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Reasoning for mathematical statements
frequently used as an assumption for further mathematical work. Proofs employ logic expressed in mathematical symbols, along with natural language that usually
Mathematical_proof
Form of mathematical proof
Induction puzzles Proof by exhaustion Matt DeVos, Mathematical Induction, Simon Fraser University Gerardo con Diaz, Mathematical Induction Archived 2
Mathematical_induction
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]
List of long mathematical proofs
List_of_long_mathematical_proofs
Field of knowledge
period, sets were not considered to be mathematical objects, and logic, although used for mathematical proofs, belonged to philosophy and was not specifically
Mathematics
its original proof Mathematical induction and a proof Proof that 0.999... equals 1 Proof that 22/7 exceeds π Proof that e is irrational Proof that π is irrational
List_of_mathematical_proofs
Branch of mathematical logic
Proof theory is a major branch of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating
Proof_theory
Subfield of automated reasoning and mathematical logic
reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major
Automated_theorem_proving
Argument that leads to a logical absurdity
is quite freely used in mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof. This argument form traces
Reductio_ad_absurdum
mathematical content is not beautiful, and some theorems or proofs are beautiful but may be written about inelegantly. The beauty of a mathematical theory
Glossary of mathematical jargon
Glossary_of_mathematical_jargon
Mathematical proof by James Garfield
published by the Mathematical Association of America.) Del Arte, Alonso (February 2019). "A future president once published a mathematical proof". medium.com
Garfield's proof of the Pythagorean theorem
Garfield's_proof_of_the_Pythagorean_theorem
Interactive theorem prover software
science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human–machine
Proof_assistant
"rigor" may remain useful for teaching to beginners what is a mathematical proof. Mathematics is used in most sciences for modeling phenomena, which then
Philosophy_of_mathematics
2005 film by John Madden
shown invigorated, believing that he has seen the beginnings of a new mathematical proof that will prove his triumph over mental illness. In the present, Catherine
Proof_(2005_film)
Aesthetic value of mathematics
beauty in mathematics may be connected to other aesthetic or non-aesthetic values. Some authors identify mathematical elegance with mathematical beauty;
Mathematical_beauty
Mathematical proofs of basic properties of addition of the natural numbers
contains mathematical proofs for some properties of addition of the natural numbers: the additive identity, commutativity, and associativity. These proofs are
Proofs involving the addition of natural numbers
Proofs_involving_the_addition_of_natural_numbers
1995 publication in mathematics
correct the proof to the satisfaction of the mathematical community. The corrected proof was published in 1995 in the journal Annals of Mathematics in the
Wiles's proof of Fermat's Last Theorem
Wiles's_proof_of_Fermat's_Last_Theorem
Non-contradiction of a theory
complete. A consistency proof is a mathematical proof that a particular theory is consistent. The early development of mathematical proof theory was driven
Consistency
Proof assistant and programming language
selected sections of the mathematical text. Macbeth is using Lean to teach students the fundamentals of mathematical proof with instant feedback. In
Lean_(proof_assistant)
Adhering absolutely to certain constraints with consistency
rigour). Mathematical rigour is often cited as a kind of gold standard for mathematical proof. Its history traces back to Greek mathematics, especially
Rigour
In mathematics, a statement that has been proven
important theorems. In mathematical logic, the concepts of theorems and proofs have been formalized in order to allow mathematical reasoning about them
Theorem
Mathematical proof expressed visually
In mathematics, a proof without words (or visual proof) is an illustration of an identity or mathematical statement which can be demonstrated as self-evident
Proof_without_words
Subfield of mathematics
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory
Mathematical_logic
Mathematical proof at least partially generated by computer
computer-assisted proof is a mathematical proof that has been at least partially generated by computer. Most computer-aided proofs to date have been implementations
Computer-assisted_proof
Category of mathematical proof
problems gave rise to research into more complicated mathematical structures. Some of the most important proofs of impossibility found in the 20th century were
Proof_of_impossibility
Method of proof in mathematics
In mathematics, a constructive proof is a method of proof that demonstrates the existence of a mathematical object by creating or providing a method for
Constructive_proof
Establishment of a theorem using inference from the axioms
verification Mathematical proof Proof assistant Proof calculus Proof theory Proof (truth) De Bruijn factor Kassios, Yannis (February 20, 2009). "Formal Proof" (PDF)
