====== Corpus Demonstratum: Collection of Proofs and Arguments====== Welcome to our comprehensive collection of mathematical proofs and philosophical arguments. This wiki aims to be a definitive resource for students, scholars, and enthusiasts seeking rigorous demonstrations across the spectrum of mathematical disciplines and philosophical traditions. ===== About This Project ===== This encyclopedia serves multiple purposes: * To collect and preserve important proofs in accessible formats * To provide clear explanations with appropriate levels of rigor * To highlight connections between different areas of mathematics and philosophy * To trace the historical development of key theorems and arguments * To serve as an educational resource for learners at various levels ===== Getting Started ===== * [[en:wiki:math|Mathematical expression formatting guide]] * [[en:templates:mathematical|Mathematical proof template]] * [[en:templates:philosophical|Philosophical argument template]] ===== Mathematical Proofs ===== ==== Foundations of Mathematics ==== * [[en:start:proofs:foundations:logic|Logic and Set Theory]] * [[en:start:proofs:foundations:logic:incompleteness|Gödel's Incompleteness Theorems]] * [[en:start:proofs:foundations:logic:compactness|Compactness Theorem]] * [[en:start:proofs:foundations:logic:completeness|Completeness Theorem]] * [[en:start:proofs:foundations:logic:zfc|ZFC Axioms and Consequences]] * [[en:start:proofs:foundations:logic:choice|Axiom of Choice and Equivalents]] * [[en:start:proofs:foundations:numbers|Number Systems]] * [[en:start:proofs:foundations:numbers:peano|Peano Axioms]] * [[en:start:proofs:foundations:numbers:integers|Construction of Integers]] * [[en:start:proofs:foundations:numbers:rationals|Construction of Rational Numbers]] * [[en:start:proofs:foundations:numbers:reals|Construction of Real Numbers]] * [[en:start:proofs:foundations:numbers:complex|Complex Numbers]] ==== Number Theory ==== * [[en:start:proofs:number:elementary|Elementary Number Theory]] * [[en:start:proofs:number:elementary:division|Division Algorithm]] * [[en:start:proofs:number:elementary:euclidean|Euclidean Algorithm]] * [[en:start:proofs:number:elementary:fundamental|Fundamental Theorem of Arithmetic]] * [[en:start:proofs:number:elementary:fermat|Fermat's Little Theorem]] * [[en:start:proofs:number:elementary:euler|Euler's Theorem]] * [[en:start:proofs:number:analytic|Analytic Number Theory]] * [[en:start:proofs:number:analytic:pnt|Prime Number Theorem]] * [[en:start:proofs:number:analytic:dirichlet|Dirichlet's Theorem on Primes]] ==== Algebra ==== * [[en:start:proofs:algebra:group|Group Theory]] * [[en:start:proofs:algebra:group:lagrange|Lagrange's Theorem]] * [[en:start:proofs:algebra:group:sylow|Sylow Theorems]] * [[en:start:proofs:algebra:group:isomorphism|Isomorphism Theorems]] * [[en:start:proofs:algebra:ring|Ring Theory]] * [[en:start:proofs:algebra:ring:ideals|Ideal Theory]] * [[en:start:proofs:algebra:ring:ufd|Unique Factorization Domains]] * [[en:start:proofs:algebra:field|Field Theory]] * [[en:start:proofs:algebra:field:extensions|Field Extensions]] * [[en:start:proofs:algebra:field:splitting|Splitting Fields]] * [[en:start:proofs:algebra:galois|Galois Theory]] * [[en:start:proofs:algebra:galois:fundamental|Fundamental Theorem of Galois Theory]] * [[en:start:proofs:algebra:galois:solvability|Solvability by Radicals]] * [[en:start:proofs:algebra:linear|Linear Algebra]] * [[en:start:proofs:algebra:linear:determinants|Determinants]] * [[en:start:proofs:algebra:linear:eigenvalues|Eigenvalues and Eigenvectors]] * [[en:start:proofs:algebra:linear:diagonalization|Diagonalization]] ==== Analysis ==== * [[en:start:proofs:analysis:calculus|Calculus]] * [[en:start:proofs:analysis:calculus:limits|Limit Theorems]] * [[en:start:proofs:analysis:calculus:mvt|Mean Value Theorem]] * [[en:start:proofs:analysis:calculus:fundamental|Fundamental Theorem of