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About Pierre-Simon Laplace, the Creator of the Laplace Transform.

On a day like today, on 5 March 1827, one of the greatest mathematicians mankind has ever seen the birth of, Pierre-Simon Laplace, died in the French capital. In addition to being a mathematician, Laplace was also a very successful physicist and astronomer, whose contributions were fundamental to the development of celestial mechanics, mathematical analysis and the study of probability. He helped to consolidate and extend the work of Sir Isaac Newton with his treatise ‘Traité de Mécanique Céleste’ (Treatise on celestial mechanics), which explains the stable systems in the solar system and provides the necessary foundations for what is now modern astronomy.

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Main Mathematical Contributions.

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• About Celestial Mechanics:

It was truly revolutionary for astronomy, mathematics and physics in general how Laplace brilliantly applied mathematical analysis to celestial mechanics, which is why he was able to successfully explain the perturbations described in planetary orbits, and thus also explain the stability of planetary systems.

It is also very important to mention one of his most famous theories, his ‘nebular theory’, which states that the formation of the solar system was the result of the action of a rotating nebula.

• Probability Theory:

Laplace managed to formulate a central theorem of probability theory, such as the central limit theorem, as well as the constant application of probabilities to the resolution of problems related to astronomy and geodesy.

• Mathematical Analysis:

It is in this area of mathematics where we can find what is perhaps his most important work and contribution to mathematics and science in general, due to its immense scope and repercussions. And we are talking of course about the ‘Laplace Transform’, which is a tool that, among many things, is of great importance when solving Differential Equations.

He also developed the Laplace equation, which appears frequently in many problems related to physics and mathematics.

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Life and Performance.

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Pierre-Simon was born on 23 March 1749, in the French town of Beaumont-en-Auge, Normandy. His demonstration of an impressive talent for mathematics was a very precocious act in his life, from which he would, for example, attain a teaching position at the prestigious École Militaire in Paris at a very early age, and also achieve the important achievement of attaining membership of the French Academy of Sciences.

During the period of the French Revolution he was a political pragmatist, working for Napoleon Bonaparte, as well as for the revolutionary government of the time. He was appointed as Minister of the Interior by Bonaparte for a brief period. Lapalce was particularly renowned for his incredible ability to apply his scientific knowledge to solving real-life problems, making him an important player in the political chess game of his time.

Key Publications:

• 'Traité de Mécanique Céleste (Treatise on Celestial Mechanics)(1799-1825)'.

  This would be his magnum opus, which would, among other things, accomplish the important task of establishing the already famous Newtonian mechanics with greater rigour, managing to explain the behaviour of the solar system by means of perfectly structured mathematical laws and theorems.

• 'Théorie Analytique des Probabilités' (Analytical Probability Theory) (1812) .

  A fundamental treatise, up to the present day, on the theory of probability, a treatise that would help shape modern probability.

• 'Exposition du Système du Monde' (Exposure of the world system) (1796).

  This was a scientific work aimed at disseminating his revolutionary nebular theory to explain the formation of planetary systems, as well as other no less important concepts of astronomy.

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In conclusion, we can be sure that the scientific work of Pierre-Simon Laplace continues to influence our understanding of science today. He left us such useful tools as the Laplace transform, a tool that is very present in today's technological structure. The edifice of modern mathematics continues to be built on Laplace's scientific contributions, and the same is true for physics and engineering in the 21st century.

Thank you, Laplace.

Some of His Contributions.

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Pierre-Simon Laplace Portrait Image Source

Note: All the images related to Laplace Contributions are crafted by me using the text editor based on LaTeX: Beamer. The Structure of this article is by my authorship too.

Regards.

References

Part II Section 18.6 of Jaynes, E. T. & Bretthorst, G. L. (2003). Probability Theory: The Logic of Science. Cambridge University Press. ISBN 978-0-521-59271-0

Weisstein, Eric W. "Laplace Transform." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LaplaceTransform.html

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