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This question comes up often, but there is no up to date scholarly study of it that I know of. The most comprehensive recent accounts (and they are rather brief) seem to be Jeff Miller's Earliest Uses of Symbols of Operation and Peterson's post on Math Forum, parts of which are aped on various pop-sites, often without attribution. But Peterson admits:"I have not found a definitive answer yet".

This question comes up often, but there is no up to date scholarly study of it that I know of. The most comprehensive recent accounts (and they are rather brief) seem to be Jeff Miller's Earliest Uses of Symbols of Operation and Peterson's post on Math Forum, parts of which are aped on various pop-sites, often without attribution. But Peterson admits:"I have not found a definitive answer yet".

"I have not yet found any twentieth-century declarations that resolved these issues, so I do not know how they were resolved... There is still some development in this area, as we frequently hear from students and teachers confused by texts that either teach or imply that implicit multiplication ($2\times$) takes precedence over explicit multiplication and division ($2\times x$, $2/x$) in expressions such as $a/2b$, which they would take as $a/(2b)$, contrary to the generally accepted rules."

"I have not yet found any twentieth-century declarations that resolved these issues, so I do not know how they were resolved... There is still some development in this area, as we frequently hear from students and teachers confused by texts that either teach or imply that implicit multiplication ($2x$) takes precedence over explicit multiplication and division ($2\times x$, $2/x$) in expressions such as $a/2b$, which they would take as $a/(2b)$, contrary to the generally accepted rules."

This question comes up often, but there is no up to date scholarly study of it that I know of. The most comprehensive accounts seems to be Jeff Miller's Earliest Uses of Symbols of Operation and Peterson's post on Math Forum, parts of which are aped on various pop-sites, often without attribution. But Peterson admits:"I have not found a definitive answer yet".

For my part, I suspect that the rise of computers and formal languages, and the involvement of research mathematicians in school education (see the New Math movement) in the 1960-s put further pressures for the canonization of the Wells-Hart rules. In the Soviet Union, to the threat of which the New Math was a response, this happened even earlier, around 1930s. It was not fully successful even to this day. Witness not only the aforementioned deviations, but even the questioning of the utility of the convention. As of 2007, Wu wrote in “Order of operations” and other oddities in schoolmathematic:

"One of the flaws of the school mathematics curriculum is that it wastes timein fruitless exercises in notation, definitions, and conventions, when it should be spending the time on mathematics of substance. Such flaws manifest themselves in assessment items which assess, not whether students know real mathematics, but whether they could memorize arcane rules or senseless conventions whose raison-d’ˆetre they know nothing about. An example is the convention known as the Rules for the Order of Operations, introduced into the school curriculum in the fifth or sixth grade."

This question comes up often, but there is no up to date scholarly study of it that I know of. The most comprehensive recent accounts (and they are rather brief) seem to be Jeff Miller's Earliest Uses of Symbols of Operation and Peterson's post on Math Forum, parts of which are aped on various pop-sites, often without attribution. But Peterson admits:"I have not found a definitive answer yet".

For my part, I suspect that the rise of computers and formal languages, and the involvement of research mathematicians in school education (see the New Math movement) in the 1960-s put further pressures for the canonization of the Wells-Hart rules. In the Soviet Union, to the threat of which the New Math was a response, this happened even earlier, around 1930s. It was not fully successful even to this day. Witness not only the aforementioned deviations, but even the questioning of the utility of the whole convention. As of 2007, Wu wrote in “Order of operations” and other oddities in school mathematics:

"One of the flaws of the school mathematics curriculum is that it wastes time in fruitless exercises in notation, definitions, and conventions, when it should be spending the time on mathematics of substance. Such flaws manifest themselves in assessment items which assess, not whether students know real mathematics, but whether they could memorize arcane rules or senseless conventions whose raison-d’etre they know nothing about. An example is the convention known as the Rules for the Order of Operations, introduced into the school curriculum in the fifth or sixth grade."