Why does boldface not work on Greek letters?

[PeroK]

If you look at the Latex, both these characters ought to be in boldface, but the Greek letter does not appear in bold.

$\mathbf a$, $\mathbf{\alpha}$

Is that something Latex can't do?

 

[Wrichik Basu]

You can use \boldsymbol from amsmath:
$\boldsymbol{\alpha \beta \xi}$
See this answer on TeX-LaTeX SE.