Is it possible to use Linux Libertine as a mathematical font?

There is a new LaTeX math package called newtx with a libertine option that matches Libertine text, using Libertine Roman italic and Greek together with symbols from the old txfonts package, remetrized so as not to be as cramped, and with optical versions of math italic and symbols. Versions prior to 0.93 were problematic, but 0.93, which should appear shortly on CTAN, seems to work well.

To provide a more current answer to this, there is now Libertinus, a fork of Linux Libertine with bug fixes and pretty nice math support (check out this example document).

\documentclass[varwidth,border=1mm]{standalone}

\usepackage[
    math-style=ISO,
    bold-style=ISO,
    partial=upright,
    nabla=upright
]{unicode-math}

\setmainfont{Libertinus Serif}
\setsansfont{Libertinus Sans}
\setmathfont{Libertinus Math}


\begin{document}
The formula \(E=mc^2\) is arguably the most famous formula in physics.

In mathematics, it could be \(\mathrm{e}^{\mathrm{i}\uppi}-1=0\).

\(\displaystyle \sum_{k=0}^\infty \frac{1}{k^2} = \frac{\uppi^2}{6}\), and
\(\displaystyle \int\displaylimits_{-\infty}^\infty 
   \exp\left(-\frac{x^2}{2}\right) = \sqrt{2\uppi}\).

\(\alpha\beta\gamma\delta\epsilon\zeta\eta\theta\iota\kappa\lambda\mu\nu\xi\pi\rho\sigma\tau\upupsilon\phi\chi\psi\omega \varepsilon\vartheta\varrho\varsigma\varphi\varkappa\)

\(\upalpha\upbeta\upgamma\updelta\upepsilon\upzeta\upeta\uptheta\upiota\upkappa\uplambda\upmu\upnu\upxi\uppi\uprho\upsigma\uptau\upupsilon\upphi\upchi\uppsi\upomega \upvarepsilon\upvartheta\upvarrho\upvarsigma\upvarphi\upvarkappa\)

\(\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega\)

\(\upAlpha\upBeta\upGamma\upDelta\upEpsilon\upZeta\upEta\upTheta\upIota\upKappa\upLambda\upMu\upNu\upXi\upPi\upRho\upSigma\upTau\upUpsilon\upPhi\upChi\upPsi\upOmega\)
\end{document}

It's not too hard to use it for the variables and constants (letters). For XeLaTeX, you could use the mathspec package. For regular PDFLaTeX, you could use the mathastext package, e.g.:

\usepackage[T1]{fontenc}
\usepackage{libertine}
\usepackage[italic]{mathastext}

That will give you Computer Modern symbols with Libertine letters and numbers. See the mathastext documentation for options regarding Greek, etc. If you load another symbol font (eulervm, etc.) before loading these you'll get its symbols with libertine letters. Personally I like to load txfonts for symbols, and then load these.

I don't know to make it work if you want the few symbols it contains (which is more than most fonts, but certainly not quite enough either), you could probably use unicode-math, but you'll have to switch back to other fonts for the many symbols it lacks.