational numbers) may be the causes that diverted them from algebra to geometry. Indeed, it is in geometry that the Greeks stand out, culminating in Euclid's work, entitled "The Elements." Succeeding Euclid we find the works of Archimedes and Apollonius of Perga.

Archimedes develops geometry by introducing a new method, called the "exhaustion method," which would be a true germ from which an important branch of mathematics (boundary theory) would later emerge. Apollonius of Perga, a contemporary of Archimedes, begins his studies of the so-called conical curves: the ellipse, the parable, and the hyperbole, which play a very important role in today's mathematics. By the time of Apollonius and Archimedes, Greece had ceased to be the cultural center of the world. This, through Alexander's conquests, had moved to the city of Alexandria. After Apollonius and Archimedes, Greek mathematics enters its sunset.

December 10, 641, the city of Alexandria falls under the green flag of Allah. The Arab armies, then engaged in the so-called Holy War, occupy and destroy the city, and with it all the works of the Greeks. The science of the Greeks goes into eclipse. But Hellenic culture was too strong to succumb in one blow; henceforth mathematics enters a latent state. The Arabs, in their rush, conquer India by finding another type of mathematical culture there: Algebra and Arithmetic.

Hindus introduce a completely new symbol into the hitherto known numbering system: the ZERO. This causes a real revolution in the "art of calculating". The spread of Hindu culture through the Arabs begins. These bring to Europe the so-called "Arabic Numerals", invented by Hindus. One of the greatest propagators of mathematics at that time was undoubtedly the Arabic Mohamed Ibn Musa Alchwarizmi, whose name resulted in our language the words digits and Algorithm.

Alchwarizmi propagates his work, "Aldschebr Walmakabala", which literally means restoration and comfort. (From this work originates the name Algebra). Mathematics, which was in a latent state, is beginning to wake up. In the year 1202, the Italian mathematician Leonardo de Pisa, nicknamed "Fibonacci" resurrects mathematics in his work entitled "Leber abaci" in which he describes the "art of calculating" (Arithmetic and Algebra). In this book Leonardo presents solutions of equations of the 1st, 2nd and 3rd degrees. At this time Algebra begins to take its formal sapecto. A german monk. Jordanus Nemorarius is already starting to use letters to mean any number, and in addition introduces the signs of + (plus) and - (minus) in the form of the letters p (plus = plus) and m (minus = minus).

Another German mathematician, Michael Stifel, now uses the plus (+) and minus (-) signs as we currently use them. It is the algebra that is born and set in full development. This development is finally consolidated in the work of the French mathematician, François Viète, called "Algebra Speciosa". In it the alphabetic symbols have a general meaning, being able to designate numbers, segments of lines, geometric entities, etc.

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