Informal mathematics, also called naïve mathematics, has historically been the predominant form of mathematics at most times and in most cultures, and...

invalid structure Informal fallacy, the complement Informal mathematics, also called naïve mathematics Formal cause, Aristotle's intrinsic, determining...

Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world...

Tanswell, Fenner Stanley (2024). Mathematical Rigour and Informal Proof. Cambridge Elements in the Philosophy of Mathematics. Cambridge University Press....

usually admits some ambiguity. In most mathematical literature, proofs are written in terms of rigorous informal logic. Purely formal proofs, written fully...

Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research-and-application-based professional...

non-mathematicians, use the term folk mathematics to refer to the informal mathematics studied in many ethno-cultural studies of mathematics.[citation needed] Although...

foundations of mathematics. Unlike axiomatic set theories, which are defined using formal logic, naive set theory is defined informally, in natural language...

from outside a system. An informal illustration of this is categorizing the proposition "2+2=4" as belonging to mathematics while categorizing the proposition...

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions...

Mathematical practice comprises the working practices of professional mathematicians: selecting theorems to prove, using informal notations to persuade...

Informal fallacies are a type of incorrect argument in natural language. The source of the error is not necessarily due to the form of the argument, as...

Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations...

In theoretical computer science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation...

explains that his purpose is to challenge formalism in mathematics, and to show that informal mathematics grows by a logic of "proofs and refutations". The...

In mathematics, Diophantine geometry is the study of Diophantine equations by means of powerful methods in algebraic geometry. By the 20th century it...

γῆ (gê) 'earth, land' and μέτρον (métron) 'a measure') is a branch of mathematics concerned with properties of space such as the distance, shape, size...

In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations...

(trígōnon) 'triangle' and μέτρον (métron) 'measure') is a branch of mathematics concerned with relationships between angles and side lengths of triangles...

Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure,...

of expressing information symbolically, as in a mathematical formula or a chemical formula. The informal use of the term formula in science refers to the...

Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing...

Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a...

Folk mathematics may refer to: The mathematical folklore that circulates among mathematicians The informal mathematics used in everyday life Folk theorem...

Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical...

The National Museum of Mathematics or MoMath is a mathematics museum in Manhattan, New York City. It opened on December 15, 2012, with over thirty interactive...

many applications to other areas of mathematics as well as the ordinary mode of reasoning of informal mathematics in calculus and applications to physics...

In mathematics and logic, a vacuous truth is a conditional or universal statement (a universal statement that can be converted to a conditional statement)...

read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode...

establish was that no theorem of informal mathematics is final or perfect. This means that, in non-axiomatic mathematics, we should not think that a theorem...