Leonhard Euler – The Revolutionary Genius Who Shaped Modern Mathematics (1707–1783)

Leonhard Euler – The Revolutionary Genius Who Shaped Modern Mathematics (1707–1783)

Welcome to History with BMResearch, where we explore the extraordinary legacy of Leonhard Euler, a pioneering mathematician whose groundbreaking work shaped modern science. In this video, we dive deep into Euler’s life—from his early days in Basel to his revolutionary contributions in differential equations, infinite series, and mathematical notation. Euler’s story is not just about complex theories like the Basel Problem or the Euler Identity; it is a tale of relentless genius set against the backdrop of Enlightenment history. Our journey spans across Basel, St. Petersburg, and Berlin, highlighting his influence in graph theory, number theory, and even optical theories. With tags such as Mathematics, Genius, Enlightenment, and Scientific Revolution, this biography celebrates Euler’s enduring legacy as a scientific pioneer whose work continues to inspire generations. Join us as we unravel the remarkable narrative of Euler's life and his transformative impact on modern science.

0:00 – Intro: The Blind Genius Who Changed Mathematics
0:55 – Early Life, Family, and Education in Basel
2:07 – Mentorship by the Bernoulli Family
3:59 – Euler’s Move to St. Petersburg and New Beginnings
5:46 – Russia’s Turbulence and Euler’s First Major Works
8:56 – Rise at the St. Petersburg Academy
11:27 – Marriage, Family Life, and Mathematical Breakthroughs
13:18 – Vision Loss and the Invitation to Berlin
14:37 – Berlin Years: Astronomy, Fluid Dynamics, and Mechanics
17:39 – Daily Routine, Reputation, and Court Conflicts
19:38 – Blindness and Groundbreaking Work in Optics
22:03 – Inner Vision: Math Beyond Sight
23:55 – Return to Russia Under Catherine the Great
26:31 – Educational Works and Standardizing Notation
27:44 – Mathematical Notation: e, f(x), i, and Σ
30:26 – Euler’s Mastery of Differential Equations
32:49 – Integral Calculus and the Institutiones Calculi
34:44 – Euler’s Work Style, Mentorship, and Personal Life
36:07 – Creating the Language of Mathematics
39:52 – Euler Diagrams and Logical Visualization
41:14 – Solving the Seven Bridges of Königsberg
43:08 – Foundations of Graph Theory and Network Science
45:32 – Infinite Series and the Basel Problem
48:09 – Divergent Series and the Birth of the Zeta Function
50:35 – Letters and Scientific Correspondence
53:08 – Collaborations with Goldbach, Lagrange, and Others
55:42 – Full Blindness and Unmatched Productivity
58:14 – Integral Calculus and Final Years of Research
59:28 – Euler’s Death and His Enduring Legacy
1:00:49 – Faith, Science, and the Harmony of Reason
1:05:53 – Legacy: Modern Mathematics Built on Euler’s Foundations

Sources
Boyer, C. B. (1991). A History of Mathematics (2nd ed.). Wiley.
Cajori, F. (1991). A History of Mathematics (Vol. 1 & 2). Dover Publications.
Dunham, W. (1999). Euler: The Master of Us All. Mathematical Association of America.
Kline, M. (1972). Mathematical Thought from Ancient to Modern Times. Oxford University Press.
Simmons, G. F. (1992). Calculus Gems: Brief Lives and Memorable Mathematics. McGraw-Hill.

#LeonhardEuler, #MathGenius, #MathematicsHistory, #EnlightenmentScience, #EulerLegacy

Image Credit
By Jakob Emanuel Handmann - This file was derived from: Leonhard Euler.jpgEdited by: BammeskOriginal source: Kunstmuseum Basel, Public Domain, https://commons.wikimedia.org/w/index...
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