science: The Evolution of Mathematics and Physics

In mathematics the calculus invented by Newton and G. W. Leibniz was developed by the Bernoullis, Leonhard Euler, and J. L. Lagrange into a powerful tool that was to be used not only in mathematics but also in physics and astronomy. Newtonian physics spread to the Continent slowly, its acceptance being hindered by adherents of the older Cartesian philosophy and by disputes over priority in the invention of the calculus. However, by the late 18th cent. it was firmly established. Other branches of physics came into their own during this period. The study of electricity expanded to include electric currents and magnetism, and it was finally synthesized in the theory of electromagnetic radiation of J. C. Maxwell in the second half of the 19th cent. These discoveries provided the foundation for the technological advances in communications and in other fields using electrical energy. The wave theory of light was revived at the beginning of the 19th cent. by Thomas Young and developed by others; Maxwell's theory showed that light was one form of electromagnetic energy. In the 18th cent. scientists thought that heat was a kind of fluid called caloric. However, by the early 19th cent. it became apparent that heat is a form of motion—the motion of the particles of which substances are composed. The classical theory of heat and thermodynamics was developed by J. P. Joule, Lord Kelvin, R. J. E. Clausius, and others, who showed the relation between heat and other forms of energy and formulated the law of conservation of energy. Maxwell, Ludwig Boltzmann and others developed statistical mechanics, which treats matter as a large aggregate of many particles and applies statistical methods to the prediction of its behavior.

Sections in this article:

• Introduction
• Promise and Problems of Modern Science
• Modern Science and Technology
• Astronomy beyond the Visual Spectrum
• The Abstraction of Mathematics
• Biology Becomes an Interdisciplinary Science
• Advances in Chemistry
• Quantum Theory and the Theory of Relativity
• The Impact of Elementary Particles
• Revolutions in Modern Science
• Science and the Industrial Revolution
• New Ideas in Biology
• Birth of Modern Geology
• Advances in Astronomy
• Innovations in Chemistry
• The Evolution of Mathematics and Physics
• The Age of Classical Science
• The Impact of Sir Isaac Newton
• Improved Communication of Scientific Knowledge
• The Rejection of Traditional Paradigms
• The Scientific Revolution
• The Craft Tradition and Early Empiricism in Europe
• Muslim Preservation of Learning
• Scientific Progress in China and India
• Influence of the Alexandrian Schools
• Early Greek Contributions to Science
• Practical Applications in the Ancient Middle East
• The Beginnings of Science
• Branches of Specialization
• Role of Measurement and Experiment
• The Scientific Method
• Bibliography

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