@@ -1,38 +1,37 @@
 """
-========================
-Math Fontfamily Example
-========================
+===============
+Math fontfamily
+===============
 
 A simple example showcasing the new *math_fontfamily* parameter that can
 be used to change the family of fonts for each individual text
-element in a plot. If no parameter is set, the global value
+element in a plot.
+
+If no parameter is set, the global value
 :rc:`mathtext.fontset` will be used.
 """
 
 import matplotlib.pyplot as plt
 
-plt.figure(figsize=(9, 4))
+plt.figure(figsize=(6, 5))
 
 # A simple plot for the background.
-plt.plot(range(11), color="0.9", label=r'Math Font Example')
-
-# Here we hold the text, we will mix normal text and math text
-msg = r"This is a normal text and "
-msg+= r"$this\ is\ a\ text\ in\ math\ mode,\ look,\ I\ can\ do\ this\ "
-msg+= r"\int_{0}^{\infty } x^2 dx !$"
+plt.plot(range(11), color="0.9")
 
-# Now we set the text to be shown
-plt.text(0, 6, msg, size=11, math_fontfamily='cm')
+# A text mixing normal text and math text.
+msg = (r"Normal Text. $Text\ in\ math\ mode:\ "
+       r"\int_{0}^{\infty } x^2 dx$")
 
-# The parameter math_fontfamily migth be aliased to math_font, the
-# code below will work just as well.
-plt.text(0, 3, msg, size=11, math_font='dejavuserif')
+# Set the text in the plot.
+plt.text(1, 7, msg, size=12, math_fontfamily='cm')
 
-# Also, we can call *math_fontfamily* and *math_font* in most places where
-# there is text, like in the title:
-titleMsg = r"$This\ is\ a\ title\ in\ math\ mode,\ look:\ "
-titleMsg+= r"\int_{0}^{\infty } x^2 dx !$"
+# Set another font for the next text.
+plt.text(1, 3, msg, size=12, math_fontfamily='dejavuserif')
 
-plt.title(titleMsg, math_font='stixsans', size=14)
+# *math_fontfamily* can be used in most places where there is text,
+# like in the title:
+plt.title(r"$Title\ in\ math\ mode:\ \int_{0}^{\infty } x^2 dx$",
+          math_fontfamily='stixsans', size=14)
 
+# Note that the normal text is not changed by *math_fontfamily*.
 plt.show()
@@ -943,41 +943,41 @@ def set_fontconfig_pattern(self, pattern):
     def get_math_fontfamily(self):
         """
         Return the name of the font family used for math text.
+
         The default font is :rc:`mathtext.fontset`.
         """
-
         if self._math_fontfamily is None:
             return rcParams['mathtext.fontset']
         return self._math_fontfamily
 
-    def set_math_fontfamily(self, fontset):
+    def set_math_fontfamily(self, fontfamily):
         """
-        The *math_fontfamily* is the family of fonts used in case this text is
-        rendered in math mode. If no *math_fontfamily* is defined, the
-        fontset defined in :rc:`mathtext.fontset` will be used.
+        Set the font family for text in math mode.
+
+        If not set explicitly, :rc:`mathtext.fontset` will be used.
 
         Parameters
         ----------
-        fontset : str, the name of the fontset. Available fontsets are defined
-        in the matplotlibrc.template file :ref:`here
-        <customizing-with-matplotlibrc-files>`
+        fontfamily : str
+            The name of the font family.
+
+            Available font families are defined in the 
+            matplotlibrc.template file 
+            :ref:`here <customizing-with-matplotlibrc-files>`
 
         See Also
         --------
         .text.Text.get_math_fontfamily
         """
-        if fontset is None:
+        if fontfamily is None:
             self._math_fontfamily = None
             return
-        # here we validate the parameter fontset just as if it were
-        # passed to rcParams['mathtext.fontset'], but with a customized text
-        valid_fonts = _validators['mathtext.fontset'].valid.values()
-        if fontset not in valid_fonts:
-            msg = (f"Parameter math_fontfamily ({fontset}) must be one of "
-                   f"the following: {[*valid_fonts]}")
-            raise ValueError (msg)
 
-        self._math_fontfamily = fontset
+        valid_fonts = _validators['mathtext.fontset'].valid.values()
+        # _check_in_list() Validates the parameter math_fontfamily as
+        # if it were passed to rcParams['mathtext.fontset']
+        cbook._check_in_list(valid_fonts, math_fontfamily=fontfamily)
+        self._math_fontfamily = fontfamily
 
     def copy(self):
         """Return a copy of self."""
 
@@ -3364,7 +3364,8 @@ def _parse_cached(self, s, dpi, prop, ps_useafm):
         else:
             backend = self._backend_mapping[self._output]()
             fontset_class = cbook._check_getitem(
-                self._font_type_mapping, fontset=prop.get_math_fontfamily())
+                self._font_type_mapping,
+                fontset=prop.get_math_fontfamily())
             font_output = fontset_class(prop, backend)
 
         fontsize = prop.get_size_in_points()
 
@@ -372,6 +372,6 @@ def test_math_fontfamily():
     f1, ax1 = plt.subplots(figsize=(12, 3))
     ax1.plot(range(11), color="0.9")
     ax1.text(0.2, 7, r"$\mathit{This\ text\ should\ have\ one\ font} $",
-             size=24, math_font='dejavusans')
+             size=24, math_fontfamily='dejavusans')
     ax1.text(0.2, 3, r"$\mathit{This\ text\ should\ have\ another} $",
-             size=24, math_font='dejavuserif')
+             size=24, math_fontfamily='dejavuserif')
@@ -114,7 +114,6 @@ def _get_textbox(text, renderer):
     "fontvariant": ["variant"],
     "verticalalignment": ["va"],
     "fontweight": ["weight"],
-    "math_fontfamily": ["math_font"],
 })
 class Text(Artist):
     """Handle storing and drawing of text in window or data coordinates."""
@@ -1048,30 +1047,36 @@ def set_fontsize(self, fontsize):
     def get_math_fontfamily(self):
         """
         Return the font family name for math text rendered by Matplotlib.
+
         The default value is :rc:`mathtext.fontset`.
+
         See Also
         --------
         set_math_fontfamily
         """
         return self._fontproperties.get_math_fontfamily()
 
-    def set_math_fontfamily(self, fontset):
+    def set_math_fontfamily(self, fontfamily):
         """
         Set the font family for math text rendered by Matplotlib.
+
         This does only affect Matplotlib's own math renderer. It has no effect
         when rendering with TeX (``usetex=True``).
 
         Parameters
         ----------
-        fontset : str, the name of the fontset. Available fontsets are defined
-in the :ref:`matplotlibrc.template file <customizing-with-matplotlibrc-files>`.
+        fontfamily : str
+            The name of the font family.
 
-        See also
-        ----------
-        :doc:`/tutorials/text/mathtext`
-        .text.Text.set_mathtext_fontset
+            Available font families are defined in the
+            :ref:`matplotlibrc.template file
+            <customizing-with-matplotlibrc-files>`.
+
+        See Also
+        --------
+        get_math_fontfamily
         """
-        self._fontproperties.set_math_fontfamily(fontset)
+        self._fontproperties.set_math_fontfamily(fontfamily)
 
     def set_fontweight(self, weight):
         """