diff --git a/INSTALL.rst.txt b/INSTALL.rst.txt
index 30f58fa6d31c..2b92267514f6 100644
--- a/INSTALL.rst.txt
+++ b/INSTALL.rst.txt
@@ -26,8 +26,13 @@ Building NumPy requires the following installed software:
 
    This is required for testing NumPy, but not for using it.
 
+4) Hypothesis__ (optional) 5.3.0 or later
+
+   This is required for testing NumPy, but not for using it.
+
 Python__ http://www.python.org
 pytest__ http://pytest.readthedocs.io
+Hypothesis__ https://hypothesis.readthedocs.io/en/latest/
 
 
 .. note::
diff --git a/doc/TESTS.rst.txt b/doc/TESTS.rst.txt
index 9023c7100c5d..007840b399c1 100644
--- a/doc/TESTS.rst.txt
+++ b/doc/TESTS.rst.txt
@@ -360,7 +360,17 @@ deterministic by setting the random number seed before generating it.  Use
 either Python's ``random.seed(some_number)`` or NumPy's
 ``numpy.random.seed(some_number)``, depending on the source of random numbers.
 
+Alternatively, you can use `Hypothesis`_ to generate arbitrary data.
+Hypothesis manages both Python's and Numpy's random seeds for you, and
+provides a very concise and powerful way to describe data (including
+``hypothesis.extra.numpy``, e.g. for a set of mutually-broadcastable shapes).
+
+The advantages over random generation include tools to replay and share
+failures without requiring a fixed seed, reporting *minimal* examples for
+each failure, and better-than-naive-random techniques for triggering bugs.
+
 
 .. _nose: https://nose.readthedocs.io/en/latest/
 .. _pytest: https://pytest.readthedocs.io
 .. _parameterization: https://docs.pytest.org/en/latest/parametrize.html
+.. _Hypothesis: https://hypothesis.readthedocs.io/en/latest/
diff --git a/numpy/conftest.py b/numpy/conftest.py
index a843f725fc8b..1d3e0349fedb 100644
--- a/numpy/conftest.py
+++ b/numpy/conftest.py
@@ -3,6 +3,7 @@
 """
 import os
 
+import hypothesis
 import pytest
 import numpy
 
@@ -12,6 +13,12 @@
 _old_fpu_mode = None
 _collect_results = {}
 
+# See https://hypothesis.readthedocs.io/en/latest/settings.html
+hypothesis.settings.register_profile(
+    name="numpy-profile", deadline=None, print_blob=True,
+)
+hypothesis.settings.load_profile("numpy-profile")
+
 
 def pytest_configure(config):
     config.addinivalue_line("markers",
diff --git a/numpy/core/tests/test_arrayprint.py b/numpy/core/tests/test_arrayprint.py
index cd3e501a5ca0..008ca20e6f6d 100644
--- a/numpy/core/tests/test_arrayprint.py
+++ b/numpy/core/tests/test_arrayprint.py
@@ -1,6 +1,8 @@
 # -*- coding: utf-8 -*-
 import sys
 import gc
+from hypothesis import given
+from hypothesis.extra import numpy as hynp
 import pytest
 
 import numpy as np
@@ -393,6 +395,18 @@ def test_wide_element(self):
             "[ 'xxxxx']"
         )
 
+    @given(hynp.from_dtype(np.dtype("U")))
+    def test_any_text(self, text):
+        # This test checks that, given any value that can be represented in an
+        # array of dtype("U") (i.e. unicode string), ...
+        a = np.array([text, text, text])
+        # casting a list of them to an array does not e.g. truncate the value
+        assert_equal(a[0], text)
+        # and that np.array2string puts a newline in the expected location
+        expected_repr = "[{0!r} {0!r}\n {0!r}]".format(text)
+        result = np.array2string(a, max_line_width=len(repr(text)) * 2 + 3)
+        assert_equal(result, expected_repr)
+
     @pytest.mark.skipif(not HAS_REFCOUNT, reason="Python lacks refcounts")
     def test_refcount(self):
         # make sure we do not hold references to the array due to a recursive
diff --git a/numpy/core/tests/test_numeric.py b/numpy/core/tests/test_numeric.py
index 3bc4cd187100..135acc51dfb3 100644
--- a/numpy/core/tests/test_numeric.py
+++ b/numpy/core/tests/test_numeric.py
@@ -14,6 +14,9 @@
     assert_warns, HAS_REFCOUNT
     )
 
