Of course, the practical advantages of using the specialized language also play an enormous part here; among them are making expressions visible, reducing time spent recopying, and so on. 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.
At that time mathematicians were so carried away by the rush of discoveries that they simply were not interested in logical subtleties. Addition was done by totalling separately the symbols 1s, 10s, s, etc in the numbers to be added, and multiplication was a laborious process based on successive doublings division was based on the inverse of this process.
These representations are equivalent to one another but they are not at all equivalent to the representation of the whole or fractional number. Pierre de Fermat owned a copy, studied it, and made notes in the margins.
It is sometimes said that Descartes ''reduced geometry to algebra" which means, of course numerical algebra, arithmetic algebra. This was exactly the concept Descartes used. But as soon as some external cause brought about an interruption in the oral tradition. By recognizing mathematical statements as objects to work with.
The goal of mathematics is to create linguistic models of reality, and all means which lead to this goal are good. Indeed the works of Apollonius were but little read and were even partly lost.
Nonetheless, the properly geometrical ideas of Descartes and Fermat are practically identical. The use of such a language changes one's view of the relation between language and reality. This was exactly the concept Descartes used.
This was as true of their mathematics as anything else, and they adopted elements of mathematics from both the Babylonians and the Egyptians. Geometric quantities were thought of as necessarily something spatial and, because of incommensurability not reducible to a number.
We have become so accustomed to placing irrational numbers together with rational ones that we are no longer aware of the profound difference which exists between them. This can be seen from his remarkable works on number theory.
They were Archimedes B. I thought that in order the better to consider them in detail, I should picture them in the form of lines, because I could find no method more simple nor mole capable of being distinctly represented to my imagination and senses.
Foundations and philosophy In order to clarify the foundations of mathematicsthe fields of mathematical logic and set theory were developed.
In fact, let us suppose the opposite, namely that the diagonal of a square stands in some ratio m: Furthermore, it fell to Euclidhalf a century later, to prove that these were the only possible convex regular polyhedra.
So although al-Khwarizmi does not use a special algebraic language, his book contains the first outlines of the algebraic approach. Without these, one is wandering about in a dark labyrinth.
In particular, he was convinced that geometry was the key to unlocking the secrets of the universe. All the methods known previously fall into place in a harmonious system, new methods open up, new equations and whole classes of equations come under consideration the law of branching growth of the penultimate leveland new concepts appear which have absolutely no meaning within arithmetic proper:The decline of Greek mathematics was in part caused by external factors--the political storms that engulfed Mediterranean civilization.
Nonetheless, internal factors were decisive. Jan 11, · The Decline of Greek Mathematics Nicomachus of Gerasa Diophantus of Alexandria Pappus of Alexandria The End of Alexandrian Dominance Proclus of Alexandria Boethius Athenian Fragments Byzantine Mathematicians 9 Ancient and Medieval China Format: Paperback.
The word mathematics comes from Ancient Greek μάθημα (máthēma), meaning "that which is learnt", "what one gets to know", hence also "study" and "science".
The word for "mathematics" came to have the narrower and more technical meaning "mathematical study" even in Classical times.
Decline of Greek Mathematics Figure Ancient Greece Summary of the Greek Achievements What are the accomplishments of Greek mathematicians? • The Greeks are to be credited with making mathematics abstract Making mathe- matics abstract was the greatest contribution that Greeks made and it was of immea- surable significance.
Plato played an important role in encouraging and inspiring Greek intellectuals to study mathematics as well as philosophy.
His Academy taught mathematics as a branch of philosophy, as Pythagoras had done, and the first 10 years of the 15 year course at the Academy involved the study of science and mathematics, including plane and solid. Buy Greek Mathematical Thought and the Origin of Algebra (Dover Books on Mathematics) But in the Renaissance, a decline started to take place.
This decline is linked with an alienation of ancient math within the corpus of modern thought. It is essential that a truer knowledge of Greek math, musical theory, and philosophy be restored. Reviews: 8.Download