Formal_proof
Proof in set theory
Cantor's diagonal argument (among various similar names) is a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence
Cantor's_diagonal_argument
Type of mathematical proof
Proof by exhaustion, also known as proof by cases, proof by case analysis, complete induction or the brute force method, is a method of mathematical proof
Proof_by_exhaustion
American play
recently deceased mathematical genius in his fifties and professor at the University of Chicago, and her struggle with mathematical genius and mental
Proof_(play)
Study of discrete mathematical structures
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a one-to-one
Discrete_mathematics
Averages of repeated trials converge to the expected value
Bernoulli. It took him over 20 years to develop a sufficiently rigorous mathematical proof which was published in his Ars Conjectandi (The Art of Conjecturing)
Law_of_large_numbers
Certain type of mistaken proof
In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy
Mathematical_fallacy
1998 mathematics book by Aigner and Ziegler
Proofs from THE BOOK is a book of mathematical proofs by Martin Aigner and Günter M. Ziegler, first published in 1998. The book is inspired by and named
Proofs_from_THE_BOOK
Large number coined by Ronald Graham
problem in the mathematical field of Ramsey theory. It is much larger than many other large numbers introduced as effective bounds in mathematics, such as Skewes's
Graham's_number
Basic framework of mathematics
Foundations of mathematics are the logical and mathematical frameworks that allow the development of mathematics without generating self-contradictory
Foundations_of_mathematics
reasoning and mathematical rigor in proofs) and expanded the subject matter of mathematics. The ancient Romans used applied mathematics in surveying,
History_of_mathematics
Marking an argument as obvious or trivial
Proof by intimidation (or argumentum verbosum) is a humorous phrase used mainly in mathematics to refer to a specific form of hand-waving whereby one attempts
Proof_by_intimidation
Abbreviation at completion of a proof
abbreviation is placed at the end of mathematical proofs and philosophical arguments in print publications, to indicate that the proof or the argument is complete
Q.E.D.
Semi-Rigorous Mathematical Culture". The Mathematical Intelligencer 16:4, pages 11–18, December 1994. Proof and other dilemmas: mathematics and philosophy
Future_of_mathematics
page lists notable examples of incomplete or incorrect published mathematical proofs. Most of these were accepted as complete or correct for several years
List_of_incomplete_proofs
Relation between sides of a right triangle
possibly the most for any mathematical theorem. The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands
Pythagorean_theorem
Symbol used in mathematics and typography
In mathematics, the tombstone, halmos, end-of-proof, or Q.E.D. symbol "∎" (or "□") is a symbol used to denote the end of a proof, in place of the traditional
Tombstone_(typography)
proofs, and even formal theories are considered as mathematical objects in proof theory. In philosophy of mathematics, the concept of "mathematical objects"
Mathematical_object
Proof by Alan Turing
second proof (after Church's theorem) of the negation of Hilbert's Entscheidungsproblem; that is, the conjecture that some purely mathematical yes–no
Turing's_proof
Sufficient evidence/argument for truth
proposition Proof procedure Proof complexity Standard of proof Proving a negative Proof of impossibility – Category of mathematical proof Proof and other
Proof_(truth)
Method of deriving conclusions
the formal sciences, such as mathematics and computer science, where they are used to prove theorems. Mathematical proofs often start with a set of axioms
Rule_of_inference
Proposition in mathematics that is unproven
In mathematics, a conjecture is a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or
Conjecture
Mathematical proof technique using contradiction
In mathematics, a proof by infinite descent, also known as Fermat's method of descent, is a particular kind of proof by contradiction used to show that
Proof_by_infinite_descent
High school math competition
scorers on both six-question, nine-hour mathematical proof competitions are invited to join the Mathematical Olympiad Program to compete and train to
United States of America Mathematical Olympiad
United_States_of_America_Mathematical_Olympiad
Proof that is not easily verified by hand
In the philosophy of mathematics, a non-surveyable proof is a mathematical proof that is considered infeasible for a human mathematician to verify and
Non-surveyable_proof
Conformity to reality
mathematicians employ several proof methods to establish theorems, such as direct proof, proof by contradiction, and mathematical induction. Formal logic studies
Truth
Proof that only uses basic techniques
In mathematics, an elementary proof is a mathematical proof that only uses basic techniques. More specifically, the term is used in number theory to refer
Elementary_proof
Quality of an algorithm being correct with respect to a specification