Calculus]] * [[en:start:proofs:analysis:real|Real Analysis]] * [[en:start:proofs:analysis:real:sequences|Convergence of Sequences]] * [[en:start:proofs:analysis:real:series|Convergence of Series]] * [[en:start:proofs:analysis:real:riemann|Riemann Integration]] * [[en:start:proofs:analysis:real:lebesgue|Lebesgue Integration]] * [[en:start:proofs:analysis:complex|Complex Analysis]] * [[en:start:proofs:analysis:complex:cauchy|Cauchy's Integral Theorem]] * [[en:start:proofs:analysis:complex:residue|Residue Theorem]] * [[en:start:proofs:analysis:complex:laurent|Laurent Series]] * [[en:start:proofs:analysis:functional|Functional Analysis]] * [[en:start:proofs:analysis:functional:baire|Baire Category Theorem]] * [[en:start:proofs:analysis:functional:hahn-banach|Hahn-Banach Theorem]] * [[en:start:proofs:analysis:functional:spectral|Spectral Theory]] ==== Geometry and Topology ==== * [[en:start:proofs:geometry:euclidean|Euclidean Geometry]] * [[en:start:proofs:geometry:euclidean:pythagoras|Pythagorean Theorem]] * [[en:start:proofs:geometry:euclidean:congruence|Triangle Congruence Theorems]] * [[en:start:proofs:geometry:euclidean:similarity|Similar Triangles]] * [[en:start:proofs:geometry:differential|Differential Geometry]] * [[en:start:proofs:geometry:differential:curves|Theory of Curves]] * [[en:start:proofs:geometry:differential:surfaces|Theory of Surfaces]] * [[en:start:proofs:geometry:differential:manifolds|Manifolds]] * [[en:start:proofs:topology:point-set|Point-Set Topology]] * [[en:start:proofs:topology:point-set:metric|Metric Spaces]] * [[en:start:proofs:topology:point-set:continuity|Continuous Functions]] * [[en:start:proofs:topology:point-set:compactness|Compactness]] * [[en:start:proofs:topology:algebraic|Algebraic Topology]] * [[en:start:proofs:topology:algebraic:fundamental|Fundamental Group]] * [[en:start:proofs:topology:algebraic:homology|Homology Groups]] * [[en:start:proofs:topology:algebraic:fixed-point|Fixed Point Theorems]] ==== Applied Mathematics ==== * [[en:start:proofs:applied:probability|Probability Theory]] * [[en:start:proofs:applied:probability:axioms|Kolmogorov Axioms]] * [[en:start:proofs:applied:probability:distributions|Probability Distributions]] * [[en:start:proofs:applied:probability:limit|Limit Theorems]] * [[en:start:proofs:applied:differential|Differential Equations]] * [[en:start:proofs:applied:differential:first-order|First-Order ODEs]] * [[en:start:proofs:applied:differential:linear|Linear ODEs]] * [[en:start:proofs:applied:differential:pde|Partial Differential Equations]] ==== Famous Theorems and Problems ==== * [[en:start:proofs:famous:fermat|Fermat's Last Theorem]] * [[en:start:proofs:famous:four-color|Four Color Theorem]] * [[en:start:proofs:famous:poincare|Poincaré Conjecture]] * [[en:start:proofs:famous:riemann|Riemann Hypothesis]] * [[en:start:proofs:famous:p-np|P vs NP Problem]] ===== Philosophical Arguments and Proofs ===== ==== Metaphysics ==== * [[en:start:proofs:philosophy:metaphysics:ontology|Ontological Arguments]] * [[en:start:proofs:philosophy:metaphysics:ontology:anselm|Anselm's Ontological Argument]] * [[en:start:proofs:philosophy:metaphysics:ontology:descartes|Descartes' Ontological Argument]] * [[en:start:proofs:philosophy:metaphysics:ontology:modal|Modal Ontological Arguments]] * [[en:start:proofs:philosophy:metaphysics:causation|Causation]] * [[en:start:proofs:philosophy:metaphysics:causation:cosmological|Cosmological Arguments]] * [[en:start:proofs:philosophy:metaphysics:causation:kalam|Kalam Cosmological Argument]] * [[en:start:proofs:philosophy:metaphysics:causation:regress|Infinite Regress Arguments]] * [[en:start:proofs:philosophy:metaphysics:mind|Philosophy of Mind]] * [[en:start:proofs:philosophy:metaphysics:mind:dualism|Arguments for Dualism]] * [[en:start:proofs:philosophy:metaphysics:mind:physicalism|Arguments for Physicalism]] * [[en:start:proofs:philosophy:metaphysics:mind:mary|Knowledge Argument (Mary's