A list of theorems, proofs, and references. Algebraic and natural deducation proofs have been formalized in Isabelle. Proofs by method of truth table have been generated by computer program to ensure their validity. Whenever possible, I reference free resources, such as Khan Academy, Sarada Herke, Numberphile, ProofWiki, Wikipedia, etc. Failing that, I reference established mathematical texts.

Teachers of mathematics, high-school seniors, undergraduates, and amateur mathematicians.

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- Boolean algebra course
- Differential calculus course
- Order theory course
- Plane trigonometry course
- Propositional logic course

- Prime number
- Commutative
- Union
- Sum of list
- Odd polyomino
- Right-distributive
- Equinumerous
- Order theory
- De Morgan's laws
- Semigroup
- Simple directed graph
- Combinator calculus
- Minimum and maximum
- Subset relation
- Central vertex
- Predicate
- Irrational number
- Strictly monotone
- Figurate number
- Monoid
- Associative
- Group
- Composition of monotone functions
- Injection
- Sine
- Palindromic number
- Preorder
- Free polyomino
- Biconditional
- Hadwiger-Nelson problem
- Monohedral tiling
- Order of a polyomino
- Law of sines
- Maximum
- Infinite series
- Set
- Integer divides
- Traceable graph
- Modulo addition
- Disjunction
- Product of list
- Connected regular graph
- Algebraic number
- Proof by induction
- Golden ratio
- Ring
- Material conditional
- Integer addition
- Pseudo-polyomino
- Thue equation
- Self-distributive
- Complex number
- Cancellative
- Propositional logic
- Cosine
- Mersenne number
- Edge-to-edge tiling
- GCD
- Bicentric quadrilateral
- Natural number subtraction
- Sign function
- Identity rule
- Polyform
- Perfect number
- Eccentricity
- Intersection
- Platonic solid
- Asymmetric relation
- Hamiltonian cycle
- Binary relation
- Cartesian product
- Modus tollendo tollens
- Vector
- Cantor's theorem
- Total order
- Number theory
- Anti-symmetric relation
- Hexominoes
- Parity
- Total preorder
- Left-distributive
- Lobster tree
- Semiring
- Tournament
- Modus ponendo ponens
- Cycle graph
- Cartesian product of two graphs
- Recursive set

- Predicate logic
- Integer triangle
- LCM
- Differential calculus
- Difference of two squares
- Graph
- Constant rule
- Negation
- Modus tollendo ponens
- Integer multiplication
- Peano arithmetic
- Countable set
- Rational triangle
- Abstract algebra
- Left identity element
- Rep-tile
- Completely multiplicative
- Automorphism group
- Binomial coefficient
- Equal to
- Coprime
- Set equality
- Natural number exponentiation
- Integer
- Conjunction
- Algebraic structure
- Syllogism
- Left self-distributive
- Antisymmetric relation
- Natural number less than
- Tessellation
- Integer LCM
- Total function
- Number spiral
- Append
- Boolean algebra
- Diameter of a graph
- Rational number
- Hypothetical syllogism
- Degree of rotational symmetry
- Non-planar graph
- Fixed polyomino
- Cofunction identities
- Recursively enumerable
- Modus ponendo tollens
- Pascal's identity
- One-sided polyomino
- Fermat number
- Closed curve
- Spanning tree
- Distributive
- Directed graph
- Left-cancellative
- Polygon
- Monotonic function
- Integer GCD
- Ordering
- Fault-free rectangle
- Natural number GCD
- Angle trisection
- Matrix multiplication
- Composition
- Prototile
- Function
- Language
- Square number
- Strict ordering
- Decision problem
- Tangent
- Archimedean graph
- Pick's theorem
- Natural number LCM
- Cyclic quadrilateral
- Convex polyhedron
- Reverse
- Linear algebra
- Right-cancellative
- Involution
- Matrix addition
- Travelling salesman problem
- Hexagon
- Trigonometry
- Dot product
- Polyiamond
- Conjunction and disjunction
- Integral drawing
- Right self-distributive
- Absolute difference