Nida Haider Paper III

Nida Haider Paper III

1383054

The Road to Modern Math

With the fall of the Greeks and the rise of the Romans, progress of mathematics slowed down in the European continent and the extended empire. The Romans maintained the Greek libraries and learning centers but were not as interested in promoting new discoveries as they were in acquiring new land. Mathematics took a back seat, serving only as a practical tool. The rise in the power of the Church discouraged any sort of learning other than that pertaining to God and the Bible. The final halt to the trickle of academic innovation came with the fall of the Roman Empire. The learning centers and the libraries were no longer maintained and various barbarian tribes form the north took over Rome, pillaging in victory. Paganism and dogmatic religion intertwined thus superstition prevailed. There was no longer a common language like Latin and Greek for the sharing of ideas nor was there a conducive environment for the academia to exchange thoughts. These events were followed by the Little Ice Age. Famine and disease spread, and people become isolated. The Black plague further took a toll on the continent wiping out a majority of the population. There was little in academic progress as everyone was busy surviving.

Around the 13th century things began to change. As living conditions improved, trade regained momentum and many ancient texts were rediscovered and translated.The expansion of trade and commerce in general created a growing practical need for mathematics. Merchants used the crude roman numerals and noblemen sent their children to abacus schools. Works from Hellenistic Greek and the Islamic scholars were now spreading into Europe and intriguing minds that were eager to fill in the vacant niches of academia.12th Century translation of Al-Khwarizmi's work on algebra into Latin by Robert of Chester and the translated complete text ofEuclid's “Elements” by Adelard of Bath, Herman of Carinthia and Gerard of Cremona stirred up the hibernating mathematical minds.

The challenging of the monarchs and the authority of the church brought on the Age of Enlightenment where the Europeans were questioning everything. For them, if these long standing supreme authorities were no longer revered, what other truths were there to challenge? Thus, math and scientific investigation and discovery took center stage in Europe.

The abundance of mathematical advancement after the end of the middle ages created such a competitive atmosphere leading to such extreme thoroughness and rigor at the time that most of the concepts and ideas that came out of Europe during that spell remain unchanged as of today. There are many great names frequently mentioned in relation to these solid mathematical ideas. Leibniz; the Bernoulli brothers, Sir Isaac Newton and Descartes are revered as the inventors of calculus, graphical analysis and algebraic analysis. They refined mathematics to the form we see it in today, however, equally worthy of mention are those names who bridged the gap between the knowledge of antiquity and the east with the west while setting the stepping stones for the mathematical boom that occurred during the 17th to 19th century Europe. The ideas of Euclid, Archimedes and Diophantus at one end and the mathematical genius of Al-Khwarizmi at the other were taken and built upon. Notation was developed and great mathematical ideas like differentiation and point geometry were toyed with in isolation eventually stirring up a mathematical storm.

Fibonacci of Italy traveled the northern Arab world with his father where he learned the Hindu Arabic numerals and realized the ease they provided in error free calculations. Thus, he played a big role in their acceptance throughout Europe with his book“Liber Abaci” ("Book of Calculation”). During the Crusades it was difficult to promote anything from the Muslim world, however the ease of lining up the place values and representation of fractions soon set suspicions aside and the Roman numerals became obsolete. Although Fibonacci is most famous for his recursive number sequence also known by his name, his most useful contribution was the introduction of the zero to Europe. His book explainedhow to use Zero as a place holder and talked about decimal places even though the notation was yet to come. His book also discussed conversions and ratios as how to deal with weighing coins and converting weights, and how to divide Pisa’s money into pieces, by separatingthe ItalianPisan currency“thebezant” using decimals. The book also introduced the bar notation for fractions and copied the Arabic way of writing the whole number to the right of the fraction.

Fibonacci discovered his famous sequence as he observed the breeding and number of rabbits, adding the new generation to the old. He did not realize the intriguing properties of his sequence at the time, nor was he aware of its existence in ancient India.

The ease of the Hindu-Arabic numerals along with the coming of the printing press greatly accelerated the sharing and collective advancement of mathematics in Europe.

Nicole Oresme of France was one of the most important intellectual figures of the 14th century. A philosopher, theologian, astronomer and mathematician, he took part in the teaching of scholastic philosophy and wrote several commentaries on Aristotle. One of his most important mathematical works is the “Questiones on the Elements of Euclid” that surveys problems suggested by Euclid's text. Among the subjects he investigated as a mathematician are the quantitative change of qualities like velocity which he represented graphically and thus he was the pioneer of graphical analysis and used coordinate geometry even before it was invented by Descartes. He also set the ideas for differentiation and integration that would be defined much later.

Without the standardization of notation and a symbolic language for mathematics, the mathematical revolution of the 17th century would have been much less collaborated and probably greatly delayed. Johan Widermann from Germany published both the `+` and `-` signs in his book the “Mercantile Arithmetic (1489)” representing the deficits and surpluses of trade. It is also said that he also may have given lectures on making easy calculations using a calculating board of sorts as a lead into algebra. Robert Recorde, aWelshphysician and mathematician invented the"equals" sign(=) while Franceso Pellos of Italy gave us the decimal point.

One of the first mathematicians to use letters to represent numbers was Francois Viete of France in his “In artem analyticam isagoge (1591)”, while Thomas Harriot pioneered the writing of mathematics in a purely symbol form. He introduced many symbols, such as a dot to represent multiplication, as well as `<` and `>` in “Artis Analyticae Praxis”. The dot for multiplication was later attributed to Leibniz and Johnn Bernoulli.

At the end of the 16th century, mathematics was coming closer to the merger of the two distinct tracts inherited form the past. From the Greeks came the tools of geometry and the Arabs provided procedures for the resolution in algebra. At the time of Vieta, 16th Century, algebra went back and forth between arithmetic, which gave the appearance of a list of rules, and geometry which seemed more rigorous. The need of the hour was to give algebra the rigorous foundation that geometry enjoyed by reproducing it in a more geometrical manner. Along with this, it was necessary to give geometry a more algebraic sense, allowing the analytical calculation in the plane. Vieta gave algebra a foundation as strong as in geometry. He then ended the algebra of procedures inherited from the Arabs who wrote out the equations in words, thus creating the first symbolic algebra and claiming that with it, all problems could be solved. Carving out the road to calculus.

Many unsung intellects brought order to the discipline of mathematics. For some, their names are lost, for others, their contributions are attributed to another. By the end of the 16th century the ground work had been laid out for the revolutionary mathematics that came out of Europe after the Enlightenment. Today L Hopital, and Euler and other such big names can be found amongst the list of genius mathematicians, however their findings would not have come as easy if it were not for these small steps that enabled future mathematicians to take big leaps and set the stage for a new era in academia, the modern age of mathematics.

Works Cited

Oresme, N., & Busard, H. L. (2010).Questiones super geometriam Euclidis. Stuttgart: Steiner

Viète, F. (2006).The Analytic art: nine studies in algebra, geometry, and trigonometry from the Opus restitutae mathematicae analyseos, seu, Algebrâ novâ. Mineola (N.Y.): Dover Publications.