Using \gather and \align together

Question

I'm very picky regarding alignment inside my proofs. What's frustrating me right now is that I have some lines that I want to be center-aligned (using \begin{gather}) and others that I wish to align at the "=" sign (using \begin{align}). My idea for how to do this was to just switch between the two within one proof, but this creates extra spacing (because closing one and opening another comes with implicit spacing).

I've messed around with adding in \vspace[-20pt] or something to that effect, but it's a rather clumsy solution and I've had problems with it. Also, ideally I would be able to go from align to gather back to align and have the second align keep aligned with the first, and obviously closing and reopening everything doesn't allow this.

Can anybody think of a better way to switch between the two alignment structures? Perhaps using a box to nest my gathers within align or something. Essentially, I usually like most of my proof in align but then want a couple of tangential points in gather. I've spent a while pondering the amsmath readme (and this website), but I can't find an answer.

Many thanks in advance!

Here's a little example coding to demonstrate the issue with my current scheme:

\documentclass{article}
\usepackage{amsmath}
\usepackage{amsthm}
\begin{document}
\begin{proof}
\begin{align*}
10 &= 2+2+2+2+2 \\
&= 3+3+3+1
\end{align*}\begin{gather*}
\intertext{But now it puts this annoying large space above this line...}
5=5
\end{gather*}
\end{proof}
\end{document}

Answer 1

[Note: the improvement below, actually does not work.]

[Note: there is an important improvement to this code below.]

The closest I can get to a solution is

\documentclass[10pt,a4paper]{article}

\usepackage{amsmath,amsthm,mathtools}

\begin{document}
\begin{proof}
  \begin{align*}
    15 &= 5+4+3+2+1 = \sum_{i=1}^5 i \\
    120&=5\cdot4\cdot3\cdot2\cdot1 = 5! \\
    \shortintertext{
      \[ e^{\pi i} + 1 = 0 \]
      \[ x^n + y^n = z^n \]
    } 
    27 &= 3^3 \qedhere
  \end{align*}
\end{proof}
\end{document}

which gives as result

and actually the spacing is quite nice, I think.

---

Failing important edit

I think the below code is nicer, and even gives better results.

\documentclass[10pt,a4paper]{article}

\usepackage{amsmath,amsthm,mathtools}

\begin{document}
\begin{proof}
  \begin{align*}
    15 &= 5+4+3+2+1 = \sum_{i=1}^5 i \\
    120&=5\cdot4\cdot3\cdot2\cdot1 = 5! \\
    \begin{gathered}
      e^{\pi i} + 1 = 0 \\
      x^n + y^n = z^n
    \end{gathered} 
    27 &= 3^3 \qedhere
  \end{align*}
\end{proof}
\end{document}

Credits go to barbara beeton (please vote up her comment on her own answer).

Answer 2

taking a hint from @PeterGrill, here's a method of combining all the parts into one, using gather* since the "single" line is to be center-aligned, and the sub-environment aligned to take care of the multi-line expression.

since you're using amsthm, i've also taken the liberty to use \qedhere to position the "tombstone" on the last line of the display.

\documentclass{article}
\usepackage{mathtools}
\usepackage{amsthm}
\begin{document}
\begin{proof}
\begin{gather*}
 \begin{aligned}
10 &= 2+2+2+2+2 \\
   &= 3+3+3+1
\end{aligned}
\shortintertext{No annoying large space above this line...}
  5=5
\qedhere
\end{gather*}
\end{proof}
\end{document}

Answer 3

As per Adjust vspace between multiple align environments you should never use two consecutive display math environments.

Single align environment:

You could just use a single align* environment. I would also recommend using \shortintertext form the \mathtools package as that provides tighter vertical spacing:

\documentclass{article}
\usepackage{showframe}
\usepackage{mathtools}
\usepackage{amsthm}
\begin{document}
\begin{proof}
\begin{align*}
    10 &= 2+2+2+2+2\\
       &= 3+3+3+1
    \shortintertext{Now this no longer puts an annoying large space above this line...}
    5 &=5 \qedhere
\end{align*}
\end{proof}
\end{document}

---

Using align within gather:

Alternatively, you could also use gather to center some equations and also align other portions, but this dot not look very good, especially with short text snippets in between.

\documentclass{article}
\usepackage{showframe}
\usepackage{mathtools}
\usepackage{amsthm}
\begin{document}
\begin{proof}
\begin{gather*}
\begin{align*}
10 &= 2+2+2+2+2 &\\
   &= 3+3+3+1
\end{align*}
    \shortintertext{Now this no longer puts an annoying large space above this line...}
5=5 \qedhere
\end{gather*}
\end{proof}
\end{document}