The True Adventure's of Raya Lorene Wasson.
The History of Math

By: Raya Wasson

    
     I recently have done some research on the history of math. I honestly couldn’t believe how much history there really is behind mathematics. It starts so much further back than I had thought also. Math comes from all over the world, from different cultures but each one has influenced the other. Math connects the world more than you’d have thought. Lets start with a few short facts.

     The most ancient mathematical texts available today are, Pimpton 322 (Babylonian math c.1900 BC), Rhind Mathematical Papyrus (Egyptian math c.2000-1800 BC), and Moscow Mathematical Papyrus (Egyptian math c. 1890 BC). They all concern the Pythagorean theorem, which seems to be the most ancient and widespread math development after basic arithmetic and geometry. The Pythagorean theorem is used today also. Not to mention, the Greek and the Hellenistic contribution greatly refined the methods and expanded the subject matter of math (mathematical rigor in proofs).

     Now, lets start with the 6th century BC with the Pythagoreans, who coined the term mathematics from the ancient Greek mathema, meaning, “subject of instruction”. Chinese mathematics made early contributions such as the place value system in the 6th century.

     Now moving on to prehistoric math. The oldest possibly mathematical object is the Lebomo Bone. It was discovered in the Lebomo Mountains of Swaziland. It has been dated to approximately 35,000 BC. It is a bone that has 29 distinct notches cut into a Baboon’s fibula. Prehistoric artifacts discovered in Africa and France, dated between 35,000 and 20,000 years old, suggest early attempts to quantify time. The Ishango Bone was found near the headwaters of the Nile River and it may be as much as 20,000 years old. It consists of a series of tally marks carved into three columns running the length of the bone. This bone is evidence of either the earliest demonstration of sequences of prime numbers or a six-month lunar calendar.

     Lets go to the ancient near east. Babylonian mathematics refers to any mathematics of the people of Mesopotamia from the days of the early Sumerians through the Hellenistic period, almost to the dawn of Christianity.  More than 400 clay tablets have been unearthed since the 1850’s. The majority of recovered clay tablets date from 1,800 BC to 1,600 BC and cover topics which include fractions, algebra, quadratic and cubic equations, and the calculation of regular reciprocal pairs. They are all written in Cuneiform script and some appear to be graded homework.

     The earliest evidence of written math dates back to the ancient Sumerians, who are the ones who built the earliest civilization in Mesopotamia. The Sumerians developed a complex system of metrology from 3,000 BC. From 2,500 BC onwards, the Sumerians wrote multiplication tables on clay tables and dealt with geometrical exercises and division problems.

     Babylonian mathematics was written using a sexagesimal (base 60) numeral system. From this derives the modern day usage of 60 seconds in 1 minute, 60 minutes in 1 hour, and 360 (60*6) degrees in a circle, as well as the use of seconds and minutes of arc to denote fractions of a degree.


     Next we go to Egypt, they have the Rhind Papyrus, which is an instruction manual for students in arithmetic and geometry. It gave area formulas, methods for multiplication, division, and working with unit fractions. It also has composite and prime numbers, arithmetic, geometric and harmonic means, and simplistic understandings of both the Sieve of Eratosthenes and perfect number theory.  Not to mention, it also shows how to solve first order linear equations as well as arithmetic and geometric series.

      There is also a Moscow Papyrus, which consists of word problems and for entertainment; although, I don’t quite understand how math is that fun. Also, there is the Berlin Papyrus (1,300 BC) and it helps you solve second-order algebraic equation.

     The Greeks used logic to get calculations from definitions and axioms and used mathematical rigors to prove them. It is thought to have begun with Thales of Miletus (624-546 BC) and Pythagoras of Somas (582-507 BC). This was probably inspired by Egyptian and Babylonian math.


        One of those great men is Pythagoras. He was an Ionian Greek philosopher, mathematician and the founder of the religious movement called Pythagoreanism.  According to legend, Pythagoras traveled to Egypt to learn math, geometry, and astronomy from Egyptian priests. He also established the Pythagorean School, whose doctrine it was that math ruled the universe and whose motto was “all is number”. Not to mention, the Pythagorean theorem was his creation.

     Next on out list of important Greek mathematicians is Thales of Miletus. Thales used geometry to solve problems such as calculating the height of pyramids and the distance of ships from shore. He was the first individual to whom a mathematical discovery has been attributed.

     Eudoxus of Cnidus was another one of these great men. Eudoxus was an astronomer and a mathematician. All of his own works have been lost so we don’t have much information on him besides secondary source information. He developed the method of exhaustion, a precursor of modern integration.