exists, which is currently not known in number theory. A proof would have to be a mathematical proof, assuming both the algorithm and specification are given
Correctness (computer science)
Correctness_(computer_science)
Mathematical use of "there exists"
n\times n=25} . The mathematical proof of an existential statement about "some" object may be achieved either by a constructive proof, which exhibits an
Existential_quantification
Logical principle
in the original): In his second problem, [Hilbert] had asked for a mathematical proof of the consistency of the axioms of the arithmetic of real numbers
Law_of_excluded_middle
Process of repeating items in a self-similar way
function – Result of repeatedly applying a mathematical function Mathematical induction – Form of mathematical proof Mise en abyme – Technique of placing a
Recursion
Mathematical calculation with a counter-intuitive result
paradox is a mathematical calculation that has a result which seems counterintuitive to many people. The Universal Book of Mathematics states the problem
Potato_paradox
Mathematical term; concerning axioms used to derive theorems
required purely algebraic proofs. Further, he used a construction of the Jacobian as an "abstract variety": an intrinsic mathematical object, rather than a
Axiomatic_system
Proving or disproving the correctness of certain intended algorithms
done by ensuring the existence of a formal proof of a mathematical model of the system. Examples of mathematical objects used to model systems are: finite-state
Formal_verification
all the steps in the proof and all the important ideas faithfully, while restating the proof in the modern language of mathematical logic. This outline
Original proof of Gödel's completeness theorem
Original_proof_of_Gödel's_completeness_theorem
Branch of mathematical logic
Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. Its defining
Reverse_mathematics
Mathematical proof technique
mathematical olympiad problems in the light of the first olympiad problem to use it in a solution that was proposed for the International Mathematics
Vieta_jumping
17th-century conjecture proved by Andrew Wiles in 1994
New York: The Mathematical Association of America. ISBN 978-0-88385-451-8. Benson, Donald C. (2001). The Moment of Proof: Mathematical Epiphanies. Oxford
Fermat's_Last_Theorem
Alternative decimal expansion of 1
just the mathematical tools of comparison and addition of (finite) decimal numbers, without any reference to more advanced topics. The proof given below
0.999...
Hungarian mathematician (1913–1996)
and of keeping the most elegant mathematical proofs to himself. When he saw a particularly beautiful mathematical proof he would exclaim, "This one's from
Paul_Erdős
Argument that uses faulty reasoning
special case is a mathematical fallacy, an intentionally invalid mathematical proof with a concealed, or subtle, error. Mathematical fallacies are typically
Fallacy
Mathematical logical symbol of 3 dots
In logical argument and mathematical proof, the therefore sign, ∴, is generally used before a logical consequence, such as the conclusion of a syllogism
Therefore_sign
Topics referred to by the same term
Alcohol proof, a measure of an alcoholic drink's strength Proof may also refer to: Formal proof, a construct in proof theory Mathematical proof, a convincing
Proof
Collection of mathematical objects
In mathematics, a set is a collection of different things; the things are called elements or members of the set and are typically mathematical objects:
Set_(mathematics)
modern mathematics due to its mathematical elegance and its connections to the theory of Diophantine approximations. Stephen Lucas calls this proof "one
Proof_that_22/7_exceeds_π
Area of mathematical logic
of mathematical logic such as proof theory, model theory is often less concerned with formal rigour and closer in spirit to classical mathematics. This
Model_theory
Limitative results in mathematical logic
"ideal" (infinitistic) mathematical principles in the proofs of "real" (finitistic) mathematical statements by giving a finitistic proof that the ideal principles
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Relationship between programs and proofs
language theory and proof theory, the Curry–Howard correspondence is a direct relationship between computer programs and mathematical proofs. It is also known
Curry–Howard_correspondence
1976 book by Imre Lakatos
Proofs and Refutations: The Logic of Mathematical Discovery is a 1976 book by philosopher Imre Lakatos expounding his view of the progress of mathematics
Proofs_and_Refutations
Proofs in enumerative combinatorics
In mathematics, the term combinatorial proof is often used to mean either of two types of mathematical proof: A proof by double counting. A combinatorial
Combinatorial_proof
Summary of a mathematical proof
number of applications of the deduction rules. A proof of a formula S is itself a string of mathematical statements related by particular relations (each
Proof sketch for Gödel's first incompleteness theorem
Proof_sketch_for_Gödel's_first_incompleteness_theorem
Indian physicist
science, including its aspects that pertain to time and the nature of mathematical proof, are rooted in the theocratic needs of the Roman Catholic Church.
