diff --git a/crates/stdlib/src/math.rs b/crates/stdlib/src/math.rs
index cb406e515..4b23b7b7b 100644
--- a/crates/stdlib/src/math.rs
+++ b/crates/stdlib/src/math.rs
@@ -368,6 +368,11 @@ mod math {
 
     #[pyfunction]
     fn ceil(x: PyObjectRef, vm: &VirtualMachine) -> PyResult {
+        // `math_ceil`: an exact float skips the `__ceil__` lookup.
+        if let Some(f) = x.downcast_ref_if_exact::<PyFloat>(vm) {
+            let v = try_f64_to_bigint(f.to_f64().ceil(), vm)?;
+            return Ok(vm.ctx.new_int(v).into());
+        }
         // Only call __ceil__ if the class defines it - if it exists but is not callable,
         // the error should be propagated (not fall back to float conversion)
         if x.class().has_attr(identifier!(vm, __ceil__)) {
@@ -378,14 +383,16 @@ mod math {
             let v = try_f64_to_bigint(v?.to_f64().ceil(), vm)?;
             return Ok(vm.ctx.new_int(v).into());
         }
-        Err(vm.new_type_error(format!(
-            "type '{}' doesn't define '__ceil__' method",
-            x.class().name(),
-        )))
+        Err(vm.new_type_error(format!("must be real number, not {}", x.class().name())))
     }
 
     #[pyfunction]
     fn floor(x: PyObjectRef, vm: &VirtualMachine) -> PyResult {
+        // `math_floor`: an exact float skips the `__floor__` lookup.
+        if let Some(f) = x.downcast_ref_if_exact::<PyFloat>(vm) {
+            let v = try_f64_to_bigint(f.to_f64().floor(), vm)?;
+            return Ok(vm.ctx.new_int(v).into());
+        }
         // Only call __floor__ if the class defines it - if it exists but is not callable,
         // the error should be propagated (not fall back to float conversion)
         if x.class().has_attr(identifier!(vm, __floor__)) {
@@ -396,10 +403,7 @@ mod math {
             let v = try_f64_to_bigint(v?.to_f64().floor(), vm)?;
             return Ok(vm.ctx.new_int(v).into());
         }
-        Err(vm.new_type_error(format!(
-            "type '{}' doesn't define '__floor__' method",
-            x.class().name(),
-        )))
+        Err(vm.new_type_error(format!("must be real number, not {}", x.class().name())))
     }
 
     #[pyfunction]
diff --git a/extra_tests/snippets/stdlib_math.py b/extra_tests/snippets/stdlib_math.py
index 08182f2fc..00d6c5f3a 100644
--- a/extra_tests/snippets/stdlib_math.py
+++ b/extra_tests/snippets/stdlib_math.py
@@ -102,6 +102,30 @@ with assert_raises(TypeError):
     math.ceil(object())
 with assert_raises(TypeError):
     math.floor(object())
+with assert_raises(TypeError) as cm:
+    math.floor("1.5")
+assert str(cm.exception) == "must be real number, not str"
+with assert_raises(TypeError) as cm:
+    math.ceil(None)
+assert str(cm.exception) == "must be real number, not NoneType"
+
+assert math.floor(-0.5) == -1 and math.ceil(-0.5) == 0
+with assert_raises(OverflowError):
+    math.floor(INF)
+with assert_raises(ValueError):
+    math.ceil(NAN)
+
+
+class FloatFloor(float):
+    def __floor__(self):
+        return "sub floor"
+
+    def __ceil__(self):
+        return "sub ceil"
+
+
+assert math.floor(FloatFloor(1.5)) == "sub floor"
+assert math.ceil(FloatFloor(1.5)) == "sub ceil"
 
 isclose = math.isclose