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Understanding Mathematics


a. Etymology

The word "mathematics" comes from the Ancient Greek μάθημα (mathema), meaning assessment, learning, science narrows scope, and a technical meaning "mathematical study", even in ancient times as well. The word nature is μαθηματικός (mathēmatikós), relating to the assessment, or studious, a more meaningful mathematical away. In particular, μαθηματικὴ τέχνη (mathēmatikḗ tékhnē), in the Latin ars mathematica, meaning the art of mathematics.

The plural form is often used in English, as well as in French les mathématiques (and rarely used as a singular derivative la mathématique), refers to the Latin plurals tend neutral mathematica (Cicero), based on the Greek plural τα μαθηματικά (ta Mathematics), who used Aristotle, which roughly translated means "all things mathematical". However, in English, nouns take singular mathematics when used as a verb. In the various conversations, often abbreviated as mathematics math maths in North America and elsewhere.

b. History


Evolution can be seen as a series of mathematical abstraction that always multiply, or words of another extension point. Abstraction at first, which also applies to many animals, is about numbers: a statement that two apples and two oranges (for example) have the same number.

In addition to knowing how to chop physical objects, prehistoric man also recognized the magnitude chopping abstract, such as time of day, season, year. Basic arithmetic (addition, subtraction, multiplication, and division) naturally followed.

The next step requires a writing or other systems to record the number, such as a rope or string bersimpul called Quipu used by the Inca to store numerical data. Number system there are many and diverse, the first known written numbers in the manuscript heritage of Ancient Egypt in the Middle Kingdom Egyptian Rhind Mathematical Gazette.

c. Mayan number system

The use of mathematics is the oldest in trading, land measurement, painting and weaving patterns and the recording of time and never flourished until the year 3000 BC to the face when the ancient Babylonians and Egyptians began using arithmetic, algebra and geometry for taxation other financial matters, building and construction, and astronomy. A systematic assessment of mathematics in his own righteousness began in ancient Greece between 600 and 300 BC.

Mathematics has since flourished immediately, and there is a beneficial interaction between mathematics and science, beneficial to both parties. Mathematical discoveries were made throughout history and continues today. According to Mikhail B. Sevryuk, in the January 2006 issue of the Bulletin of the American Mathematical Society, "The number of papers and books included in the Mathematical Reviews database since 1940 (the first year of operation of MR) is now more than 1.9 million, and more than 75 thousand articles added to the base data each year. Much of the work in this ocean contain new mathematical theorems and their proofs. "

d. Mathematics as science

Carl Friedrich Gauss, regards itself as the "prince of mathematicians", and said mathematics as "the queen of Sciences".

Carl Friedrich Gauss said mathematics as "the queen of Sciences". In the original language, Latin Regina Scientiarum, also in German Konigin der Wissenschaften, the word corresponding to science means (field) knowledge. Clearly, even this original meaning in the English language, and there is no doubt that mathematics is in this context is a science. The narrow specialization of meaning to natural science is in the latter. When one considers the science is limited to the physical world, then mathematics, or at least pure mathematics, is not a science.

Albert Einstein stated that "as far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality."

Many philosophers believe that mathematics is not terpalsukan based experiments, and thus by definition not science Karl Popper. [23] However, in the important work of the 1930s on mathematical logic showed that mathematics can not be reduced to logic, and Karl Popper concluded that "most mathematical theories, such as physics and biology, is hypothetical-deductive: mathematics therefore be closer to the natural sciences that hypothesis-the hypothesis is a conjecture (conjecture), rather than as a novelty." [24] The other sage, say Imre Lakatos, have applied a version of the forgery to the mathematics itself.

A review of alternatives is that certain scientific fields (such as theoretical physics) are mathematics with axioms that are intended so that it corresponds to reality. In fact, a theoretical physicist, J. M. Ziman, proposed that science is public knowledge and thus includes mathematics. [25] In some cases, sharing with many mathematical knowledge of physics, namely extracting logical effects of some contention. Intuition and experimentation also play a role in the formulation of conjectures-conjectures, both in mathematics, as well as in the sciences (other).

Mathematics continues to grow on probation, given its importance in mathematics, and computation and simulation are playing an increasingly stronger, both in science and in mathematics, mathematics weaken objeksi which does not use the scientific method. In his book published in 2002, A New Kind of Science, Stephen Wolfram postulates that computational mathematics deserves to be explored empirically as a scientific field in its own right / truth.

Opinions mathematicians to this is a wide range. Many mathematicians feel that to call their area a science is tantamount to lowering levels of interest aesthetic side, and its history in the traditional seven liberal arts, others feel that neglect this link to science is the same as rolling a blind eye to the fact that the interface between mathematics and its applications in science and engineering had driven much development in mathematics.

One way to play this viewpoint difference is in the philosophy debate whether mathematics is created (as in art) or discovered (as in science). It is reasonable for the university when it is divided into sections that include the department of Science and Mathematics, indicating that the fields are seen as allied to but they are not two sides of the same coin. In practice, mathematicians are typically grouped together scientists at the level of rough, but separated at the final stage. This is one of the many things to consider in the philosophy of mathematics.

Awards mathematics generally maintained in order to remain separate from correspondence with science. The valuable award in mathematics is the Fields Medal (medal field), beginning on 1936 and now held every four years. The award is often considered the equivalent of Nobel Prize science.

Wolf Prize in Mathematics, instituted in 1978, recognizes future achievement, and another major international award, Gifts Abel, introduced in 2003. It is awarded for specific segments of work, can be a renewal, or a settlement leading to a well-established field.

A list containing 23 well-known open problem, called "Hilbert's problems", compiled in 1900 by German mathematician David Hilbert. This list is a great grab persulangan among mathematicians, and at least nine of those problems are now solved

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