diff --git a/stdlib/_typeshed/__init__.pyi b/stdlib/_typeshed/__init__.pyi
index 6dd0b38c2e65..8c0005294bf0 100644
--- a/stdlib/_typeshed/__init__.pyi
+++ b/stdlib/_typeshed/__init__.pyi
@@ -40,6 +40,11 @@ class SupportsLessThan(Protocol):
 
 SupportsLessThanT = TypeVar("SupportsLessThanT", bound=SupportsLessThan)  # noqa: Y001
 
+class SupportsGreaterThan(Protocol):
+    def __gt__(self, __other: Any) -> bool: ...
+
+SupportsGreaterThanT = TypeVar("SupportsGreaterThanT", bound=SupportsGreaterThan)  # noqa: Y001
+
 class SupportsDivMod(Protocol[_T_contra, _T_co]):
     def __divmod__(self, __other: _T_contra) -> _T_co: ...
 
diff --git a/stdlib/builtins.pyi b/stdlib/builtins.pyi
index d6fa9d22cb85..13bee2a153f0 100644
--- a/stdlib/builtins.pyi
+++ b/stdlib/builtins.pyi
@@ -13,6 +13,8 @@ from _typeshed import (
     StrOrBytesPath,
     SupportsAnext,
     SupportsDivMod,
+    SupportsGreaterThan,
+    SupportsGreaterThanT,
     SupportsKeysAndGetItem,
     SupportsLenAndGetItem,
     SupportsLessThan,
@@ -1141,18 +1143,18 @@ class map(Iterator[_S], Generic[_S]):
 
 @overload
 def max(
-    __arg1: SupportsLessThanT, __arg2: SupportsLessThanT, *_args: SupportsLessThanT, key: None = ...
-) -> SupportsLessThanT: ...
+    __arg1: SupportsGreaterThanT, __arg2: SupportsGreaterThanT, *_args: SupportsGreaterThanT, key: None = ...
+) -> SupportsGreaterThanT: ...
 @overload
-def max(__arg1: _T, __arg2: _T, *_args: _T, key: Callable[[_T], SupportsLessThan]) -> _T: ...
+def max(__arg1: _T, __arg2: _T, *_args: _T, key: Callable[[_T], SupportsGreaterThan]) -> _T: ...
 @overload
-def max(__iterable: Iterable[SupportsLessThanT], *, key: None = ...) -> SupportsLessThanT: ...
+def max(__iterable: Iterable[SupportsGreaterThanT], *, key: None = ...) -> SupportsGreaterThanT: ...
 @overload
-def max(__iterable: Iterable[_T], *, key: Callable[[_T], SupportsLessThan]) -> _T: ...
+def max(__iterable: Iterable[_T], *, key: Callable[[_T], SupportsGreaterThan]) -> _T: ...
 @overload
-def max(__iterable: Iterable[SupportsLessThanT], *, key: None = ..., default: _T) -> SupportsLessThanT | _T: ...
+def max(__iterable: Iterable[SupportsGreaterThanT], *, key: None = ..., default: _T) -> SupportsGreaterThanT | _T: ...
 @overload
-def max(__iterable: Iterable[_T1], *, key: Callable[[_T1], SupportsLessThan], default: _T2) -> _T1 | _T2: ...
+def max(__iterable: Iterable[_T1], *, key: Callable[[_T1], SupportsGreaterThan], default: _T2) -> _T1 | _T2: ...
 @overload
 def min(
     __arg1: SupportsLessThanT, __arg2: SupportsLessThanT, *_args: SupportsLessThanT, key: None = ...