    There is also Archimedes of Syracuse (287-212 BC), born in Syracuse Sicily and dies when he was about 75 years old. A Roman soldier despite orders that he should not be harmed during the Siege of Syracuse killed him. Before that happened, he used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave remarkably accurate approximations of Pi. He also studies the spiral bearing his name, formulas for the volumes of surfaces of revolution, and an ingenious system for expressing very large numbers.

      Continuing on our Greek mathematician journey, there is Aristotle. He was born 384 BC and died in 322 BC. As a Greek philosopher his writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology. He was the first to write down the laws of logic. Logic was a big part of math back then and still is.

     Last, but not least, there was Euclid of Alexandria or “Father of Geometry”. Euclid is the earliest example of the format still used in math today, definition, axiom, theorem, and proof. He also studied conics. He wrote a book called, Elements. Elements, was known to all educated people in the West until the middle of the 20th century. It included the Pythagorean theorem, proof that the square root of two is irrational and that there are infinity many prime numbers.

     Next we have Chinese math. Chinese math was so different than other math that it is assumed that they devolved it by themselves. Two important people in the Chinese math culture are Mohist and Mozi. I don’t know anything about them.

     Now, we move on to Indian math. The oldest math records from India are the Shatapath Brahmona. They also have the Sulba Sutras (800 BC-200 AD). It is the appendices to religious texts, which give simple rules for constructing altars of various shapes. Then, the Panini (5th century BC) formulated the rules for Sanskrit grammar. There was also the Pingala (3rd-1st century BC) binary numeral system. It contained Fibonacci’s numbers. The Surya Siddhanta (400) introduced the trigonometric functions of sine, cosine, inverse sine, and laid down rules to determine the true motions of the luminaries, which conforms to their actual positions in the sky.

     Still in Indian math, in the 5th century AD, Aryabhata wrote the Arybhatiya. It contains rules of calculation used in astronomy. In the 7th century AD, the Brahmagupta theorem/ formula was discovered. So was the Fibonacci sequence. Now, moving on to the 12th century, Bhaskara II who lived in southern India wrote extensively on all math.

       In the 14th century, Mudhava of Sangamagrama, the founder of the so-called Kerala School of Mathematics, found the Madhava-Lebniz series, and, using the 21 terms, computed the value of Pi as 3.14159265359. Wrapping up the Indian math portion of my paper is the 16th century. In the 16th century Jyesthadeva consolidated many of the Kerala School’s developments and theorem in the Yuktibhasa.

       Now we go to Islamic math, starting with the 9th century. Persian mathematician, Muhammad ibn Mu’sa’ al-khwa’rimi’ wrote several important books on Hindu-Arabic numerals and on methods for solving equations, first to teach math in elementary form. In the 13th century Nasir Al-Din Tusi made advances in spherical trigonometry. Next, the 15th century. Ghiyath al-kashi computed the value of Pi to the 16th decimal place.

     There isn’t much on Roman and Medieval European math besides that they believed in something a little odd. They made you believed that god had ordered all things in measure, number, and weight. I kind of see where they are coming from but at the same time don’t quite understand how everything can be related to math.

      We now move on to Renaissance math. In the 12th century European scholars traveled to Spain and Sicily seeking scientific Arabic texts. Thomas Bradwardine proposed that speed (v) increases in the arithmetic proportion as the ratio of force (f) to resistance (r) increases in geometric proportion. Also during the Renaissance, math and accounting were closely linked.

    Last thing we visit here, in this paper, is the Scientific Revolution. Isaac Newton found some of the laws of physics, which explain Kepler’s laws in the 17th century. Also in the 17th century, Gottfried Wilhelm Leibniz, in Germany, developed calculus notation. It is still in use today. In the 18th century Leonhard Euler created the graph theory. The 19th century brought abstract algebra. Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras.

     The 20th century math became a major profession with jobs in the teaching and industry. In 1900, David Hilbert set out a list of 23 unsolved problems in math. Today, only 10 have been solved, 7 are partially solved and 2 are still open. The other 4 are too loosely formulated to be stated as solved or unsolved. In the 20th century they discovered differential geometry. Einstein used it in his general relativity.

      The 21st century brought a few things and people are still researching so who knows what will be next? In 2000, the Clay Mathematics Institute announced the seven Millennium Prize Problems, and in 2003, Grigori Perelman solved the Poincare conjecture, he declined to accept any awards.

      This concludes my paper on the history of math. I hope you learned something. I sure learned a lot about math and I have a new found respect for math majors. This is a hard subject and it’s really hard to learn all this stuff. Math really is, everywhere.

http://en.wikipedia.org/wiki/History_of_mathematics