History of Mathematics

Mathematics is an abstract field of knowledge that is built with the help of logical reasoning on concepts such as numbers, figures, structures and transformations. According to Berggren, JL, 2004, the discovery of mathematics at the time of Mesopotamia and Ancient Egypt, are based on many original documents are still written by the scribe. Although the documents in the form of artifacts is not too much, but they are considered to be able to express mathematics in these times. Mathematical artifacts found indicate that the Mesopotamian nation has had many remarkable mathematical knowledge, although they are still primitive mathematical and deductive have not been prepared as it is now. Mathematics in Ancient Egyptian times can be learned from the artifacts found are then referred to as the Rhind Papyrus (edited the first time in 1877), has given an idea of ​​how mathematics in ancient Egypt has been growing rapidly. Artifacts related to math found related to areas such as the royal kingdom 3000 BC Sumerian, Akkadian and Babylonian regime (2000 BC), and the Assyrian empire (1000 BC), Persian (6-4 century BC), and Greece (century to 3-1 BC).

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At least ancient Greek mathematician noted that Thales and Pythagoras important. Thales and Pythagoras thought pioneered in the field of geometry, but Pythagoras who start doing or making mathematical proofs. Until the reign of Alexander the Great of Greece and thereafter, has recorded monumental work of Euclidean form of the work book called Element (elements) which is the first book that compiled Geometry deduction. Important treatise of the early period of Islamic mathematics much missing, so there are still unanswered questions about the relationship between the many early Islamic mathematics and mathematicians from Greece and India. In addition, the number of relatively small number of documents that caused us trouble to explore the extent to which the role of Islamic mathematicians in the development of mathematics in Europe next. But a clear, sizable donations Islamic mathematicians simultaneously with the rise of modern thought emerged himpunanelah dark ages until about the 15th century AD himpunanelah.

The invention of the printing press printing in the modern era, which is around the 16th century, has enabled the mathematicians to each other to communicate more intensively, thus able to publish works great. Hilbert came up to his day who sought to create a system of mathematics as a single, complete and consistent. But Hilbert effort can then be broken or found guilty by his own student named Godel which states that it is impossible to single mathematical created, complete and consistent. Geometry and Algebra ancient issue, can be found in the documents stored in Berlin. One of the problems such as estimating the length of the diagonal of a rectangle. They menggunakanhubungan between the long sides of the rectangle and then they find a right-angled triangle. The relationship between the sides of the bracket then known as the Pythagorean Theorem. The Pythagorean theorem actually been used for more than 1000 years before being discovered by Pythagoras.

The Babylonians had found sexagesimal number system is then useful to perform calculations related to the sciences of astrology. Babylonian astronomers at the time have been trying to predict an event by associating with astronomical phenomena such as lunar eclipses and planetary tipping point in the cycle (conjunction, opposition, stationary point, and the first and last visibility). They found the technique to calculate the position (expressed in degrees of latitude and longitude, measured relative to the Sun's annual path is clear movement) with successively adding the appropriate term in arithmetic progression. Mathematics in Ancient Egypt as well as due to the influence of Masopotamia and Babylon, but also influenced by the Egyptian context has a wide stream and long live the Egyptian society with civilization. The issue arose because of the public relations activities of the Egyptians faced survive natural conditions that can lead to conflict between them, such as how to demarcate the region, alongside paddy fields or himpunanelah Nile flood occurred which resulted in their land silted up to a few meters. From one of these cases later appeared notion or idea about the area, boundaries and forms. So the days of ancient Egypt, Geometry has grown rapidly as a branch of mathematics.

In a relatively short time (maybe only a century or less), a method developed by the Babylonians and Ancient granular been up to the hands of the Greeks. For example, Hipparchus (2nd century BC) prefers geometric approach Greek predecessors, but then he uses the method of Mesopotamia and adopted the sexagesimal style. Through the Greeks were forwarded to the medieval Arab scientists and from there to Europe, where it still stands out in mathematical astronomy during the Renaissance and early modern period. To this day remains in use minutes and seconds to measure time and angles. Aspects of Babylonian mathematics that has come to Greece has increased the quality of the mathematical work with not only believe denganbentuk-physical form only, melainan gained confidence through mathematical proofs. The principles of the Pythagorean theorem known since the days of Babylon is laid which is about a thousand years before the Greek era, began to be proven mathematically by Pythagoras in ancient Greece.

