Hyphenation points within rigidly typeset formulas

Question

Because I am not fond of the look of tracking ("stretching") for math formulas, I generally use ${...}$ instead of $...$ for math formulas. (Please respect this aesthetic preference of mine.) However quite often, this leads to overshoot lines. Here is some working example code leading to this problem:

\documentclass{article}

\begin{document}

Consider the following claim: ${a \in S \cap T}$ or
maybe ${a^2 + b^2 = c^2}$ and ${e^{\pi i} + 1 = 0}$, but
not ${xy = abc = uvw}$ or ${a/b = c/d = \frac{e}{f}}$
are interesting formulas. The preceding text was meant
to cause overshoot mathematical formulas.

\end{document}

Specifically, here the word "preceding" is broken between lines 2 and 3 as pre-ceding, but line 1 has the formula ${e^{\pi i} + 1 = 0}$ overshoot into the margin. The end of the equals sign aligns (roughly) with the end of the hyphen in "pre-ceding", with "0," being placed into the margin.

I would like to indicate an optional math formula line break before the equals sign. Is there a way to specify optional linebreak points for math formulas (just like \- can be used to indicate a hyphenation point for a word), while maintaining the constraint that math formulas are never tracked?

Answer 1

If you really never want to have the spacing in math formulas stretched or shrunk, you can use the answers to How to change default for spacing around binary relations? Namely, set the flexible spaces \thickmuskip and \medmuskip to some constant values:

\thickmuskip=5mu
\medmuskip=4mu

These are the default values, but without the stretch and shrink. Hence you'll get the same spacing as with your ${...}$ method, but formulas can be broken at the end of the line.

If you add the above to the preamble of your example code (and remove the extra {}, of course), you'll see that the $e^{\pi i} + 1 = 0$ will be broken after the equals sign, which is very much by design – Knuth specifically programmed TeX not to put a break before relational symbols. If you still want a break before the equals sign, you can put a \break command there, but I don't recommend this. For an optional break you can use \allowbreak or, if that doesn't suffice, something like \penalty-100.