Physics is the foundation of human technological advancement. Physics also helps the advancement of other sciences. Physics explains chemical reactions in the atomic level. Loui Pasteur was not a physician he was a physicist/chemist. He used a microscope, an invention based on the science of physics to see very small and discovered microbes. Can medical science be called a science without the knowledge of bacteria and viruses? Just think of technological advances; electricity we use everywhere for lighting, refrigerator, radio, TV, computer etc. Transportation inventions, large and small vehicles, planes and hundreds of other machineries and equipment in industries all are based on the science of physics. Foundation of physics itself is on mathematics, therefore students should know the importance and value of mathematics as the foundation of physics and not as a boredom subject. When students know the value of mathematics, they become interested to learn mathematics. Following are based on my memory of the mathematics history. I do not mention the name of the history books, otherwise I must quote and not write from memory. I have an excellent memory and believe what I am going to state will be fundamentally correct, any mistake would be on minor details.
Geometry was known by the ancient civilizations. We know that from remnants of the ancient monuments and structures. Geometry was the first branch of mathematics that was developed. The first steps regarding geometry as a science was taken by the Greek philosophers in particular by Pythagoras, 6th cent. B.C. and Euclides. Pythagoras wrote the very important Pythagorean theorem. Euclides who lived about 300 years later wrote a detailed book of geometry dealing with the fundamentals of geometry.
Different nations used various numerals. Many nations used their alphabets as numerals, like ABGaD numerals that have sequence of the Hebrew alphabets, by Jews and Arabs. Indians invented the ten based numerals. From the ancient stone carvings in India the following can be understood. Indians originally wrote ten as a circle ‘O’, (like X by Latins) since they considered ten as the complete number, maybe because of ten fingers and they also regarded circle as the perfect shape. Indians originally wrote; one circle as (10), two circles as (20), three circles as (30), …. . Later they made those figures shorter by writing the number of circles in front of one circle, like 5O instead of (OOOOO). This eventually ended into the invention of the ten based numerals, (Decimal numerals) and then ‘O’ without a number on front of it represented nothing or zero. One to nine digits originally resembled finger signs for each number. After the break-up of the Persian Empire to small pieces by the Arab conquerers the present day Afghanistan and part of north east Iran was ruled by a Sultan Mahmood, an Uzbek. He did not speak Parsi and had hired a brilliant minister as his adviser and translator, named Beeroony. Beeroony knew Turkish and Arabic fluently besides Parsi, his mother tongue. Both Sultan Mahmood and Beeroony were devout Muslims. Sultan Mahmoud repeatedly waged wars on western India ( present-day Pakistan), as holy wars and converted Hindus to Islam. Beeroony quickly learned the Indian dialects of those regions to teach the new converts the basics of Islam. Beeroony learned the Indian numerals from the Indians as a result. He realized what a great system of numerals It was. Indeed it has to be considered the second greatest human invention after the Alphabets. The Indian numerals can write numbers, shorter, easier and systematically. Its most important advantage over the other numerals is that the numbers can be written under each other for adding, subtracting and multiplying plus a systematic method for dividing. Beeroony wrote the first book of arithmetic in Arabic since for a devout muslim knowing Arabic was a sours of pride. It should be mentioned also here that because of the poetic and literature style of Quran, Arabic language is a precise, rich in define words with a unique and outstanding grammar. He called his book “Alhessab”, (theArithmetic). Unfortunately he did not mention in his book the source of the numerals as Indian. Maybe he did not want to give credits to the Indians as he believed them “Koffar, (blasphemers). However, he did not claim to be the inventor of the decimal numerals either. The concepts of adding, subtracting, multiplying and dividing existed before. Pythagoras had made his famous multiplication table long before, but without the decimal numerals the systematic four arithmetic operations is not possible. Most historians consider Beeroony as the inventor of all four arithmetic operations. Some historians believe that adding and subtracting methods had existed before. However, at least the first book of arithmetic and multiplying and dividing operations are his works.