In the days of Ancient Greece, during the period from about 600 BC to 300 BC, known as the classical period of mathematics, mathematics changed from function to structure a coherent practical deductive knowledge. Change the focus of practical problem solving knowledge of the truth to the general mathematical theory of change and the development of mathematical objects into a discipline. The Greeks showed concern for the logical structure of mathematics. The followers of Pythagoras trying to find the exact

The length of the hypotenuse of a right triangle. But they can not find a certain number of the same scale as it applies to all sides of the triangle. It is then known as Incommensurability issues, namely the scale is not the same in order to obtain a certain number of the hypotenuse. If forced to use the same scale (or commensurabel) then in the end they find that the length of the hypotenuse is not an integer but irrational numbers.

Achievements of the Ancient Greeks is a monumental work of Euclidean Geometry axiomatic. The main source for reconstructing pre-Euclidean named book by Euclides Elements (elements), where most of the content is still relevant and used until the present. Element consists of 13 volumes. Book I deals with triangle congruence, the properties of parallel lines, and the relationship of the area of ​​a parallelogram and a triangle; Book II set kehimpunanaraan associated with squares, rectangles, and triangles; volume contains properties Circles, and Book IV contains the polygon in a circle. Most of the contents of Book I-III are the works of Hippocrates, and the contents of Book IV can be attributed to Pythagoras, so it can be understood that this element of the book has its history to centuries before. Book V outlines a general theory of proportion, which is a theory that does not require restrictions to the amount of worth. This general theory derived from Eudoxus.

Based on the theory, Book VI describes the rectilinear nature and generalization of the theory of congruence in Book I. Book VII-IX contains what the Greeks called "arithmetic," the theory of integers. This includes the properties of numerical proportion, the largest divisor, common multiples, and primes (Book VII); proposition in numerical progression and square (Book VIII), and specific outcomes, such as the unique factorization into primes in, the existence of which is not limited number of primes, and the formation of a "perfect" numbers, ie numbers which equals the number of divisors (Book IX). In some form, originating from Theaetetus Book VII and Book VIII of Archytas. X book presents the theory of irrational lines and comes from the work of Theaetetus and Eudoxus. Xiberisi book about waking up space; Book XII prove theorems on the ratio of a circle, the ratio of the ball, and the volume of pyramids and cones. Heritage of Greek mathematics, especially in geometry, is very large. From the early period of the Greek people do not set goals in terms of mathematics practical procedure but as a theoretical discipline is committed to developing a general proposition and a formal demonstration. The range and diversity of their findings, especially those from the 3rd century BC, geometry has become the subject matter for ages himpunanelah that, although the tradition is transmitted to the Middle Ages and the Renaissance is incomplete and flawed.

The rapid rise of mathematics in the 17th century was based in part on the renewal of the ancient mathematics and mathematics on the Greek era. Mechanics of Galileo and calculations made Kepler and Cavalieri, a direct inspiration for the Archimedes. The study of geometry by Apollonius and Pappus stimulated by new approaches in geometry-for example, by Descartes developed analytic and projective theory of Girard Desargues.

Revival of mathematics in the 17th century along with the rise of the thinking of the philosopher as an anti-thesis of a dark age where truth is dominated by the Church. Then Copernicus is a groundbreaking figure who challenged the Church's position that the earth as the center of the universe, and instead he expressed the idea that it is the sun that the Earth was not the center of the solar system, while the surrounding earth. This revival era became known as the Modern Age, which is characterized by the emergence of figures such mathematicians as well as philosophical thinker Immanuel Kant, Rene Descartes, David Hume, Galileo, Kepler, Cavalieri, and so on.