C._K._Raju
Expertise and trained intuition in math
gauge of mathematics students' erudition in mathematical structures and methods, and can overlap with other related concepts such as mathematical intuition
Mathematical_maturity
(mathematics) Axiomatization Axiomatic system Axiom schema Axiomatic method Formal system Mathematical proof Direct proof Reductio ad absurdum Proof by
List of mathematical logic topics
List_of_mathematical_logic_topics
Proof of the infinitude of primes
classical proof, Furstenberg's proof is a proof by contradiction. The proof was published in 1955 in the American Mathematical Monthly while he was still
Furstenberg's proof of the infinitude of primes
Furstenberg's_proof_of_the_infinitude_of_primes
Criteria of simplicity for mathematical proofs
criterion of simplicity in mathematical proofs and the development of a proof theory with the power to prove that a given proof is the simplest possible
Hilbert's twenty-fourth problem
Hilbert's_twenty-fourth_problem
Nonconstructive method for mathematical proofs
pioneered by Paul Erdős, for proving the existence of a prescribed kind of mathematical object. It works by showing that if one randomly chooses objects from
Probabilistic_method
Ancient Chinese mathematics text
The Nine Chapters on the Mathematical Art is a Chinese mathematics book, composed by several generations of scholars from the 10th–2nd century BCE, its
The Nine Chapters on the Mathematical Art
The_Nine_Chapters_on_the_Mathematical_Art
Logic constructed only from NAND gates
NAND gates. The mathematical proof for this was published by Henry M. Sheffer in 1913 in the Transactions of the American Mathematical Society (Sheffer
NAND_logic
Mathematics National Mathematics Talent Contests Indian Olympiad Qualifier in Mathematics Regional Mathematical Olympiad Indian National Mathematical
List of mathematics competitions
List_of_mathematics_competitions
Problem in computer science
some functions are mathematically definable but not computable. A key part of the formal statement of the problem is a mathematical definition of a computer
Halting_problem
Mathematical study of the meaning of programming languages
closely related to, and often crosses over with, the semantics of mathematical proofs. Semantics describes the processes a computer follows when executing
Semantics (programming languages)
Semantics_(programming_languages)
In combinatorics
Guinness Book of World Records as the largest number ever appearing in a mathematical proof. The theorem involves sets of strings, all having the same length
Graham–Rothschild_theorem
Way of arriving to a mathematical proof
In mathematics and logic, a direct proof is a way of showing the truth or falsehood of a given statement by a straightforward combination of established
Direct_proof
Area of mathematics
Systems sciences, which directly requires mathematical models from systems engineering Solving mathematical problems by computer simulation as opposed
Computational_mathematics
Type of proof technique
double counting, also called counting in two ways, is a combinatorial proof technique for showing that two expressions are equal by demonstrating that
Double counting (proof technique)
Double_counting_(proof_technique)
Mathematical concept
harder it is to write a formal mathematical proof instead of an informal one. It was created by the Dutch computer-proof pioneer Nicolaas Govert de Bruijn
De_Bruijn_factor
Hypothetical mathematical code in the Quran
letters and surahs. Advocates believe that the code represents a mathematical proof of the divine authorship of the Quran. The most notable proponent
Quran_code
Erroneous method of proof
In logic and mathematics, proof by example (sometimes known as inappropriate generalization) is a logical fallacy whereby the validity of a statement is
Proof_by_example
Mathematically obvious
refers to a simple technical aspect of some proof or definition. The origin of the term in mathematical language comes from the medieval trivium curriculum
Triviality_(mathematics)
Formal specification language
also used to write machine-checked proofs of correctness both for algorithms and mathematical theorems. The proofs are written in a declarative, hierarchical
TLA+
aspects of basic and advanced mathematics, methodology, mathematical statements, integrals, general concepts, mathematical objects, and reference tables
Lists_of_mathematics_topics
Natural number
various 47 sightings, and professor Donald Bentley produced a false mathematical proof that 47 was equal to all other integers. The number became a meme
47_(number)
Book by John Stillwell
Reverse Mathematics: Proofs from the Inside Out is a book by John Stillwell on reverse mathematics, the process of examining proofs in mathematics to determine
Reverse Mathematics: Proofs from the Inside Out
Reverse_Mathematics:_Proofs_from_the_Inside_Out
Branch of mathematical combinatorics
Graham's number, one of the largest numbers ever used in serious mathematical proof, is an upper bound for a problem related to Ramsey theory. Another
Ramsey_theory
MATHEMATICAL PROOF
MATHEMATICAL PROOF
Girl/Female
Gujarati, Hindu, Indian, Kannada, Telugu
Mathematician
Girl/Female
Tamil
Mathematician
Surname or Lastname
English
English : habitational name from a place in West Yorkshire named Colden, from Old English cald ‘cold’ col ‘charcoal’ + denu ‘valley’.English and Scottish : variant of Cowden.Cadwallader Colden (1688–1778), physician, botanist, and mathematician, who for fifteen years was lieutenant-governor of New York colony, was born in Dalkeith, Scotland.
