You can use AsciiMath or JLaTeXMath notation within PlantUML:
note right
Try also
<latex>P(y|\mathbf{x}) \mbox{ or } f(\mathbf{x})+\epsilon</latex>
end note
AsciiMath on activity diagram
Bob -> Alice : Can you solve: <math>ax^2+bx+c=0</math>
Alice --> Bob: <math>x = (-b+-sqrt(b^2-4ac))/(2a)</math>
AsciiMath on sequence diagram

Standalone diagram

You can also use @startmath/@endmath to create standalone AsciiMath formula.
f(t)=(a_0)/2 + sum_(n=1)^ooa_ncos((npit)/L)+sum_(n=1)^oo b_n\ sin((npit)/L)
standalone math formula
Or use @startlatex/@endlatex to create standalone JLaTeXMath formula.
\sum_{i=0}^{n-1} (a_i + b_i^2)
standalone math formula

How is this working ?

To draw those formulas, PlantUML uses two OpenSource projects:
  • AsciiMath that converts AsciiMath notation to LaTeX expression.
  • JLatexMath that displays mathematical formulas written in LaTeX. JLaTeXMath is the best Java library to display LaTeX code.
ASCIIMathTeXImg.js is small enough to be integrated into PlantUML standard distribution.

Since JLatexMath is bigger, you have to download it separately, then unzip the 4 jar files (batik-all-1.7.jarjlatexmath-minimal-1.0.3.jarjlm_cyrillic.jar and jlm_greek.jar) in the same folder as PlantUML.jar.