diff --git a/myst_parser/docutils_renderer.py b/myst_parser/docutils_renderer.py
index 1be2fda9..652b0ee5 100644
--- a/myst_parser/docutils_renderer.py
+++ b/myst_parser/docutils_renderer.py
@@ -470,6 +470,13 @@ def render_fence(self, token: SyntaxTreeNode) -> None:
         self.add_line_and_source_path(node, token)
         self.current_node.append(node)
 
+    @property
+    def blocks_mathjax_processing(self):
+        return self.sphinx_env is None or (
+            "myst_update_mathjax" in self.sphinx_env.config
+            and self.sphinx_env.config.myst_update_mathjax
+        )
+
     def render_heading(self, token: SyntaxTreeNode) -> None:
 
         if self.md_env.get("match_titles", None) is False:
@@ -490,13 +497,7 @@ def render_heading(self, token: SyntaxTreeNode) -> None:
         self.add_line_and_source_path(title_node, token)
 
         new_section = nodes.section()
-        if level == 1 and (
-            self.sphinx_env is None
-            or (
-                "myst_update_mathjax" in self.sphinx_env.config
-                and self.sphinx_env.config.myst_update_mathjax
-            )
-        ):
+        if level == 1 and self.blocks_mathjax_processing:
             new_section["classes"].extend(["tex2jax_ignore", "mathjax_ignore"])
         self.add_line_and_source_path(new_section, token)
         new_section.append(title_node)
@@ -775,6 +776,10 @@ def render_table_row(self, token: SyntaxTreeNode) -> None:
                     with self.current_node_context(para, append=True):
                         self.render_children(child)
 
+    def mark_mathjax_node(self, node):
+        if self.blocks_mathjax_processing:
+            node.attributes.setdefault("classes", []).append("mathjax_process")
+
     def render_math_inline(self, token: SyntaxTreeNode) -> None:
         content = token.content
         if token.markup == "$$":
@@ -782,18 +787,21 @@ def render_math_inline(self, token: SyntaxTreeNode) -> None:
             node = nodes.math_block(content, content, nowrap=False, number=None)
         else:
             node = nodes.math(content, content)
+        self.mark_mathjax_node(node)
         self.add_line_and_source_path(node, token)
         self.current_node.append(node)
 
     def render_math_single(self, token: SyntaxTreeNode) -> None:
         content = token.content
-        node = nodes.math(content, content)
+        node = nodes.math(content, content, classes=["mathjax_process"])
+        self.mark_mathjax_node(node)
         self.add_line_and_source_path(node, token)
         self.current_node.append(node)
 
     def render_math_block(self, token: SyntaxTreeNode) -> None:
         content = token.content
         node = nodes.math_block(content, content, nowrap=False, number=None)
+        self.mark_mathjax_node(node)
         self.add_line_and_source_path(node, token)
         self.current_node.append(node)
 
diff --git a/myst_parser/main.py b/myst_parser/main.py
index 07376cf8..7f44e8aa 100644
--- a/myst_parser/main.py
+++ b/myst_parser/main.py
@@ -47,11 +47,6 @@ class MdParserConfig:
 
     update_mathjax: bool = attr.ib(default=True, validator=instance_of(bool))
 
-    mathjax_classes: str = attr.ib(
-        default="tex2jax_process|mathjax_process|math|output_area",
-        validator=instance_of(str),
-    )
-
     @enable_extensions.validator
     def check_extensions(self, attribute, value):
         if not isinstance(value, Iterable):
diff --git a/myst_parser/mathjax.py b/myst_parser/mathjax.py
index 85a62af3..1a5bfbe9 100644
--- a/myst_parser/mathjax.py
+++ b/myst_parser/mathjax.py
@@ -19,22 +19,6 @@
 logger = logging.getLogger(__name__)
 
 
-def log_override_warning(app: Sphinx, version: int, current: str, new: str) -> None:
-    """Log a warning if MathJax configuration being overriden."""
-    if logging.is_suppressed_warning("myst", "mathjax", app.config.suppress_warnings):
-        return
-    config_name = (
-        "mathjax3_config['options']['processHtmlClass']"
-        if version == 3
-        else "mathjax_config['tex2jax']['processClass']"
-    )
-    logger.warning(
-        f"`{config_name}` is being overridden by myst-parser: '{current}' -> '{new}'. "
-        "Set `suppress_warnings=['myst.mathjax']` to ignore this warning, or "
-        "`myst_update_mathjax=False` if this is undesirable."
-    )
-
-
 def override_mathjax(app: Sphinx):
     """Override aspects of the mathjax extension.
 
@@ -51,43 +35,6 @@ def override_mathjax(app: Sphinx):
             None,
         )
 
-    if not app.env.myst_config.update_mathjax:  # type: ignore[attr-defined]
-        return
-
-    mjax_classes = app.env.myst_config.mathjax_classes  # type: ignore[attr-defined]
-
-    if "mathjax3_config" in app.config:
-        # sphinx 4 + mathjax 3
-        app.config.mathjax3_config = app.config.mathjax3_config or {}  # type: ignore[attr-defined]
-        app.config.mathjax3_config.setdefault("options", {})
-        if (
-            "processHtmlClass" in app.config.mathjax3_config["options"]
-            and app.config.mathjax3_config["options"]["processHtmlClass"]
-            != mjax_classes
-        ):
-            log_override_warning(
-                app,
-                3,
-                app.config.mathjax3_config["options"]["processHtmlClass"],
-                mjax_classes,
-            )
-        app.config.mathjax3_config["options"]["processHtmlClass"] = mjax_classes
-    elif "mathjax_config" in app.config:
-        # sphinx 3 + mathjax 2
-        app.config.mathjax_config = app.config.mathjax_config or {}  # type: ignore[attr-defined]
-        app.config.mathjax_config.setdefault("tex2jax", {})
-        if (
-            "processClass" in app.config.mathjax_config["tex2jax"]
-            and app.config.mathjax_config["tex2jax"]["processClass"] != mjax_classes
-        ):
-            log_override_warning(
-                app,
-                2,
-                app.config.mathjax_config["tex2jax"]["processClass"],
-                mjax_classes,
-            )
-        app.config.mathjax_config["tex2jax"]["processClass"] = mjax_classes
-
 
 def html_visit_displaymath(self: HTMLTranslator, node: nodes.math_block) -> None:
     """Override for sphinx.ext.mathjax.html_visit_displaymath to handle amsmath.