## Mathematical proof |

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In **proof** is an inferential argument for a ^{[2]}^{[3]}^{[4]} along with accepted rules of *all* possible cases and showing that it holds in each), rather than enumerate many confirmatory cases. An unproved proposition that is believed to be true is known as a

Proofs employ

- history and etymology
- nature and purpose
- methods
- undecidable statements
- heuristic mathematics and experimental mathematics
- ending a proof
- see also
- references
- sources
- external links

The word "proof" comes from the Latin *probare* meaning "to test". Related modern words are the English "probe", "probation", and "probability", the Spanish *probar* (to smell or taste, or (lesser use) touch or test),^{[5]} Italian *provare* (to try), and the German *probieren* (to try). The early use of "probity" was in the presentation of legal evidence. A person of authority, such as a nobleman, was said to have probity, whereby the evidence was by his relative authority, which outweighed empirical testimony.^{[6]}

Plausibility arguments using heuristic devices such as pictures and analogies preceded strict mathematical proof.^{[7]} It is likely that the idea of demonstrating a conclusion first arose in connection with ^{[8]} The development of mathematical proof is primarily the product of *Elements*^{[9]} In addition to theorems of geometry, such as the *Elements* also covers number theory, including a proof that the square root of two is irrational and that there are infinitely many prime numbers.

Further advances took place in ^{[10]} An *Al-Fakhri* (1000) by ^{[11]}

Modern

Other Languages

Afrikaans: Bewys

Alemannisch: Beweis (Mathematik)

العربية: برهان رياضي

aragonés: Demostración matematica

asturianu: Demostración matemática

azərbaycanca: Riyazi isbat

Bân-lâm-gú: Chèng-bêng

башҡортса: Математик иҫбатлау

беларуская: Матэматычны доказ

беларуская (тарашкевіца): Матэматычны доказ

български: Математическо доказателство

bosanski: Matematički dokaz

català: Demostració (matemàtiques)

čeština: Matematický důkaz

Cymraeg: Prawf mathemategol

dansk: Bevis (matematik)

Deutsch: Beweis (Mathematik)

Ελληνικά: Μαθηματική απόδειξη

español: Demostración en matemática

Esperanto: Matematika pruvo

فارسی: برهان (ریاضی)

français: Démonstration (logique et mathématique)

galego: Proba matemática

贛語: 數學證明

한국어: 증명 (수학)

हिन्दी: गणितीय उपपत्ति

hrvatski: Matematički dokaz

Bahasa Indonesia: Pembuktian matematika

íslenska: Stærðfræðileg sönnun

italiano: Dimostrazione matematica

עברית: הוכחה

ქართული: მათემატიკური დამტკიცება

қазақша: Дәлелдеу

Latina: Demonstratio mathematica

latviešu: Matemātisks pierādījums

lietuvių: Matematinis įrodymas

la .lojban.: cipra

magyar: Matematikai bizonyítás

македонски: Математички доказ

മലയാളം: തെളിവ് ഗണിതശാസ്ത്രത്തിൽ

Bahasa Melayu: Bukti matematik

Nederlands: Wiskundig bewijs

日本語: 証明

Nordfriisk: Bewis

norsk: Matematisk bevis

norsk nynorsk: Matematisk bevis

occitan: Demostracion matematica

ਪੰਜਾਬੀ: ਗਣਿਤਕ ਸਬੂਤ

پنجابی: میتھمیٹیکل ثبوت

Patois: Matimatikal pruuf

Plattdüütsch: Bewies (Mathematik)

polski: Dowód (matematyka)

português: Prova matemática

română: Demonstrație matematică

русиньскый: Математічне доказательство

русский: Математическое доказательство

Scots: Mathematical pruif

sicilianu: Dimustrazzioni matimàtica

සිංහල: ගණිතමය ඔප්පු කිරීම්

Simple English: Mathematical proof

slovenčina: Dôkaz (matematika)

slovenščina: Matematični dokaz

српски / srpski: Математички доказ

srpskohrvatski / српскохрватски: Dokaz (matematika)

suomi: Matemaattinen todistus

svenska: Matematiskt bevis

Tagalog: Pang-matematikang patibay

தமிழ்: கணித நிறுவல்

татарча/tatarça: Математик исбатлау

Türkçe: Matematiksel ispat

українська: Доведення

اردو: ریاضیاتی ثبوت

Tiếng Việt: Chứng minh toán học

文言: 證明

Winaray: Pruweba panmatematika

吴语: 证明

ייִדיש: מאטעמאטישער דערווייז

粵語: 數學證明

žemaitėška: Matematėnis iruodėms

中文: 證明