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