+from hypothesis import assume, given, strategies as st
+from hypothesis.extra import numpy as hynp
+
 
 class TestResize:
     def test_copies(self):
@@ -2018,6 +2021,68 @@ def test_NaT_propagation(self, arr, amin, amax):
         actual = np.clip(arr, amin, amax)
         assert_equal(actual, expected)
 
+    @given(data=st.data(), shape=hynp.array_shapes())
+    def test_clip_property(self, data, shape):
+        """A property-based test using Hypothesis.
+
+        This aims for maximum generality: it could in principle generate *any*
+        valid inputs to np.clip, and in practice generates much more varied
+        inputs than human testers come up with.
+
+        Because many of the inputs have tricky dependencies - compatible dtypes
+        and mutually-broadcastable shapes - we use `st.data()` strategy draw
+        values *inside* the test function, from strategies we construct based
+        on previous values.  An alternative would be to define a custom strategy
+        with `@st.composite`, but until we have duplicated code inline is fine.
+
+        That accounts for most of the function; the actual test is just three
+        lines to calculate and compare actual vs expected results!
+        """
+        # Our base array and bounds should not need to be of the same type as
+        # long as they are all compatible - so we allow any int or float type.
+        dtype_strategy = hynp.integer_dtypes() | hynp.floating_dtypes()
+
+        # The following line is a total hack to disable the varied-dtypes
+        # component of this test, because result != expected if dtypes can vary.
+        dtype_strategy = st.just(data.draw(dtype_strategy))
+
+        # Generate an arbitrary array of the chosen shape and dtype
+        # This is the value that we clip.
+        arr = data.draw(hynp.arrays(dtype=dtype_strategy, shape=shape))
+
+        # Generate shapes for the bounds which can be broadcast with each other
+        # and with the base shape.  Below, we might decide to use scalar bounds,
+        # but it's clearer to generate these shapes unconditionally in advance.
+        in_shapes, result_shape = data.draw(
+            hynp.mutually_broadcastable_shapes(
+                num_shapes=2,
+                base_shape=shape,
+                # Commenting out the min_dims line allows zero-dimensional arrays,
+                # and zero-dimensional arrays containing NaN make the test fail.
+                min_dims=1  
+                            
+            )
+        )
+        amin = data.draw(
+            dtype_strategy.flatmap(hynp.from_dtype)
+            | hynp.arrays(dtype=dtype_strategy, shape=in_shapes[0])
+        )
+        amax = data.draw(
+            dtype_strategy.flatmap(hynp.from_dtype)
+            | hynp.arrays(dtype=dtype_strategy, shape=in_shapes[1])
+        )
+        # If we allow either bound to be a scalar `nan`, the test will fail -
+        # so we just "assume" that away (if it is, this raises a special
+        # exception and Hypothesis will try again with different inputs)
+        assume(not np.isscalar(amin) or not np.isnan(amin))
+        assume(not np.isscalar(amax) or not np.isnan(amax))
+
+        # Then calculate our result and expected result and check that they're
+        # equal!  See gh-12519 for discussion deciding on this property.
+        result = np.clip(arr, amin, amax)
+        expected = np.minimum(amax, np.maximum(arr, amin))
+        assert_array_equal(result, expected)
+
 
 class TestAllclose:
     rtol = 1e-5
diff --git a/test_requirements.txt b/test_requirements.txt
index a4b0fcc30155..f4286d85d81c 100644
--- a/test_requirements.txt
+++ b/test_requirements.txt
@@ -1,4 +1,5 @@
 cython==0.29.14
+hypothesis==5.3.0
 pytest==5.3.5
 pytz==2019.3
 pytest-cov==2.8.1