diff --git a/sphinx/builders/html/__init__.py b/sphinx/builders/html/__init__.py
index a78d54a16..87b9c5c45 100644
--- a/sphinx/builders/html/__init__.py
+++ b/sphinx/builders/html/__init__.py
@@ -1166,7 +1166,11 @@ def setup_js_tag_helper(app: Sphinx, pagename: str, templatename: str,
         else:
             # str value (old styled)
             attrs.append('src="%s"' % pathto(js, resource=True))
-        return '<script %s>%s</script>' % (' '.join(attrs), body)
+
+        if attrs:
+            return '<script %s>%s</script>' % (' '.join(attrs), body)
+        else:
+            return '<script>%s</script>' % body
 
     context['js_tag'] = js_tag
 
diff --git a/tests/test_ext_math.py b/tests/test_ext_math.py
index bd124c8c6..ebe2c0f38 100644
--- a/tests/test_ext_math.py
+++ b/tests/test_ext_math.py
@@ -215,11 +215,23 @@ def test_math_compat(app, status, warning):
 
 @pytest.mark.sphinx('html', testroot='ext-math',
                     confoverrides={'extensions': ['sphinx.ext.mathjax'],
-                                   'mathjax_config': {'extensions': ['tex2jax.js']}})
-def test_mathjax_config(app, status, warning):
+                                   'mathjax3_config': {'extensions': ['tex2jax.js']}})
+def test_mathjax3_config(app, status, warning):
     app.builder.build_all()
 
     content = (app.outdir / 'index.html').read_text()
+    assert MATHJAX_URL in content
+    assert ('<script>window.MathJax = {"extensions": ["tex2jax.js"]}</script>' in content)
+
+
+@pytest.mark.sphinx('html', testroot='ext-math',
+                    confoverrides={'extensions': ['sphinx.ext.mathjax'],
+                                   'mathjax2_config': {'extensions': ['tex2jax.js']}})
+def test_mathjax2_config(app, status, warning):
+    app.builder.build_all()
+
+    content = (app.outdir / 'index.html').read_text()
+    assert MATHJAX_URL in content
     assert ('<script type="text/x-mathjax-config">'
             'MathJax.Hub.Config({"extensions": ["tex2jax.js"]})'
             '</script>' in content)