"Like music or art, mathematical equations can have a natural progression and logic that can evoke rare passions in a scientist. Although the lay public considers mathematical equations to be rather opaque, to a scientist an equation is very much like a movement in a larger symphony. Simplicity. Elegance. These are the qualities that have inspired some of the greatest artists to create their masterpieces, and they are precisely the same qualities that motivate scientists to search for the laws of nature. Like a work of art or a haunting poem, equations have a beauty and rhythm all their own."
Michio Kaku
"Philosophy is written in this grand book -- I mean the universe -- which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles and other geometric figures, without which it is humanly impossible to understand a single word of it."
--- GALILEO GALILEI, H Saggiatore (1623)
10 Mind Blowing Mathematical Equations | by Sean Li
What is the most beautiful equation? | Quora Forum
The Baffling and Beautiful Wormhole Between Branches of Math | by Lee Simmons - Wired Magazine
The Most Beautiful Equation of Math: Euler's Identity | by Le Nguyen Hoang
The Mathematics of Planet Earth | John Baez
Fundamental Theorem of Finite Abelian Groups
Any finite abelian group is isomorphic to a direct product of cyclic groups of prime power order.
Any two such decompositions have the same number of factors of each order.
Analogous to the Fundamental Theorem of Arithmetic.
"The movement of humanity, arising as it does from innumerable arbitrary human wills, is continuous," he [Tolstoy] writes. "To understand the laws of this continuous movement is the aim of history … only by taking infinitesimal units for observation … and attaining to the art of integrating them (that is, finding the sum of these infinitesimals) can we hope to arrive at the laws of history."
Leo Tolstoy
"The 2016 Nobel Prize in Physics was awarded "for theoretical discoveries of topological phase transitions and topological phases of matter." What does that mean?"
"Thouless later used topology to explain other bizarre behavior, what's now known as the integer Quantum Hall effect. If a semiconducting slab sits at right angles to a magnetic field, a voltage develops across the slab. But instead of increasing smoothly as the strength of the magnetic field increases smoothly, the voltage jumps up at specific intervals. In 1983, Thouless was able to link this phenomena mathematically to topological properties, explaining the jumps."
"Not only are new materials on the horizon thanks to this novel work, but interest in the field of topological physics is exploding. The great contributions of all three of the Nobel Laureates exposed a richness of questions and possibilities, inspiring many other physicists to investigate."
The above graphic represents the evolutionary development of plants from their beginnings to the present.
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Computer Science
Charles Babbage and Alan Turing are each called the "Father of Computer Science."
Turing, however, is considered the originator of the idea of Artificial Intelligence.
Tutorials exist for just about any subject under the sun. If you don't find what you're looking for in that regard, do a search on GOOGLE or any preferred search engine.