This is a list of unusually long mathematical proofs. Such proofs often use computational proof methods and may be considered non-surveyable.
As of 2011[update], the longest mathematical proof, measured by number of published journal pages, is the classification of finite simple groups with well over 10000 pages. There are several proofs that would be far longer than this if the details of the computer calculations they depend on were published in full.
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is a listof unusually longmathematicalproofs. Such proofs often use computational proof methods and may be considered non-surveyable. As of 2011[update]...
some ambiguity. In most mathematical literature, proofs are written in terms of rigorous informal logic. Purely formal proofs, written fully in symbolic...
Proofs and Refutations: The Logic ofMathematical Discovery is a 1976 book by philosopher Imre Lakatos expounding his view of the progress of mathematics...
his proof has not been accepted as correct in the mainstream mathematical community. ListoflongmathematicalproofsListof disproved mathematical ideas...
rule used in formal proofs, and is the foundation of most correctness proofs for computer programs. Despite its name, mathematical induction differs fundamentally...
important theorems. In mathematical logic, the concepts of theorems and proofs have been formalized in order to allow mathematical reasoning about them...
and a mathematical fallacy in a proof, in that a mistake in a proof leads to an invalid proof while in the best-known examples ofmathematical fallacies...
Proof theory is a major branch ofmathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating...
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory...
for any mathematical theorem. The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years. When...
Haken–Apple proofof the Four Color Theorem) Perminov, V. Ya. (1988). "On the Reliability ofMathematicalProofs". Philosophy ofMathematics. 42 (167 (4))...
logically imposed, such as mathematicalproofs which must maintain consistent answers; or socially imposed, such as the process of defining ethics and law...
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation...
century, and all of these problems gave rise to research into more complicated mathematical structures. Some of the most important proofsof impossibility...
consists of a formal language for writing mathematical definitions and proofs, a proof assistant, which is able to mechanically check proofs written in...
methods ofmathematics, and find out the place ofmathematics in people's lives. The philosophy ofmathematics has two major themes: mathematical realism...
Many mathematical problems have been stated but not yet solved. These problems come from many areas ofmathematics, such as theoretical physics, computer...
the listof Folk Mathematics.[citation needed] Folk psychology Mathematical Platonism Pseudomathematics Ethnomathematics Numeracy Imre Lakatos, Proofs and...
of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof...
other countries International Mathematical Modeling Challenge — team contest for high school students International Mathematical Olympiad (IMO) — the oldest...
Foundations ofmathematics is the study of the philosophical and logical and/or algorithmic basis ofmathematics, or, in a broader sense, the mathematical investigation...
attempt to list examples in mathematics. To qualify for inclusion, an article should be about a mathematical object with a fair amount of concreteness...
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