During the eighteenth century, mathematics experienced advances in algebra and calculus, with the work of mathematicians such as Euler and Lagrange leading to new developments in several fields including number theory, mechanics, and geometry.
During the eighteenth century, mathematics experienced significant advancements in algebra and calculus, with the work of mathematicians such as Leonhard Euler and Joseph-Louis Lagrange leading to new developments in several fields including number theory, mechanics, and geometry.
One interesting fact is that Euler made important contributions to both mathematics and physics during the eighteenth century. He introduced the concept of a function in calculus and is credited with the formula e^(iπ) + 1 = 0, known as Euler’s Identity, which is considered one of the most beautiful equations in mathematics.
Lagrange also made significant contributions to mathematics during this time, with his work on the calculus of variations and the theory of analytic functions being particularly noteworthy.
According to the book “A History of Mathematics” by Carl B. Boyer and Uta C. Merzbach, “The eighteenth-century mathematics was dominated by France, and the work of Lagrange, Laplace, Monge, and many others brought French mathematics to the forefront of world science.”
In addition, the eighteenth century saw the rise of new mathematical societies and academies, such as the Royal Society in London and the French Academy of Sciences in Paris, which helped to promote the exchange of ideas and the development of new mathematical theories.
Here is a table summarizing some of the major mathematical developments of the eighteenth century:
|Mathematician||Field of Study||Major Contributions|
|Leonhard Euler||Calculus||Introduction of the concept of a function, development of the formula e^(iπ) + 1 = 0 (Euler’s Identity)|
|Joseph-Louis Lagrange||Calculus, Number Theory||Work on the calculus of variations and the theory of analytic functions|
|Jean le Rond d’Alembert||Calculus||Development of a solution to the one-dimensional wave equation|
|Pierre-Simon Laplace||Probability Theory||Development of Laplace’s equation and the Laplace transform|
|Gaspard Monge||Geometry||Development of the theory of descriptive geometry|
As the philosopher and mathematician Gottfried Wilhelm Leibniz once said, “Mathematics is the key and gate to the sciences.” The developments of the eighteenth century certainly attest to this statement, as new mathematical theories paved the way for breakthroughs in physics, engineering, and other fields.
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This video covers the history of mathematics and its applications, discussing topics such as set theory, logic, the Euclidean algorithm, and calculus. It also covers group theory and its applications in physics and chemistry, and mentions some of the most famous unsolved mathematical problems.
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Eighteenth-century mathematics emphasized a practical, engineering-like analysis of the material parts of physical systems. In Newtonian kinematics, for example, objects were often idealized as to shape, reduced to point masses, or treated only with regard to the motion of their center of mass.
One can easily name one main intrinsic reason: invention of Calculus in the very end of the previous century, and “invention of mathematical physics” by Newton.
It happened in the very beginning of 18-s century that sufficiently many people suddenly realized that mathematics can effectively explain the world.
But of course, there were also outside reasons, like development of industry and capitalism. That is people were interested in the explanation of the world.
By “invention of physics” I mean rigorous formulation of principal laws of mechanics and explanation of Kepler laws, explanation of tides, explanation of the shape of the Earth. All this was shortly confirmed by measurements, and these discoveries made an enormous impression. For the first time it was evident to many people that mathematics can really explain the world.
On the other hand, the external reasons were also important: people ( also kings and governments) were really INTERESTED in these questions, they payed for …
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Leonhard Euler (1707-1783) was arguably the greatest mathematician of the eighteenth century (His closest competitor for that title is Lagrange) and one of the most prolific of all time; his publication list of 886 papers and books may be exceeded only by Paul Erdös. Euler’s complete works fill about 90 volumes.