diff --git a/src/de.rs b/src/de.rs
index 6c18ae3..6411293 100644
--- a/src/de.rs
+++ b/src/de.rs
@@ -191,6 +191,9 @@ enum ErrorKind {
         available: &'static [&'static str],
     },
 
+    /// Unquoted string was found when quoted one was expected
+    UnquotedString,
+
     #[doc(hidden)]
     __Nonexhaustive,
 }
@@ -1428,7 +1431,7 @@ impl<'a> Deserializer<'a> {
                 start,
                 end,
             },
-            Some((span, Token::Keylike(key))) => self.number_or_date(span, key)?,
+            Some((span, Token::Keylike(key))) => self.parse_keylike(at, span, key)?,
             Some((span, Token::Plus)) => self.number_leading_plus(span)?,
             Some((Span { start, .. }, Token::LeftBrace)) => {
                 self.inline_table().map(|(Span { end, .. }, table)| Value {
@@ -1451,13 +1454,25 @@ impl<'a> Deserializer<'a> {
                         expected: "a value",
                         found: token.1.describe(),
                     },
-                ))
+                ));
             }
             None => return Err(self.eof()),
         };
         Ok(value)
     }
 
+    fn parse_keylike(&mut self, at: usize, span: Span, key: &'a str) -> Result<Value<'a>, Error> {
+        if key == "inf" || key == "nan" {
+            return self.number_or_date(span, key);
+        }
+
+        let first_char = key.chars().next().expect("key should not be empty here");
+        match first_char {
+            '-' | '0'..='9' => self.number_or_date(span, key),
+            _ => Err(self.error(at, ErrorKind::UnquotedString)),
+        }
+    }
+
     fn number_or_date(&mut self, span: Span, s: &'a str) -> Result<Value<'a>, Error> {
         if s.contains('T')
             || s.contains('t')
@@ -2076,7 +2091,7 @@ impl std::convert::From<Error> for std::io::Error {
 
 impl fmt::Display for Error {
     fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
-        match self.inner.kind {
+        match &self.inner.kind {
             ErrorKind::UnexpectedEof => "unexpected eof encountered".fmt(f)?,
             ErrorKind::InvalidCharInString(c) => write!(
                 f,
@@ -2131,6 +2146,10 @@ impl fmt::Display for Error {
                 "unexpected keys in table: `{:?}`, available keys: `{:?}`",
                 keys, available
             )?,
+            ErrorKind::UnquotedString => write!(
+                f,
+                "invalid TOML value, did you mean to use a quoted string?"
+            )?,
             ErrorKind::__Nonexhaustive => panic!(),
         }
 
diff --git a/test-suite/tests/datetime.rs b/test-suite/tests/datetime.rs
index 74b5939..6c08748 100644
--- a/test-suite/tests/datetime.rs
+++ b/test-suite/tests/datetime.rs
@@ -68,15 +68,15 @@ fn bad_times() {
     );
     bad!(
         "foo = T",
-        "failed to parse datetime for key `foo` at line 1 column 7"
+        "invalid TOML value, did you mean to use a quoted string? at line 1 column 7"
     );
     bad!(
         "foo = T.",
-        "expected newline, found a period at line 1 column 8"
+        "invalid TOML value, did you mean to use a quoted string? at line 1 column 7"
     );
     bad!(
         "foo = TZ",
-        "failed to parse datetime for key `foo` at line 1 column 7"
+        "invalid TOML value, did you mean to use a quoted string? at line 1 column 7"
     );
     bad!(
         "foo = 1997-09-09T09:09:09.09+",
diff --git a/test-suite/tests/invalid.rs b/test-suite/tests/invalid.rs
index ccc9338..f04d860 100644
--- a/test-suite/tests/invalid.rs
+++ b/test-suite/tests/invalid.rs
@@ -197,7 +197,7 @@ test!(
 test!(
     text_after_array_entries,
     include_str!("invalid/text-after-array-entries.toml"),
-    "invalid number at line 2 column 46"
+    "invalid TOML value, did you mean to use a quoted string? at line 2 column 46"
 );
 test!(
     text_after_integer,
@@ -222,5 +222,5 @@ test!(
 test!(
     text_in_array,
     include_str!("invalid/text-in-array.toml"),
-    "invalid number at line 3 column 3"
+    "invalid TOML value, did you mean to use a quoted string? at line 3 column 3"
 );
diff --git a/test-suite/tests/parser.rs b/test-suite/tests/parser.rs
index eab9f5a..169df79 100644
--- a/test-suite/tests/parser.rs
+++ b/test-suite/tests/parser.rs
@@ -491,7 +491,10 @@ fn number_underscores() {
 fn bad_underscores() {
     bad!("foo = 0_", "invalid number at line 1 column 7");
     bad!("foo = 0__0", "invalid number at line 1 column 7");
-    bad!("foo = __0", "invalid number at line 1 column 7");
+    bad!(
+        "foo = __0",
+        "invalid TOML value, did you mean to use a quoted string? at line 1 column 7"
+    );
     bad!("foo = 1_0_", "invalid number at line 1 column 7");
 }
 
@@ -537,14 +540,20 @@ fn booleans() {
 
     bad!(
         "foo = true2",
-        "failed to parse datetime for key `foo` at line 1 column 7"
+        "invalid TOML value, did you mean to use a quoted string? at line 1 column 7"
+    );
+    bad!(
+        "foo = false2",
+        "invalid TOML value, did you mean to use a quoted string? at line 1 column 7"
     );
-    bad!("foo = false2", "invalid number at line 1 column 7");
     bad!(
         "foo = t1",
-        "failed to parse datetime for key `foo` at line 1 column 7"
+        "invalid TOML value, did you mean to use a quoted string? at line 1 column 7"
+    );
+    bad!(
+        "foo = f2",
+        "invalid TOML value, did you mean to use a quoted string? at line 1 column 7"
     );
-    bad!("foo = f2", "invalid number at line 1 column 7");
 }
 
 #[test]