diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index 6e8cbc34be062..afeee24dfe290 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -960,6 +960,7 @@ Reshaping
 - Bug in :func:`concat` was not allowing for concatenation of ``DataFrame`` and ``Series`` with duplicate keys (:issue:`33654`)
 - Bug in :func:`cut` raised an error when non-unique labels (:issue:`33141`)
 - Ensure only named functions can be used in :func:`eval()` (:issue:`32460`)
+- Bug in :func:`Dataframe.aggregate` and :func:`Series.aggregate` was causing recursive loop in some cases (:issue:`34224`)
 - Fixed bug in :func:`melt` where melting MultiIndex columns with ``col_level`` > 0 would raise a ``KeyError`` on ``id_vars`` (:issue:`34129`)
 
 Sparse
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index dfc938918f03a..d48fc9aeddca5 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -7333,8 +7333,12 @@ def aggregate(self, func, axis=0, *args, **kwargs):
         result = None
         try:
             result, how = self._aggregate(func, axis=axis, *args, **kwargs)
-        except TypeError:
-            pass
+        except TypeError as err:
+            exc = TypeError(
+                "DataFrame constructor called with "
+                f"incompatible data and dtype: {err}"
+            )
+            raise exc from err
         if result is None:
             return self.apply(func, axis=axis, args=args, **kwargs)
         return result
diff --git a/pandas/tests/series/test_apply.py b/pandas/tests/series/test_apply.py
index 589f8933efa96..e6f86dda05893 100644
--- a/pandas/tests/series/test_apply.py
+++ b/pandas/tests/series/test_apply.py
@@ -42,7 +42,9 @@ def test_apply(self, datetime_series):
 
     def test_apply_same_length_inference_bug(self):
         s = Series([1, 2])
-        f = lambda x: (x, x + 1)
+
+        def f(x):
+            return (x, x + 1)
 
         result = s.apply(f)
         expected = s.map(f)
@@ -56,7 +58,9 @@ def test_apply_same_length_inference_bug(self):
     def test_apply_dont_convert_dtype(self):
         s = Series(np.random.randn(10))
 
-        f = lambda x: x if x > 0 else np.nan
+        def f(x):
+            return x if x > 0 else np.nan
+
         result = s.apply(f, convert_dtype=False)
         assert result.dtype == object
 
@@ -459,6 +463,14 @@ def test_agg_cython_table_raises(self, series, func, expected):
             # e.g. Series('a b'.split()).cumprod() will raise
             series.agg(func)
 
+    def test_transform_none_to_type(self):
+        # GH34377
+        df = pd.DataFrame({"a": [None]})
+
+        msg = "DataFrame constructor called with incompatible data and dtype"
+        with pytest.raises(TypeError, match=msg):
+            df.transform({"a": int})
+
 
 class TestSeriesMap:
     def test_map(self, datetime_series):