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History of mathematics

The availability of availability of mathematics could be realized since ancient times in the form of counting. It is a very simple form of mathematics where ancient people use their thumb or some figures to count any item or things. It was the most basic form of mathematics that lay down emphasize on its availability since humanity exists. Since starting the mathematics, have become the basis of scientific inventions, calculations, new development and advancements, systematic study of shapes and objects. The huge revolution that has been faced in the history of mathematics is related to the invention of zero. It was something that had changed the dimensions of this subject. After zero, it becomes possible to focus on wide scope of mathematics and its spectrum also increases at very large scale. The role of Indian mathematicians like Aryabhata, Pinangla and Brahmgupta was immense within the invention of Zero. They provide huge level of contribution towards the use of Zero in their theorems. During their work, these philosophers and mathematicians provide the use of zero in the decimal value system. However, the role of Greek mathematicians is immense in the history of mathematics. They provided the mathematics rules that become the subject of the entire subject. It is to acknowledge that at the time of Alexander the great the period was called as Hellenistic mathematics. It is clear that Greek mathematicians used all the logics to propound specific set of rules in the history of mathematics. Babylonian mathematics is also very crucial with the perspective of understanding the history of mathematics. Mesopotamian people gave their huge contribution into the Islamic mathematics. The early civilization of Mesopotamian people provides the evidence about metrology system that is termed as highly complex in nature. Further, the multiplication calculations along with geometrical and divisional problems were also grew in the era of 2500 BC to 3000 BC. Some clay tablets have been recovered which provided the evidence about using the algebra, quadratic and cubic equations. The numeral system for Babylonian was based on sexagesimal numerical system that is generally based on 60. Thus, it is clear that current time system like 60 seconds in one minute, 60 minutes in one hour, etc. is based upon the Babylonian mathematics. The Babylonian mathematician’s principles were also similar to Romans and Greeks mathematicians. They just used the same place value system in decimal value. However, there were certain controversies into the principles and concepts given by the Babylonian mathematicians that are still required to be proved.

Ahead the Egyptian work is also equally useful with the perspective of the history of mathematics. The major work of Egyptian mathematicians is the Rhind papyrus and Moscow Papyrus. The Rhind papyrus is the work related to the formulas and methods related to division and unit fractions. Further, the multiplications and rules related to composite and prime numbers also come into the category of Rhind Papyrus. The solutions of linear series as well as the arithmetic and geometric solutions is also a part of Egypt mathematician works. In China also the role of mathematics was immense with respect to the deliver lots of contribution into such subject. There are proofs that in China the value of pie was known to the seven places to the decimal that was highly more than the west mathematicians. The pattern to solve the linear equations in China was also advanced as compare to western countries. The Gaussian reduction is something that has a high level of relevancy into the mathematics history of China. Further, the role of India is also immense within the development of mathematics. But Indians use the calculations in astronomy just to predict the stars consequences. Thus, it is clear that the calculation is very old in the Indian number system.

The zero has been propounded by the Indian mathematician and most importantly it was passed on to the western countries through Islamic mathematician. Thus, it is clear that the basis of modern mathematics has been put by the Indian mathematician. The Maya civilization is something that has huge level of relevancy with the development of Zero into the numerical value system. They number base was twenty and most significant contribution is related to providing the calendar dates. Thales, Pythagoras, Euclid, Apollonius, Archemedes, etc. these are certain mathematicians who have provided their significant contribution into the field of math over the different period of time. In different centuries, these mathematicians show their relevance to the math and its related concepts. The Pythagoras theorem is something that has changed the dimensions completely. However Greek claim to be the inventory of this principle but evidence were clear that Mesopotamian and Babylonian have also contributed in Pythagoras theorem far earlier than the Greek mathematicians.

The work of Fibonacci propounded into the 1175-1250 AD was the most crucial work into the field of mathematics. It tools place in European mathematics. At the end of Roman Empire in the west the mathematicians into the west region come to an end. But Arabic, chine, and Indian mathematicians continued their practices and increased their understanding towards its principles and concepts. The Fibonacci sequence has brought down the transformation into the field of math. The sixteenth century onwards the huge changes into the field of mathematics have been experienced. It was the era when the foundation for modern mathematics had been put into practice. The development in equation solving issues, Arabic numerical and algebra was huge into the sixteenth century. Girolamo Cardano was the one who change the dimensions for the cubic equation and provide a solution for the fourth degree polynomial equation. Francois viete developed the + and – sign during his practice period. The invention of logarithm has also done by the Francois Viete, which was used in bringing the transformation into the multiplication process. Ahead the development of rules and formulas of logarithm has been done by John Napier in the year 1614. He advances the field of the logarithm and definitely made it more interesting. Other than John Napier the seventeenth century belongs to the work of Kepler, Newton and Galileo, Descartes and Leibniz. The Logarithm actually reduces the calculation time and gives birth to new mathematics diverse ideas. Isaac Newton gave the most significant principle for the mathematics named calculus. It was one of the most important inventions into the field of math. The ground work for the probability theory was set by the Blaise Pascal and Fermat that later become the foundation for the game of gambling through combinatory.