Boy/Male
Indian
Argument, Reasoning, Proof
Boy/Male
Indian
Proof
Girl/Female
Hindu
Mathematician
Boy/Male
Muslim
Proof
Boy/Male
Bengali, Hindu, Indian, Kannada, Marathi, Sanskrit, Telugu
One who Calculates; Astrologer; Mathematician
Boy/Male
Muslim
Argument, Reasoning, Proof
Girl/Female
Indian
Many signs & proofs, Verses in the Quran, Royal
Girl/Female
Muslim
Proof
Girl/Female
Indian
Many signs & proofs, Verses in the Quran, Royal
Boy/Male
Muslim
Proof
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Punjabi, Sanskrit, Sikh, Telugu
An Astrologer; Mathematician
Surname or Lastname
English
English : from Middle English, Old French palmer, paumer (from palme, paume ‘palm tree’, Latin palma), a nickname for someone who had been on a pilgrimage to the Holy Land. Such pilgrims generally brought back a palm branch as proof that they had actually made the journey, but there was a vigorous trade in false souvenirs, and the term also came to be applied to a cleric who sold indulgences.Swedish (Palmér) : ornamental name formed with palm ‘palm tree’ + the suffix -ér, from Latin -erius ‘descendant of’.Irish : when not truly of English origin (see 1 above), a surname adopted by bearers of Gaelic Ó Maolfhoghmhair (see Milford) perhaps because they were from an ecclesiastical family.German : topographic name for someone living among pussy willows (see Palm 2).German : from the personal name Palm (see Palm 3).
Boy/Male
Indian
Proof
Girl/Female
Muslim
Many signs & proofs, Verses in the Quran, Royal
Boy/Male
Australian, Vietnamese
Complete; Mathematics
Girl/Female
Muslim
Guide, Proof
Girl/Female
Muslim
Many signs & proofs, Verses in the Quran, Royal
MATHEMATICAL PROOF
MATHEMATICAL PROOF
Female
Hungarian
Hungarian form of Greek Hagne, ÃGNES means "chaste; holy."
Girl/Female
Irish Celtic French
Oath.
Boy/Male
Gujarati, Hindu, Indian
Lord Krishna
Boy/Male
Indian, Japanese, Sanskrit
Unbound; Myriad
Girl/Female
Indian
Lighting
Boy/Male
Muslim
Prosperous
Girl/Female
German
Protector.
Girl/Female
Muslim/Islamic
Pretty
Boy/Male
British, English
From the Enclosed Meadow
Surname or Lastname
English
English : variant spelling of Wallace.
MATHEMATICAL PROOF
MATHEMATICAL PROOF
MATHEMATICAL PROOF
MATHEMATICAL PROOF
MATHEMATICAL PROOF
v.
A mathematical point; -- regularly used in old English translations of Euclid.
a.
See Mathematical.
n.
One versed in mathematics.
v. i.
To alter or change in succession; to alternate; as, one mathematical quantity varies inversely as another.
a.
Pertaining to, or having the nature of, an anathema.
n.
The act or process of making mathematical computations or of estimating results.
n.
A solution, the result of a mathematical operation; as, the answer to a problem.
n.
Learning; especially, mathematics.
a.
Pertaining to Euler, a German mathematician of the 18th century.
n.
The symbol, quantity, or thing upon which a mathematical operation is performed; -- called also faciend.
n.
One skilled in geometry; a geometrician; a mathematician.
n.
That science, or class of sciences, which treats of the exact relations existing between quantities or magnitudes, and of the methods by which, in accordance with these relations, quantities sought are deducible from other quantities known or supposed; the science of spatial and quantitative relations.
n.
Any lineal or mathematical diagram; an outline.
n.
Mixed mathematics.
a.
Of or pertaining to mathematics; according to mathematics; hence, theoretically precise; accurate; as, mathematical geography; mathematical instruments; mathematical exactness.
a.
Of or pertaining to mathematical calculations; performing or able to perform mathematical calculations.
a.
Producing mathematically perfect harmony or concord; sweetly or perfectly harmonious.
n.
One skilled in geometry; a geometer; a mathematician.
a.
Alt. of Anathematical
v. i.
To use figures in a mathematical process; to do sums in arithmetic.