# Brief History Of Mathematics | Evolution And Development Of Mathematics Over The Years # Historical Development Of Mathematics

Mathematics starts with counting. It is not reasonable, however, to suggest that early counting was mathematics. It was only when some record of the counting was kept and, therefore, some representation of numbers occurred can mathematics be said to have started.

In Babylonia mathematics developed from 2000 BC.

A place value notation number system had evolved over a lengthy period with a number base of 60 which allowed arbitrarily large numbers and fractions to be represented and so proved to be the foundation of more high powered mathematical development like:

• Number problems such as that of the Pythagorean triples were studied from at least 1700 BC.
• Systems of linear equations were studied in the context of solving number problems.
• Geometric problems relating to similar figures, area, and volume were also studied and values were obtained for n.
• Quadratic equations were also studied and these examples led to a type of numerical algebra.

## History Of Greek Mathematics(Brief Summary)

The Babylonian basis of mathematics was inherited by the Greeks and independent development by the Greeks began from around 450 BC and the major Greek progress in mathematics was from 300 BC to 200 AD.

Some important mathematics breakthroughs in Greek history are:

• Zeno of Elea's paradoxes led to the atomic theory of Democritus.
• Studies of the area lead to a form of integration.
• The theory of conic sections shows a high point in the pure mathematical study by Apollonius.
• A more precise formulation of concepts led to the realization that the rational numbers did not suffice to measure all lengths.
• A geometric formulation of irrational numbers arose.
• Further mathematical discoveries were driven by astronomy, for example, the study of trigonometry started.

After this time, mathematics progress continued in many Islamic countries. Mathematics also flourished particularly in countries like Iran, Syria, and India though, this work did not match the progress made by the Greeks but in addition to the Islamic progress, it did preserve Greek mathematics.

## History Of European Mathematics (Brief Summary)

Some important mathematics breakthroughs in European history are:

### History Of European Mathematics (16th Century)

Following are some of the key progress made in mathematics during the 16th century in Europe:

• Major progress in mathematics in Europe began again at the beginning of the 16th Century Pacioli, then Cardan, Tartaglia, and Ferrari with the algebraic solution of cubic and quadratic equations.
• The progress in algebra had a major psychological effect and enthusiasm for mathematical research, in particular, research in algebra, spread from Italy to Stevin in Belgium and Viète in France.
• Copernicus and Galileo revolutionized the applications of mathematics to the study of the universe.

### History Of European Mathematics (17th Century)

Significant mathematics findings and expansions throughout this period are:

Calculus was to be the topic of most significance to evolve in the 17th Century.

• The 17th Century saw Napier, Briggs, and others greatly extend the power of mathematics as a calculatory science with his discovery of logarithms.
• Progress towards the calculus continued with Fermat, who, together with Pascal, began the mathematical study of probability.
• Newton, building on the work of many earlier mathematicians such as his teacher Barrow, developed calculus into a tool to push forward the study of nature.
• Cavalieri made progress towards calculus with his infinitesimal methods and Descartes added the power of algebraic methods to geometry.

### History Of European Mathematics (18th Century)

Some crucial mathematics discoveries and developments in European history during the 18th century are:

• Newton's theory of gravitation and his theory of light takes us into the 18th Century. His work contained a wealth of new discoveries showing the interaction between mathematics, physics, and astronomy.
• Leibniz, whose much more rigorous approach to calculus (although still unsatisfactory) set the scene for the mathematical work of the 18th Century.
• Leibniz's influence on the various members of the Bernoulli family was important in seeing the calculus grow in power and variety of applications.

The most important mathematician of the 18th Century was Euler who, in addition to work in a wide range of mathematical areas, was to invent two new branches, namely the calculus of variations and differential geometry.

• Euler was also important in pushing forward with research in number theory begun so effectively by Fermat.
• Toward the end of the 18th Century, Lagrange was to begin a rigorous theory of functions and of mechanics.
• The period around the turn of the century saw Laplace's great work on celestial mechanics as well as major progress in synthetic geometry by Monge and Carnot.

### History Of European Mathematics (19th Century)

The 19th Century saw rapid progress in mathematics, some of the critical mathematics findings and developments during this period are:

• Fourier's work on heat was of fundamental importance.
• Non-Euclidean geometry developed by Lobachevsky and Bolyai led to the characterization of geometry by Riemann.
• In geometry Plücker produced fundamental work on analytic geometry and Steiner in synthetic geometry.

Gauss, thought by some to be the greatest mathematician of all time, studied quadratic reciprocity and integer congruences. His work in differential geometry was to revolutionize the topic. He also contributed in a major way to astronomy and magnetism.

• The 19th Century saw the work of Galois on equations and his insight into the path that mathematics would follow in studying fundamental operations.

Galois' introduction of the group concept was to herald a new direction for mathematical research which has continued through the 20th Century.

• Cauchy, building on the work of Lagrange on functions, began rigorous analysis and began the study of the theory of functions of a complex variable. This work would continue through Weierstrass and Riemann.
• Algebraic geometry was carried forward by Cayley whose work on matrices and linear algebra complemented that by Hamilton and Grassmann.

The end of the 19th Century saw Cantor invent set theory almost single-handedly while his analysis of the concept of number added to the major work of Dedekind and Weierstrass on irrational numbers.

• Fredholm's work led to Hilbert and the development of functional analysis.
• Maxwell revolutionizes the application of analysis to mathematical physics.
• Statistical mechanics was developed by Maxwell, Boltzmann, and Gibbs. It led to ergodic theory.
• The study of integral equations was driven by the study of electrostatics and potential theory.
• Sophus Lie's work on differential equations led to the study of topological groups and differential topology.

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