General Math Resources & Articles for Students and Teachers
Algebra & Trigonometry || Linear Algebra
Geometry || Algebraic Geometry || Projective Geometry || Differential Geometry
Logic & Set Theory || Number Theory || Fermat's Last Theorem
Modern/Abstract Algebra || Lie Group - Lie Algebra || Representation Theory
Mechanics || Quantum Mechanics || Quantum Field Theory
Calculus || Tensor Calculus & Relativity || Graph Theory & Combinatorics
Topology || Algebraic Topology || Differential Topology
Category Theory || Chaos Theory & Fractals
"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."
"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)
She was one of a group of black women mathematicians at NASA and its predecessor who were celebrated in the 2016 movie “Hidden Figures.”
She was the inspiration for the movie Hidden Figures and calculated the flight paths for NASA’s early missions. Interview September, 2017
The CRM-Fields-PIMS prize has become the premier Canadian award for research achievements in the mathematical sciences. It is awarded jointly by the three Canadian mathematics institutes.
The Fields Medal is awarded every four years on the occasion of the International Congress of Mathematicians to recognize outstanding mathematical achievement for existing work and for the promise of future achievement.
December 1, 2014 - Pacific Institute for the Mathematical Sciences
"The following texts were provided by the International Mathematical Union, which awards the Fields Medals. They do an excellent job of explaining in as accessible language as possible what the four 2014 medallists did to earn their awards."
Sept. 23, 2019 | CBC Radio | Audio Episode: 54 minutes
"Most problems I work on are related to geometric structures on surfaces and their deformations. In particular, I am interested in understanding hyperbolic surfaces."
Maryam Mirzakhani is the first woman to ever win the Fields Medal – known as the "Nobel Prize of mathematics" – in recognition of her contributions to the understanding of the symmetry of curved surfaces.
The first woman to win the prestigious Fields Medal prize discusses her life as a mathematician
Maryam Mirzakhani is among four young researchers to win Fields Medals, awarded every four years.
Essay by Amy Wilkinson - August 7, 2017 - The New York Times
"A brief description of the work of the winners is available at the links given below. The laudations for the winners and their talks at the Congress will appear in Volume 1 of the Proceedings."
Scientific American | by John Matson, August 20, 2010
Deccan Herald | by Kalyan Ray, Hyderabad, Aug 20, 2010
The Fields Medal, considered the Nobel Prize of math, has been awarded quadrennially since 1936 by the International Congress of Mathematicians to recognize outstanding mathematics achievement.
"for their foundational contributions to theoretical computer science and discrete mathematics, and their leading role in shaping them into central fields of modern mathematics."
Avi Wigderson and László Lovász won for their work developing complexity theory and graph theory, respectively, and for connecting the two fields.
for “pioneering the use of methods from probability and dynamics in group theory, number theory and combinatorics.”
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
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."
"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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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.
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