# Order of Operations--Mere historical accident? **URL:** \ **Category:** Factual Questions\ **Created:** [June 13, 2012, 5:09pm UTC](https://boards.straightdope.com/t/order-of-operations-mere-historical-accident/625032 "2012-06-13T17:09:56Z")\ **Posts on this page:** 5\ **Page:** 2
**Author:** ![naita](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/naita/32/5862_2.png) [@naita](https://boards.straightdope.com/u/naita)\ **Post date:** [June 14, 2012, 4:31pm UTC](https://boards.straightdope.com/t/order-of-operations-mere-historical-accident/625032/21 "2012-06-14T16:31:12Z")
> [@Kimstu](#): > > I highly recommend Jeff Miller’s online collection of original source citations documenting the earliest known occurrences of various mathematical terms and symbols. Regarding the order of [operations](http://jeff560.tripod.com/operation.html), he notes that there was no firmly established standard convention until well into the 20th century: That’s four turn of the century cites for the current convention and a single contrary cite. All from algebra texts. What were mathematicians and scientists of the day using? ---
**Author:** ![Typo\_Knig](https://avatars.discourse-cdn.com/v4/letter/t/cdc98d/32.png) [@Typo\_Knig](https://boards.straightdope.com/u/Typo_Knig)\ **Post date:** [June 14, 2012, 4:53pm UTC](https://boards.straightdope.com/t/order-of-operations-mere-historical-accident/625032/22 "2012-06-14T16:53:37Z")
> [@Kevbo](#): > > Ah Wirth: pronounced “Veert” in his native German, but mangled to “Worth” by most English speakers. > > So in German he is called by name, in English, he is called by value! Thank you, I’ll be here all week. Tip your servers generously. > I have a chance to use that joke less than 1/decade…can’t let it pass! It’s actually: > [@](#): > > “Whereas Europeans generally pronounce his name the right way (‘Nick-louse Veert’), Americans invariably mangle it into ‘Nickel’s Worth.’ This is to say that Europeans call him by name, but Americans call him by value.” — Introduction by Adriaan van Wijngaarden at the IFIP Congress (1965). [Wiki cite](http://en.wikipedia.org/wiki/Niklaus_Wirth#Quotes) ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [June 14, 2012, 5:17pm UTC](https://boards.straightdope.com/t/order-of-operations-mere-historical-accident/625032/23 "2012-06-14T17:17:56Z")
In addition to what’s been said, it’s important to note that the order of operations is one of those things where there isn’t necessarily a right way to do it, but you do need to have everybody do it the same way. If we had picked a different convention to start with, that would seem equally correct. ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [June 14, 2012, 9:42pm UTC](https://boards.straightdope.com/t/order-of-operations-mere-historical-accident/625032/24 "2012-06-14T21:42:26Z")
From a few posts above: “Whereas Europeans generally pronounce his name the right way (‘Nick-louse Veert’), Americans invariably mangle it into ‘Nickel’s Worth.’ This is to say that Europeans call him by name, but Americans call him by value.” — Introduction by Adriaan van Wijngaarden at the IFIP Congress (1965). Given the number of variations and attributions I’ve seen of this quote, it’s apparently gained true “urban legend” status. I’ve seen a variation of this attributed to [del]Worth[/del] [del]Veert[/del] Wirth himself, stated in the first person: “You may call me by name, Veert, or by value, Worth” ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [June 14, 2012, 9:49pm UTC](https://boards.straightdope.com/t/order-of-operations-mere-historical-accident/625032/25 "2012-06-14T21:49:50Z")
Okay, back to the subject of math notations: Basically, from math history as I think I understand it, math notation has gradually evolved over time, according to what mathematicians have found useful and convenient for algebraic manipulation. (See the related discussion of traditional vs Polish notation for doing algebra in another nearby thread.) Modern algebra, in a form anything like we would recognize today, began to evolve about 4 or 5 centuries ago, I think. According to one book I read once, early notation used one letter § for a linear term, and a different letter for (q) for a quadratic term. Thus, a quadratic polynomial would be written as: aq + bp + c rather than our current style: ax[sup]2[/sup] + bx + c Consider how you would have to manipulate that older notation, compared with our current style, to solve equations like that. Do you think our current style is an improvement? How would you deal with it in Polish notation (see other nearby thread for more on that). One of my math profs mentioned to me that a lot of modern notation is the way it is because there was an international convention of math teachers sometime in the early 20th century, where they argued and hashed out and voted on such matters, setting notational conventions that are in use to this day. [Previous page](https://boards.straightdope.com/t/order-of-operations-mere-historical-accident/625032.md?page=1)