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| name = Proofs and Refutations: The Logic of Mathematical Discovery ...ve to be patched up in the light of later insights, in particular failed [[Mathematical proof|proof]]s. This gives mathematics a somewhat experimental flavour. At ...

| name = Counterexamples in Topology | image = Counterexamples in Topology.jpg ...

...hod of [[mathematical proof|proof]] that demonstrates the existence of a [[mathematical object]] by creating or providing a method for creating the object. This is [[Constructivism (mathematics)|Constructivism]] is a mathematical philosophy that rejects all proof methods that involve the existence of obj ...

...3|title=A note on paracompact spaces|journal=[[Proceedings of the American Mathematical Society]]|volume=4|issue=5|pages=831–838|doi=10.1090/S0002-9939-1953-005690 ...Society, 1975, p. 4, retrievable on Google Books [https://books.google.com/books?id=_LiqC3Y3kmsC&dq=%22between+compact+and+lindel%C3%B6f%22&pg=PA4]</ref> In ...

{{Short description|Mathematical use of "for all"}} {{Infobox mathematical statement ...

...r Advanced Study]] and another two (1961–62) at the [[Courant Institute of Mathematical Sciences]]. He was appointed to Purdue in 1962. ...oof|proof]] of the Bieberbach conjecture was not initially accepted by the mathematical community. Rumors of his proof began to circulate in March 1984, but many m ...

...sity Press]] |isbn= 9781400835560 |page= 23 |url= https://books.google.com/books?id=2Sg3Vug65AsC&pg=PA23}}</ref> ...metric space as well as to the [[Baire category theorem]]. See the result about completely metrizable spaces in the list of properties below. <math>\mathr ...

...represented as a ''closed'' subgroup of the GL_''n''('''C''').) Books that follow this approach include Hall (2015)<ref>{{harvtxt|Hall|2015}}</re ...ber=2|pages=471–486|date=December 13, 2000|journal=Journal of the American Mathematical Society|doi=10.1090/S0894-0347-00-00361-1|s2cid=18936096|doi-access=free}}< ...

{{short description|American philosopher and mathematical logician}} | main_interests = [[Philosophy of mathematics]], [[mathematical logic]] ...

{{Short description|Disproved mathematical conjecture}} It is a striking example of a mathematical conjecture proven false despite a large amount of computational evidence in ...

{{Short description|Category of mathematical proof}}{{Math topics sidebar}} ...ury, and all of these problems gave rise to research into more complicated mathematical structures. ...

* Cellérier, C. (1890) [https://books.google.com/books?id=HMghAQAAIAAJ&pg=PA142 "Note sur les principes fondamentaux de l'analyse" ...ons''] (Berlin, Germany: Julius Springer, 1886), [https://books.google.com/books?id=fltYAAAAYAAJ&pg=PA97 page 97].</ref> ...

{{Short description|Mathematical space with a notion of closeness}} A topological space is the most general type of a [[space (mathematics)|mathematical space]] that allows for the definition of [[Limit (mathematics)|limits]], [ ...

...ism, the [[Wigner–Weyl transform]], that underlies an alternate equivalent mathematical representation of quantum mechanics known as [[Phase-space formulation|defo According to the standard [[mathematical formulation of quantum mechanics]], quantum observables such as <math>\hat{ ...

{{About|the number|the years|54 BC|and|AD 54|other uses|54 (disambiguation){{!}}54} ...{citation| last = Sachs | first = A. J. | year = 1947 | title = Babylonian mathematical texts. I. Reciprocals of regular sexagesimal numbers | journal = [[Journal ...

{{hatnote|This article uses forms of [[Mathematical logic|logical]] notation. For a concise description of the symbols used in ...<ref>{{cite book |last1=Tomassi |first1=Paul |url=https://books.google.com/books?id=5Funj1Zaau0C |title=Logic |date=1999 |publisher=Routledge |isbn=978-0-41 ...

...math>n</math>-plane distribution, and when <math>n = m-1</math>, one talks about ''hyperplane'' distributions. ...context, and involutivity is in general not sufficient for integrability (counterexamples in low dimensions exist). ...

...useful because many properties of topologies can be reduced to statements about a base that generates that topology—and because many topologies are most ea ...ans that a set is open if there exists an open interval of non zero radius about every point in the set. More generally, the [[Euclidean space]]s '''R'''<su ...

{{Short description|Mathematical condition}} ...d(dβ) = 0, expressed simply as d² = 0. This concept is used in mathematical physics, particularly in the context of electromagnetism and differential g ...

...nn Lantzenberger),<ref>[https://www.e-rara.ch/doi/10.3931/e-rara-4843 Rare books]</ref> wrote that a polynomial equation of degree ''n'' (with real coeffici ...1-14858-8/S0273-0979-1981-14858-8.pdf | journal=[[Bulletin of the American Mathematical Society]] | year=1981 | volume=4 | issue=1 | pages=1-36 | doi=10.1090/S0273 ...