Room)]] ==== Epistemology ==== * [[en:start:proofs:philosophy:epistemology:knowledge|Nature of Knowledge]] * [[en:start:proofs:philosophy:epistemology:knowledge:jtb|Knowledge as Justified True Belief]] * [[en:start:proofs:philosophy:epistemology:knowledge:gettier|Gettier Problems]] * [[en:start:proofs:philosophy:epistemology:knowledge:reliabilism|Reliabilist Theories]] * [[en:start:proofs:philosophy:epistemology:skepticism|Skeptical Arguments]] * [[en:start:proofs:philosophy:epistemology:skepticism:vat|Brain in a Vat]] * [[en:start:proofs:philosophy:epistemology:skepticism:demon|Descartes' Evil Demon]] * [[en:start:proofs:philosophy:epistemology:skepticism:dream|Dream Argument]] * [[en:start:proofs:philosophy:epistemology:induction|Problem of Induction]] * [[en:start:proofs:philosophy:epistemology:induction:hume|Hume's Problem of Induction]] * [[en:start:proofs:philosophy:epistemology:induction:goodman|Goodman's New Riddle of Induction]] ==== Ethics ==== * [[en:start:proofs:philosophy:ethics:normative|Normative Ethics]] * [[en:start:proofs:philosophy:ethics:normative:utilitarian|Utilitarian Arguments]] * [[en:start:proofs:philosophy:ethics:normative:kantian|Kantian Arguments]] * [[en:start:proofs:philosophy:ethics:normative:virtue|Virtue Ethics]] * [[en:start:proofs:philosophy:ethics:metaethics|Metaethics]] * [[en:start:proofs:philosophy:ethics:metaethics:realism|Moral Realism]] * [[en:start:proofs:philosophy:ethics:metaethics:error|Error Theory]] * [[en:start:proofs:philosophy:ethics:metaethics:emotivism|Emotivism]] * [[en:start:proofs:philosophy:ethics:applied|Applied Ethics]] * [[en:start:proofs:philosophy:ethics:applied:trolley|Trolley Problem]] * [[en:start:proofs:philosophy:ethics:applied:value|Value of Life Arguments]] ==== Logic and Language ==== * [[en:start:proofs:philosophy:logic:formal|Formal Logic]] * [[en:start:proofs:philosophy:logic:formal:propositional|Propositional Logic]] * [[en:start:proofs:philosophy:logic:formal:predicate|Predicate Logic]] * [[en:start:proofs:philosophy:logic:formal:modal|Modal Logic]] * [[en:start:proofs:philosophy:logic:informal|Informal Logic and Fallacies]] * [[en:start:proofs:philosophy:logic:informal:deductive|Deductive Fallacies]] * [[en:start:proofs:philosophy:logic:informal:inductive|Inductive Fallacies]] * [[en:start:proofs:philosophy:language:meaning|Theories of Meaning]] * [[en:start:proofs:philosophy:language:meaning:reference|Reference Theories]] * [[en:start:proofs:philosophy:language:meaning:use|Use Theories]] * [[en:start:proofs:philosophy:language:meaning:verification|Verification Principle]] ==== Philosophy of Science ==== * [[en:start:proofs:philosophy:science:demarcation|Demarcation Problem]] * [[en:start:proofs:philosophy:science:demarcation:popper|Popper's Falsificationism]] * [[en:start:proofs:philosophy:science:demarcation:kuhn|Kuhn's Paradigm Shifts]] * [[en:start:proofs:philosophy:science:explanation|Scientific Explanation]] * [[en:start:proofs:philosophy:science:explanation:dn|Deductive-Nomological Model]] * [[en:start:proofs:philosophy:science:explanation:causal|Causal Accounts]] * [[en:start:proofs:philosophy:science:realism|Scientific Realism vs. Anti-Realism]] * [[en:start:proofs:philosophy:science:realism:miracles|No Miracles Argument]] * [[en:start:proofs:philosophy:science:realism:pessimistic|Pessimistic Induction]] ===== How to Contribute ===== We welcome contributions from mathematicians, philosophers, educators, and enthusiasts. To contribute: * **Follow our standards**: Use the proper templates for consistency * **Use proper notation**: Ensure mathematical expressions use LaTeX via the MathJax plugin * **Provide references**: Include sources for all theorems, proofs, and arguments * **Consider accessibility**: Write clear explanations that build on prerequisites ===== Contact ===== For questions or assistance with this wiki, please contact [[mailto:ayman@aymanlafaz.com|ayman@aymanlafaz.com]].