Mathematical rigor

Rigour or rigor (see spelling differences) describes a condition of stiffness or strictness. Rigour frequently refers to a process of adhering absolutely to certain constraints, or the practice of maintaining strict consistency with certain predefined parameters. These constraints may be environmentally imposed, such as "the rigours of famine"; logically imposed, such as mathematical proofs which must maintain consistent answers; or socially imposed, such as the process of defining ethics and law.

Rigour comes to English through old French (13th c., Modern French rigueur) meaning "stiffness", which itself is based on the Latin rigorem (nominative rigor) "numbness, stiffness, hardness, firmness; roughness, rudeness", from the verb rigere "to be stiff". The noun was frequently used to describe a condition of strictness or stiffness, which arises from a situation or constraint either chosen or experienced passively. For example, the title of the book Theologia Moralis Inter Rigorem et Laxitatem Medi roughly translates as "mediating theological morality between rigour and laxness". The book details, for the clergy, situations in which they are obligated to follow church law exactly, and in which situations they can be more forgiving yet still considered moral.Rigor mortis translates directly as the stiffness (rigor) of death (mortis), again describing a condition which arises from a certain constraint (death).

Intellectual rigour is a process of thought which is consistent, does not contain self-contradiction, and takes into account the entire scope of available knowledge on the topic. It actively avoids logical fallacy. Furthermore, it requires a sceptical assessment of the available knowledge. If a topic or case is dealt with in a rigorous way, it means that it is dealt with in a comprehensive, thorough and complete way, leaving no room for inconsistencies.

Scholarly method describes the different approaches or methods which may be taken to apply intellectual rigour on an institutional level to ensure the quality of information published. An example of intellectual rigour assisted by a methodical approach is the scientific method, in which a person will produce a hypothesis based on what they believe to be true, then construct experiments in order to prove that hypothesis wrong. This method, when followed correctly, helps to prevent against circular reasoning and other fallacies which frequently plague conclusions within academia. Other disciplines, such as philosophy and mathematics, employ their own structures to ensure intellectual rigour. Each method requires close attention to criteria for logical consistency, as well as to all relevant evidence and possible differences of interpretation. At an institutional level, Peer review is used to validate intellectual rigour.

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