Topic/table/mathematics

Topic	Description	Wikipedia link	Subdivision	Skills used in research
Divergence of harmonic series	The divergence of the harmonic series	Harmonic series (mathematics)	Algebra	Mathematician
Equations	The technique of balancing and completion for solving equations	The Compendious Book on Calculation by Completion and Balancing, Algebra, and Equation	Algebra	Mathematician
Large sums	Simple formulas for certain arbitrarily large sums	Summation	Algebra	Mathematician
Pascal's triangle	A triangular configuration of numbers relating to the successive powers of any sum	Pascal's triangle	Algebra	Mathematician
Quadratic by completing square	The solving of quadratic equations by completion of the square	Completing the square	Algebra	Mathematician
Quadratic formula	A formula which solves quadratic equations	Quadratic formula	Algebra	Mathematician
Solving higher order polynomials	Methods for solving certain equations involving powers higher than the quadratic	Galois theory	Algebra	Mathematician
Systems of equations	Methods of solving systems of equations	Linear system	Algebra	Mathematician
Area enclosed by line and parabola	The area enclosed by a parabola and a line	The Quadrature of the Parabola	Geometry	Mathematician
Area of circle		Area of a disk	Geometry	Mathematician
Area of triangle from side lengths	The computation of the area of a triangle from its three side lengths alone	Heron's formula	Geometry	Mathematician
Basic geometry	Geometric objects: points, lines, circles, triangles, and so on	Geometry	Geometry	Mathematician
Chords	The properties of chords	Chord (geometry)	Geometry	Mathematician
Chord tables	A table of chord lengths indexed by angle	Ptolemy's table of chords	Geometry	Mathematician
Conic sections	The categorization and properties of conic sections	Conic section	Geometry
Existence of pi	The relationship between the area of a circle and its radius, involving the ratio of the circumference of the circle to its diameter	Pi	Geometry	Mathematician
Geometric mean	The relationship between the length of the altitude of a right triangle and the lengths of the segments into which it divides the hypotenuse	Geometric mean theorem	Geometry	Mathematician
Inscribed triangle on diameter is right	The angles of triangles inscribed in a circle with one edge on the diameter	Thales' theorem	Geometry	Mathematician
Irrational numbers	The existence of incommensurable ratios	Irrational number	Geometry
Isosceles base angles equal	The equality of the base angle of isosceles triangles	Pons asinorum	Geometry	Mathematician
Law of sines	The relatonship between the half chords of lengths and the diameter of the triangle’s circumscribed circle.	Law of sines	Geometry	Mathematician
Pi to 6 digits		Zu Chongzhi § Mathematics and Milü	Geometry	Mathematician
Pythagorean theorem	The relationship between the lengths of the hypotenuse of a right triangle and the other two sides	Pythagorean theorem	Geometry	Mathematician
Pythagorean triples 3 digit	Examples of triples of large whole numbers which, when taken together, are the lengths of the sides of a right triangle	Pythagorean triples	Geometry	Mathematician
Pythagorean triples 4 digit	Examples of triples of very large whole numbers which, when taken together, are the lengths of the sides of a right triangle	Pythagorean triples	Geometry	Mathematician
Pythagorean triples small	Examples of triples of small whole numbers which, when taken together, are the lengths of the sides of a right triangle	Pythagorean triples	Geometry	Mathematician
Similar and congruent triangles	The properties of similar and congruent triangles	Similarity (geometry) and Congruence (geometry)	Geometry	Mathematician
Sum-difference trig identities	Trigonometric identities relating to the sums and differences of angles	List of trigonometric identities § Angle sum and difference identities	Geometry	Mathematician
Surface area of sphere	The computation of the surface area of a sphere	Sphere § Surface area	Geometry	Mathematician
Volume of cone	The computation of the volume of a cone	Cone § Volume	Geometry
Volume of pyramid	The computation of the volume of different pyramids	Pyramid (geometry) § Volume	Geometry
Volume of sphere	The computation of the volume of a sphere	Sphere § Volume	Geometry
Axioms	Axiomatic reasoning	Axiomatic system	Method	Logician
Method of exhaustion	An approximation of the ratio of a circumference of a circle to its diameter, using the area of polygons and the method of exhaustion	Method of exhaustion	Method	Logician
Proof by contradiction	The method of proof by contradiction	Proof by contradiction	Method	Logician
Algebra	Notation for abbreviating the unknown and other elements of an equation in a systematic and useful fashion	Algebra	Notation	Logician
Negative numbers	Notation for negative quantities	Negative number	Notation	Logician
Place values	Positional notation	Positional notation	Notation	Logician
Scientific notation	Notation for very large numbers	Scientific notation	Notation	Logician
Symbol for addition	The idea of using symbolic notation for addition	Plus and minus signs § Plus sign	Notation	Logician
Zero	A symbol for nothingness	0 (number)	Notation	Logician
Approximation of root 2	An approximation for the length of the diagonal of a square	Square root of 2 § History	Numbers	Mathematician
Chinese remainder algorithm	An algorithm for computing a number which has given remainders when divided by several given primes	Chinese remainder theorem	Numbers	Mathematician
Division	An algorithm for dividing one number into another, possibly yielding a remainder	Euclidean division	Numbers	Mathematician
Euclid's Theorem	A proof that there are infinitely many prime numbers	Euclid's theorem	Numbers	Mathematician
Euclidean Algorithm	An algorithm for computing the greatest common divisor of two numbers	Euclidean algorithm	Numbers	Mathematician
Irrationality of root 2	A proof that the length of a diagonal of a square is incommensurable with its edge	Square root of 2 § Proofs of irrationality	Numbers
Sieve algorithm for primes	An algorithm for calculating prime numbers	Sieve of Eratosthenes	Numbers	Mathematician
Unique prime factorization	The unique decomposition of a number into products of its prime divisors	Fundamental theorem of arithmetic	Numbers	Mathematician