 Later it becomes the foundation of utility theory when the Pascal and Wager gave new dimensions to the probability theory. In the era of the eighteenth century again the dimensions were set by Leonhard Euler when he propounded the graph theory and most importantly the complex analysis and multitude of analysis were also noticeable work of Leonhard Euler. Next change or newly pioneered work did by Laplace as his work shed light on celestial mechanics and statistics. Further, the Nineteenth century took the mathematics up to the next and highest level. This century was most revolutionary century ever in the history of mathematics. In this century, the Carl Guass changed the thought process towards the math and provided lots of stunning and amazing piece of works. His work included the functions of complex variables, geometry and most importantly the convergence of series. The fundamental theorem of algebra and quadratic reciprocity law was also firstly propounded by the Carl Guass. His contribution into this field was immense. The birth of ideas related to the curves and surfaces was given by the German mathematician Bernhard Reimann. He has re shaped the understanding about the geometry and gave new dimensions to this field of mathematics. Hermann Grassman and William Hamilton provided the new facts related to the abstract algebra. At one hand, Grassman provided the knowledge about vector spaces, and Hamilton shed light on noncommunicative algebra. This was the time when the foundation of computer science came into existence. The George Boole, a British mathematician, actually propounded the Boolean algebra that includes the 0 and 1 only numbers. Nineteenth century actually reveals so many principles and fundamentals which were completely unknown or forced to be unsolved since last so many centuries. The most noticeable fact was that so many mathematical societies come into existence to teach the principles of math to students and scholars. Thus in this way the historical development of mathematics continued till the twentieth century Rmanujan, Alan Turing and recently Andrew wiles that has changed the dimensions of mathematics and brings some noticeable changes. The Andrew wiles has solved the last theorem of Fermet which remain unsolved since three centuries. In the twentieth century, it actually becomes the profession and a systematic way to focus on mathematics and its related concepts. Now challenges for upcoming mathematicians are 23 (10 have been solved,7 are partially solved, 2 are remaining and 4 are under arguable status regarding their solutions) unsolved problems which are still the challenge in the field of math and needs more concentration by the future mathematicians. Thus, it explains the brief historical development of mathematics from its distorted inception to recent concrete development. 

History of Mathematics is a multidisciplinary subject with a strong presence in Oxford, spread across a number of departments, most notably the Mathematical Institute and the History Faculty.  The research interests of the members of the group cover mathematics, its cultures and its impacts on culture from the Renaissance right up to the twentieth century.

Core research topics include the place of mathematics in the transformation of intellectual culture during the early modern period (Philip Beeley, Yelda Nasifoglu, Benjamin Wardhaugh), the development of abstract algebra during the nineteenth and twentieth centuries (Christopher Hollings, Peter Neumann), and the effects of twentieth-century politics on the pursuit of mathematics (Hollings).  The group has a strong background in the mathematics of seventeenth-century Europe, with studies of, for example, the correspondence of the seventeenth-century Savilian Professor of Geometry John Wallis and of the mathematical intelligencer John Collins (Beeley). The current 'Reading Euclid' project seeks to understand the place of Euclid's Elements within early modern British culture and education (Beeley, Nasifoglu, Wardhaugh).  In recent years, members of the group have also been involved in efforts to provide the first sober assessment of the mathematical education and abilities of Ada Lovelace (Hollings, Ursula Martin) and the first biography of pit lad-turned-mathematics professor Charles Hutton (Wardhaugh).

Current students within the group are Liu Xi (history of differential geometry), Kevin Baker (the first readers of Newton’s Principia), and Johann Gaebler (the intellectual contexts for the reception of the calculus).

Others in Oxford with interests in the history of mathematics include Howard Emmens (history of group theory), Raymond Flood (Irish mathematics), Keith Hannabuss (nineteenth-century mathematics), Daniel Isaacson (the rise of modern logic, 1879–1931), Rob Iliffe (Newton and Newtonianism), Stephen Johnston (early modern practical mathematics and instruments), Matthew Landrus (Renaissance mathematics and the arts), Robin Wilson (nineteenth-century mathematics, and the history of combinatorics).

Some case studies of research carried out by members of the group may be found here, here, and here.

Seminars

The group holds a semiregular departmental seminar, as well as an annual series of general lectures entitled 'What do historians of mathematics do?', held in Trinity Term.  Members of the group also organise a seminar in ‘the History of the Exact Sciences’ during Hilary Term (the programme for Hilary Term 2018 may be found here, with abstracts here) and a research workshop in early modern mathematics each December.  These events are complemented by Oxford’s wide range of activity in history of science, technology and medicine more generally.

Undergraduate study

Within the Mathematical Institute, the group offers the following undergraduate teaching:

Postgraduate study

The group welcomes applications for postgraduate study, which would be based either in the Mathematical Institute or the History Faculty, depending on the interests and background of the applicant.  Avenues for study include the MSc or MPhil in History of Science, Medicine and Technology, or a DPhil in the History of Mathematics.  Prospective applicants are encouraged to contact either Dr Christopher Hollings (Mathematical Institute) or Dr Benjamin Wardhaugh (History Faculty) to discuss options.

See also

British Society for the History of Mathematics

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