# What is the tag (sums-of-squares) intended for?

The tag has empty tag-wiki at the moment.

Based on the name, I would expect to see there topic such as Fermat's theorem on sums of two squares or Lagrange's four square theorem etc. (In general, mostly topics from number theory.)

But when you have a look at question actually using this tag, you will find there also questions about the sum $\sum_{k=1}^n k^2$, equations containing squares, various infinite sums.

What would be reasonable content for this tag?

I think that if this tag is supposed to be useful, then we should clarify what kind of questions it should be used for and created a reasonable tag-wiki describing this tag.

EDIT: (Jan 16 2014) I have created tag-excerpt and tag-wiki based on number-theoretical meaning of the term. Of course, if further discussion shows that we want use this tag also for some of the other meanings of the term sum of squares, we can include them in the tag-wiki and tag-excerpt, too.

• Variants of Hilbert's $17^{th}$ problem sounds legitimate candidates for this tag. – achille hui Jan 11 '14 at 6:09
• Questions about the sum-of-squares method in optimization theory would also sound on target en.wikipedia.org/wiki/Sum-of-squares_optimization . – David E Speyer Jan 15 '14 at 19:17
• @DavidSpeyer I have posted your suggestion as an answer, so that users can vote for/against having such questions also in this tag. It is CW, feel free to edit that answer further, if you wish. – Martin Sleziak Jan 16 '14 at 8:34
• As Gerry Myerson's answer received most upvotes, I have accepted it. – Martin Sleziak Jan 24 '14 at 11:43

I would restrict it to questions about representations of integers as sums of squares. But I wouldn't expect there to be lots of relevant questions, so I wouldn't mind seeing the tag expunged altogether. Those few questions that are really about representations as sums of squares could be retagged analytic-number-theory or elementary-number-theory or diophantine-equations, as appropriate.

• Given that integer sums of squares questions often have a rather algebraic flavour, I think a separate sum-of-squares tag could be quite useful. However only if it is attached to the right questions. – Marc van Leeuwen Jan 13 '14 at 8:26

Here is a suggestion for the tag-excerpt and the tag-wiki, based on Gerry Myerson posts saying that this tag is for questions about sum of squares in number theory.

This is suggestion for the tag excerpt:

For questions concerning various representation of integers as sums of squares, which are studied in number theory.

This is suggestion for the tag-wiki:

For questions concerning various representation of integers as sums of squares, which are studied in number theory.

These topics include, for example:

I am posting another answer based on David Speyer's comment.

Questions about the sum-of-squares method in optimization theory could also be included in this tag.

• While the name suggests it, I feel that this would make it a weird tag, covering two such different topics. I am not familiar with the topic in optimization, so I don't know if it is large enough to have its own tag (and I have no idea what such a tag could then be called). – Tobias Kildetoft Jan 16 '14 at 8:58
• @TobiasKildetoft I agree with you. In any case, I think that posting this answer here so that other users can upvote/downvote would be a reasonable way to find out what other MSE users think about this. – Martin Sleziak Jan 20 '14 at 15:49