Question: I would like to use Zapf's Palatino font for the text in my document, which also includes a lot of maths. And I would like a good font for the maths. This is a snapshot of what I am doing.

```
\documentclass[10pt,letterpaper]{memoir}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{mathpple}
\usepackage{upgreek}
\usepackage{mathpazo}
\usepackage{lipsum}

\begin{document}

\chapter{Demo}

Some regular text. \lipsum[1]

Now for some maths.

\begin{displaymath}
P_{N-1 + m} = \frac{C}{N-{1} + m} \binom{N_{2} - N_{1}}{m}
        \alpha^{m}\beta^{(N_{2} - N_{1}) -m}
\end{displaymath}

The number 27 is the sum of the first 5 odd prime numbers: $27 = 1+3+5+7+11$

\end{document}

```

To me the text and math fonts seem a good fit but the text does not look like Palatino.

[![enter image description here](https://i.stack.imgur.com/tdQt7.jpg)](https://i.stack.imgur.com/tdQt7.jpg)

Answer: 
I suggest that you not load the `mathpple`, `mathpazo`, and `upgreek` packages and, instead, load the `newpxtext` and `newpxmath` packages.

[![enter image description here](https://i.stack.imgur.com/kGiwH.png)](https://i.stack.imgur.com/kGiwH.png)

```
\documentclass[10pt,letterpaper]{memoir}
\usepackage{amsmath,amssymb}
%\usepackage{mathpple}
%\usepackage{upgreek}
%\usepackage{mathpazo}
\usepackage{lipsum}
\usepackage{newpxtext,newpxmath}

\begin{document}

Some regular text. \lipsum[2]

Now for some maths.
\begin{displaymath}
P_{N-1 + m} = \frac{C}{N-{1} + m} \binom{N_{2} - N_{1}}{m}\,
        \alpha^{m}\beta^{(N_{2} - N_{1}) -m}
\end{displaymath}
The number 27 is the sum of the first 5 odd prime numbers: $27 = 1+3+5+7+11$.

$\alpha\beta\gamma\delta$ vs.\ $\upalpha\upbeta\upgamma\updelta$

\end{document}

```
I would avoid using `TeX Gyre Pagella` or `newpxtext` if small caps are to be used. The proportions of some of these small caps are off. This is particularly obvious for `o.sc`. Here `O\textsc{o}o` is compared for `newpxtext` with option `largesc`, `TeX Gyre Pagella` and `mathpazo` with option `sc` (or `osf`):

[![enter image description here](https://i.stack.imgur.com/WnVjn.png)](https://i.stack.imgur.com/WnVjn.png)

Without the `largesc` option, `newpxtext` is the same as Pagella. But the uniform scaling done by `largesc` cannot help with the intrinsic proportions of the letter (it is to wide for its height). For me the availability of bold/italic small caps does not compensate for this. Related discussion at <https://tex.stackexchange.com/a/385262/140850>. 

When using `pdflatex` I use `newpxmath` together with my FPL fonts:

```
\usepackage[sc]{mathpazo} % or option osf
\usepackage{newpxmath}

```

When using `xelatex` or `lualatex` I either use the real Palatino (Linotype) for text or my [FPL Neu](https://github.com/rstub/fplneu/): 

```
\usepackage{unicode-math}
\setmainfont{FPL Neu}
\setmathfont{Asana Math} % alternative: TeX Gyre Pagella Math

```

Here the `O\textsc{o}o` sequence and the improved @-sign from that font:

[![enter image description here](https://i.stack.imgur.com/xzKRN.png)](https://i.stack.imgur.com/xzKRN.png)