Not Only Truth But Supreme Beauty

COMBINATORICS. COMBINATORICS WAS CLASSICALLY CONSIDERED THE THEORY OF SYSTEMATICALLY COUNTING HIGHLY STRUCTURED COLLECTIONS OF OBJECTS, BUT THE WORD HAS SINCE BROADENED TO MEAN ESSENTIALLY ANY MA...

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ORDER THEORY. ORDER THEORY IS THE STUDY OF GENERALIZED NOTIONS OF INEQUALITY FOR NUMBERS. IN PARTICULAR, WE ARE OFTEN INTERESTED IN CASES WHERE WE ONLY HAVE A “PARTIAL” ORDERING: YOU MIGHT HA...

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ALGEBRAIC COMBINATORICS. COMBINATORICS IS THE SYSTEMATIC STUDY OF COUNTING STRUCTURED COLLECTIONS OBJECTS. ALGEBRAIC COMBINATORICS IS DOING THIS, BUT WITH A SPECIAL EMPHASIS ON USING NOTIONS OF S...

https://proofsareart.tumblr.com/post/138437203052

ALGEBRAIC COMBINATORICS. COMBINATORICS IS THE SYSTEMATIC STUDY OF COUNTING STRUCTURED COLLECTIONS OBJECTS. ALGEBRAIC COMBINATORICS IS DOING THIS, BUT WITH A SPECIAL EMPHASIS ON USING NOTIONS OF S...

https://proofsareart.tumblr.com/post/138368044609

COMPLEX ANALYSIS. ANALYSIS IS THE STUDY OF FUNCTIONS, OR “MAPS”, THAT ARE RULES FOR TRANSFORMING OBJECTS INTO OTHER OBJECTS; COMPLEX ANALYSIS IS INTERESTED IN THOSE MAPS FOR WHICH THE ORIGINA...

https://proofsareart.tumblr.com/post/138183372626

ALGEBRA. ALGEBRA IS THE DEEP STUDY OF OPERATIONS LIKE MULTIPLICATION, WHICH TURN TWO OBJECTS INTO A SINGLE OBJECT. THIS PROOF LIES IN THE AREA OF RING THEORY, WHICH IS CONCERNED WITH THE INTERAC...

https://proofsareart.tumblr.com/post/132055895842

ALGEBRA. ALGEBRA IS THE DEEP STUDY OF OPERATIONS LIKE MULTIPLICATION, WHICH TURN TWO OBJECTS INTO A SINGLE OBJECT. THIS PROOF LIES IN THE AREA OF RING THEORY, WHICH IS CONCERNED WITH THE INTERACT...

https://proofsareart.tumblr.com/post/131845832441

COMBINATORICS. COMBINATORICS IS, NOWADAYS, A “CATCH ALL” ADJECTIVE THAT DESCRIBES A WIDE VARIETY OF MATHEMATICAL FIELDS. HOWEVER, IT BEGAN WITH WHAT IS TODAY CALLED “ENUMERATIVE COMBINATORI...

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FUNCTIONS. FUNCTIONS ARE EXTREMELY IMPORTANT MATHEMATICAL OBJECTS WHICH DICTATE RULES FOR TURNING OBJECTS OF ONE KIND INTO OBJECTS OF ANOTHER KIND. THEY ARE UBIQUITOUS IN MATHEMATICS AND ARE SO C...

https://proofsareart.tumblr.com/post/128953335856

COMBINATORICS. COMBINATORICS IS AN EXTREMELY BROAD SUBJECT THAT COVERS NEARLY ALL OF FINITE MATH. THE TERM ORIGINALLY REFERRED TO A DISCIPLINE WHICH IS NOT CALLED ENUMERATIVE COMBINATORICS, WHICH...

https://proofsareart.tumblr.com/post/126195760621

INDUCTION. INDUCTION IS A METHOD USUALLY USED TO PROVE STATEMENTS REGARDING NATURAL NUMBERS WHEN ONE ONLY HAS INFORMATION ABOUT THE “LOCAL” TRUTH OF THESE STATEMENTS. IT IS THE FORMAL MECHANI...

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TRANSCENDENTAL NUMBER THEORY. A NUMBER IS CALLED “ALGEBRAIC” IF IT IS THE ROOT OF SOME POLYNOMIAL, AND IT IS CALLED “TRANSCENDENTAL” IF IT IS NOT. ALGEBRAIC NUMBERS CAN BE THOUGHT OF AS...

https://proofsareart.tumblr.com/post/114744777626

KNOT THEORY. KNOT THEORY IS THE STUDY OF HOW CIRCLES CAN BE EMBEDDED INTO THREE-DIMENSIONAL SPACE. IT IS LIKE ORDINARY KNOT THAT WE MIGHT TIE IN A ROPE, EXCEPT AFTER WE TIE IT WE MUST FUSE THE EN...

https://proofsareart.tumblr.com/post/113214341021

COMBINATORICS. COMBINATORICS BEGAN AS THE SYSTEMATIC STUDY OF COUNTING THE NUMBER OF ELEMENTS IN PARTICULARLY COMMON SETS. NOWADAYS, THIS DEFINITION HAS BROADENED AND YOU CAN USE “COMBINATORICS...

https://proofsareart.tumblr.com/post/109730403661

DESCRIPTIVE SET THEORY. SET THEORY IS THE FORMAL STUDY OF SETS, THE OBJECTS WHICH MATHEMATICIANS USE IN ORDER TO SPEAK ABOUT MULTIPLE OBJECTS AT ONCE. DESCRIPTIVE SET THEORY RESTRICTS THE DISCU...

https://proofsareart.tumblr.com/post/107927161607

Hello, everyone! THIS POST IS, FIRST AND FOREMOST, AN APOLOGY to all of my wonderful followers, who have been the driving creative force behind about 90% of this blog’s history, who have been...

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OPERATIONS RESEARCH. OR IS THE STUDY OF OPTIMIZATION PROBLEMS, AND ONE OF THE CENTRAL METHODS USED IS CALLED INTEGER PROGRAMMING. UNFORTUNATELY, THE METHOD IS GENERALLY VERY DIFFICULT TO SOLVE, ...

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mindfuckmath : > NO, REALLY, PI IS WRONG: THE TAU MANIFESTO   >  > Happy Tau Day, everyone!  In case you don’t know, Tau = 2 Pi, or > the ratio of a circle’s�...

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MEASURE THEORY. MEASURE THEORY IS THE STUDY OF AN ABSTRACT GENERALIZATION OF NATURAL “MEASURES” OF GEOMETRIC OBJECTS, LIKE LENGTH, AREA, AND VOLUME. IN 1904, LEBESGUE DISCOVERED HOW TO TEASE ...

https://proofsareart.tumblr.com/post/90190835291

LINEAR ALGEBRA. LINEAR ALGEBRA IS THE STUDY OF SPACES WHICH ARE IN SOME SENSE “FLAT” LIKE POINTS, LINES, PLANES, AND THEIR HIGHER-DIMENSIONAL ANALOGUES. THE TOOLS OF LINEAR ALGEBRA OFTEN HELP...

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