Beeroony’s book of arithmetic created a great interest among learned in north east of the present day Iran. Mathematicians wrote numerous complicated arithmetic problems, usually regarding a merchant’s account, sending the problems to each other. Among them; the most brilliant Omar Khayam. Khayam was an outstanding Persian poet who wrote a new style of poetry called “Quartets”. Khayam was also a great astronomer. Astronomers at that time built telescopes with a long bamboo blackened inside, installed on top of a wooden frame equipped with mercury levels. He found the method to predict the time of spring equinox, the Iranian new year. He also revived the ancient Iranian calendar and made it accurate with each season to begin with a new month. Khayam found the method to determine the longest night. The ancient Iranian religion was “Mehraeen” or Mithraism. They celebrated the longest night “Mehrzad” as the birth of a new sun. They believed that Mithra, (The sun goddess) gave birth to a new sun at that midnight. Mitra now like my daughter is a Persian female name. Forty nights after the longest night, called “Chelleh” was also celebrated as they believed that the coldest time of year was over. Mithraism was also practiced by the northern Europeans before Christianity. A similar calendar with the spring as the beginning of new year was also used in Europe. With that calendar, September would be the seventh month, October, the eighth, November, the ninth and December the tenth month as their names indicate. Some science historians have reported that Khayam noticed the earth curvature by surveying from two heights as far as he could, back and forth and concluded that the earth surface must be curved (find how?). However there isn’t any writing of him indicating that he knew the earth was spherical. Khayam was the greatest mathematician of his time. To solve the most difficult arithmetic problems his colleagues and himself had devised, he and another mathematician, Khorazmi came with a brilliant method. They used the old idea of showing numbers by alphabet characters (ABGaD numerals), but not fixed amounts. In their method to solve complicated arithmetic problems, they categorized those alphabets as “known” and “unknown” amount characters. Khayam also suggested the negative amount. We know that arithmetic then was used as a mind game like chess plus for merchant accountings. Therefore most of the problems that mathematicians devised were regarding the accounts of merchants. Khayam and Khorazmi then invented algebra. Most historians credit the development of algebra more to Khayam. Khayam also invented trigonometry by drawing a right triangle on paper showing his telescope as the hypotenuse having angle (z) with the horizontal side of the right triangle, the same angle of his telescope with horizon. He designated the “head” i.e. vertical side, as the alphabet letter ‘Sin’, (Sin z) and the “shoulder” i.e. horizontal side, as the alphabet letter ‘Shin’. Latin did not have a character for ‘Sh’ sound and ‘Shin’ was translated to Co-Sine or Cos z. Is not this amazing? He also practiced alchemy. It is reported that the greatest genius, Sir Issac Newton had such a respect for Khayam that in secret he practiced alchemy in the honour of Khayam! Khayam didn’t make any book even of his poems. Everything he wrote were on some papers that he kept and also sent to his colleagues. (Paper is one of the greatest human inventions by Chines). From Khayam’s poetry it is clear that he was not a believer in Islam. Khayam unlike other Persian poets or Beeroony, did not make any book of his poetry, astronomy or mathematics. He most probably was afraid for his life, we know that another nonbeliever scientist was put to death by the order of the religious judge of the city of Ray, because Raazy1 in his, the first book of chemistry had stated a sentence in Parsi that was proof of him being a nonbeliever. His book of chemistry was also burned. Fortunately others wrote of Raazy’s chemistry works and discoveries. Others also collected Khayam’s papers and made the books of algebra, trigonometry, his astronomy methods, calendar and poetries. The first book of algebra was written by Khorazmi. He called his book: “Al ketaba’lgabra wal’moghabellah”, literary “The Book of Compulsory and Equation”. Khorazmi wrote his book in Arabic in order to take it to Baghdad and present it to the court of Khalifa of Islam to receive the traditional gift. Khorazmi as expected, received a large rewards in gold which was the tradition of that court, a praiseworthy tradition indeed! At least four more Khayam’s compatriot mathematicians; Kashi, Tusi, Bazjani and Karkhi wrote small books of algebra, trigonometry, calendar and astronomy referring to Khayam’s notes and papers.
Early during the European era of enlightenment, the European thinkers and researchers translated those books, first to Latin and later to other European languages. In the west the Indian numerals are known as Arabic numerals since Beeroony’s book of arithmetic was in Arabic. European mathematicians greatly advanced all branches of mathematics, in particular the algebra. The works of the Europeans on the advancement of mathematics is such that nearly one hundred works and names are mentioned in the history of mathematics. Here only a few are mentioned. French Descartes’s graphical representation, (Cartesian Coordinates) of the algebraic functions was one of the greatest steps forward. Napierian logarithm that is also called the natural logarithm is the only solution to one of the integral functions of Newton’s calculus that repeatedly appears in Physics. The greatest advancement in mathematics is the Newton’s calculus. It is the mathematics of nature. Tens of other mathematicians made contributions to advancement of this vital tool of physics. German Leibniz’s works on calculus were the most important of them all. Leibniz made differentials from Newton’s derivatives and integral from Newton’s primary function. Leibniz later declared that he came with the idea of calculus independent from Newton’s works. A committee requested and chaired by Newton himself, concluded that the Leibniz claim to be incorrect based on the papers that was spread by Newton’s colleagues in Europe before Leibniz works. There is another reason that Newton was the sole inventor of calculus. It is said that need is the father of invention. One can see this need and process in the history of mathematics and sciences. In “The Newtonian Mechanics” the acceleration, by its nature is the derivative of velocity and velocity the natural derivative of distance. Reversely, acceleration by its nature is the primary function of applied force, velocity the natural primary function of acceleration and distance the natural primary function of velocity. This is the need, beginning, motive and the cause for calculus, otherwise how anyone would come with such a strange idea.
Footnotes
- Alchemists believed that there was an agent “Elixir”, (Kimia in Parsi) that could convert copper to gold. Zakaria Raazy originally as an alchemist was trying to find that elixir by all kinds of mixing, heating and burning of substances. He later in his life gave up alchemy and made the foundation of chemistry. He entered the smoke of burning sulphur into water and made sulphuric acid that he called “The Essence of Sulphur”. By pouring sulphuric acid over salt and mined calcium nitrate, he made hydrochloric acid and nitric acid that he called the essence of salt and the essence of nitrate. He heated mined and refined sodium carbonate that was mainly used for glass making and made caustic soda. There is still an ancient Persian soap in use in Iran, called “Sepeedab” which is made by mixing animal spinal cord and oil with lime. Raazy instead of lime, mixed his discovered caustic soda with animal oil and made soap that he called “Saaboon”, that means rubbing. He also distilled wine and discovered alcohol. It is ironic, now we know that gold is produced at extreme heat/pressure in the centre of stars by fusion of copper atom nucleus into gold.
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