History of Mathematics

Anjana K.

1345301

Research Scholar

Christ University

Mathematics is the study of abstract ideas and topics such as quantity, structure, space, and change. Although formally introduced much later Mathematics has been a part of evolution since time immemorial. This can be said with certainty since the cave paintings provide proofs of counting and numbers. The most ancient mathematical texts available are Babylonian Mathematics in 1900 BC, Egyptian mathematics in 2000-1800 BC and the Moscow Mathematical Papyrus. All of these texts concern the Pythagorean Theorem, which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry.

The study of mathematics is attributed to Pythagoras who coined the term 'Mathematics' in 6^th century BC. After the Egyptian Mathematics, came the Chinese Mathematics. There has been a large contribution of the Chinese to the subject including the place value system. The study of the mathematics of these early civilizations were very different from that of the Greeks, who developed the model of abstract mathematics via geometry which was to serve as the model of mathematical achievement until essentially modern times. 

Mathematical Writings and Mathematical Societies

Although there have been numerous writings in mathematics the first printed arithmetic book was published in Treviso, Italy, in 1478, the first edition of Euclid's Elements appeared in 1482, and the first work on mathematics printed in the New World appeared in 1556.  The great increase in scientific and mathematical activity that began to flourish in the sixteenth century led to the formation of groups of persons who met, sometimes regularly, for discussion and an exchange of ideas. Some of these groups later crystallized into what became academies, the first of which seems to have been established in Naples around 1560. It is difficult to say where and when the first official Mathematical society was founded, but the oldest one still in existence is the Mathematische Gesellschaft  in Hamburg. It was founded in 1690 as the Kunstrechnungsliebende Societ¨at, and has long published a journal. Another early one is the Spitalfields Mathematical Society, which lasted from 1717 to 1846, initially meeting in a pub in east London; it was ultimately absorbed into the Royal Astronomical Society in 1846. The day of the amateurs passed, and the professionals began to take over with the formation of the national mathematical societies. The first such society is the Wiskundig Genootschap, founded in Amsterdam in 1778, but most national societies were founded considerably later : the Moscow Mathematical Society in 1864, the London Mathematical Society in 1865, the Soci´et´e Math´ematique de France in 1872, the Mathematical Society of Japan in 1877, The Edinburgh Mathematical Society in 1883, the Circolo Matematico di Palermo in 1884, the New York Mathematical Society (later the American Mathematical Society) in 1888 and the Deutsche Mathematiker-Vereinigung in 1890. Most of these societies commenced the publication of a mathematical journal soon after their foundation and many of these journals have played, and still play, an important role in mathematical communication.

The Accademia dei Lincei (Academy of the Lynx-like) was founded in 1603and Galileo became a member in 1611. According to Kline in France, Desargues, Descartes, Fermat, and Pascal, among others, met privately under the leadership of Mersenne from 1630, and corresponded widely. This informal group led to the chartering of the Academie Royale des Sciences in 1616 by Louis XIV. Similarly, an English group led by John Wallis began to hold meetings in 1645 in Gresham College, London. This group was given a charter by Charles II in 1662 and adopted the name of the Royal Society of London for the Promotion of Natural Knowledge; Wallis was a charter member. The Berlin Academy of Sciences was founded in 1700 with Leibniz as its first president. In Russia, Peter the Great founded the Academy of Sciences in St. Petersburg in 1724. These academies were very important for the development of science and, in particular, of mathematics; indeed, many of the most important mathematicians of the eighteenth century were supported by these academies and never had a university position. The academies promoted the exchange of ideas both by facilitating the direct contact of the leading scientists and also by the publications that the academies soon started. While there were various reasons for the support of the academies by the rulers, it is clear that one reason was that the monarchs saw the importance of the emerging science and technology for the civil and military needs of their realms, and realized that mathematics was essential for this scientific development.

Mathematics in India

In India, Mathematics emerged in the 1200 BC. Aryabhata, Brahmagupta, Bhaskara are few pioneers of Indian Mathematics. Ancient and medieval Indian mathematical works, all composed in Sanskrit, usually consisted of a section of sutras in which a set of rules or problems were stated with great economy in verse in order to aid memorization by a student. The development of expansions of trigonometric functions was one of the greatest inventions in Mathematics in India. Vedic Mathematics is credited to India too. It goes without saying that Mathematics would not have reached its present state if not for the Indian decimal system. In recent times India saw a brilliant Mathematician in Srinivasa Ramanujan who changed the way world sees number theory. 

Development of Mathematics

The progress of accounting and mathematics were somewhat linked during the renaissance. This is because people felt the need to learn basic arithmetic in order to do trade of any sort.  In   the Renaissance, the academic status of mathematics declined, because it was strongly associated with trade and commerce. Although it continued to be taught in European universities, it was seen as subservient to the study of natural and metaphysical philosophy. This trend was somewhat reversed in the seventeenth century, with the University of Aberdeen creating a Mathematics Chair in 1613, followed by the Chair in Geometry being set up in University of Oxford in 1619 and the Lucasian chair of Mathematics being established by the University of Cambridge in 1662. However, it was uncommon for mathematics to be taught outside of the universities. Isaac Newton, for example, received no formal mathematics teaching until he joined Trinity College, Cambridge in 1661. 

In the 18th and 19th centuries, the industrial revolution led to an enormous increase in urban population. Basic numeracy sills, such as ability to tell time, count money and carry out simple arithmetic, became essential. Within the public education systems, mathematics became a central part of the curriculum from an early age. 

During the 20th century, mathematics education was established as an independent field of research. Here are some of the main events in this development:

·         In 1893, a Chair in mathematics education was created at the University of Göttingen, under the administration of Felix Klein

·         The International Commission on Mathematical Instruction (ICMI) was founded in 1908, and Felix Klein became the first president of the organisation

·         A new interest in mathematics education emerged in the 1960s, and the commission was revitalised

·         In 1968, the Shell center for mathematical education was established in Nottingham

·         The first International congress for mathematical education (ICME) was held in Lyon in 1969. The second congress was in Exeter in 1972, and after that it has been held every four years