diff --git a/spring-core/src/main/java/org/springframework/core/annotation/SynthesizedMergedAnnotationInvocationHandler.java b/spring-core/src/main/java/org/springframework/core/annotation/SynthesizedMergedAnnotationInvocationHandler.java
index 24c21acf6af..1b60933326a 100644
--- a/spring-core/src/main/java/org/springframework/core/annotation/SynthesizedMergedAnnotationInvocationHandler.java
+++ b/spring-core/src/main/java/org/springframework/core/annotation/SynthesizedMergedAnnotationInvocationHandler.java
@@ -160,14 +160,12 @@ final class SynthesizedMergedAnnotationInvocationHandler<A extends Annotation> i
 	}
 
 	/**
-	 * This method currently does not address the following issues which we may
+	 * This method currently does not address the following issue which we may
 	 * choose to address at a later point in time.
 	 *
 	 * <ul>
 	 * <li>non-ASCII, non-visible, and non-printable characters within a character
 	 * or String literal are not escaped.</li>
-	 * <li>formatting for float and double values does not take into account whether
-	 * a value is not a number (NaN) or infinite.</li>
 	 * </ul>
 	 * @param value the attribute value to format
 	 * @return the formatted string representation
@@ -199,10 +197,30 @@ final class SynthesizedMergedAnnotationInvocationHandler<A extends Annotation> i
 			return Long.toString((Long) value) + 'L';
 		}
 		if (type == Float.class) {
-			return Float.toString((Float) value) + 'f';
+			float floatValue = (Float) value;
+			if (Float.isNaN(floatValue)) {
+				return "0.0f/0.0f";
+			}
+			if (floatValue == Float.POSITIVE_INFINITY) {
+				return "1.0f/0.0f";
+			}
+			if (floatValue == Float.NEGATIVE_INFINITY) {
+				return "-1.0f/0.0f";
+			}
+			return Float.toString(floatValue) + 'f';
 		}
 		if (type == Double.class) {
-			return Double.toString((Double) value);
+			double doubleValue = (Double) value;
+			if (Double.isNaN(doubleValue)) {
+				return "0.0/0.0";
+			}
+			if (doubleValue == Double.POSITIVE_INFINITY) {
+				return "1.0/0.0";
+			}
+			if (doubleValue == Double.NEGATIVE_INFINITY) {
+				return "-1.0/0.0";
+			}
+			return Double.toString(doubleValue);
 		}
 		if (value instanceof Enum<?> e) {
 			return e.name();
diff --git a/spring-core/src/test/java/org/springframework/core/annotation/MergedAnnotationsTests.java b/spring-core/src/test/java/org/springframework/core/annotation/MergedAnnotationsTests.java
index c5c386e71d6..61fc0ffe367 100644
--- a/spring-core/src/test/java/org/springframework/core/annotation/MergedAnnotationsTests.java
+++ b/spring-core/src/test/java/org/springframework/core/annotation/MergedAnnotationsTests.java
@@ -2060,6 +2060,30 @@ class MergedAnnotationsTests {
 				.isEqualTo("@%s({\"FromValueAttributeMeta\"})", ValueAttribute.class.getCanonicalName());
 	}
 
+	@Test  // gh-37244
+	void toStringForSynthesizedAnnotationsWithNonFiniteFloatingPointValues() {
+		Map<String, Object> attributes = Map.of(
+				"name", "test",
+				"floatValue", Float.NaN,
+				"doubleValue", Double.NaN);
+		RequestMapping mapping = MergedAnnotation.of(RequestMapping.class, attributes).synthesize();
+		assertThat(mapping).asString().contains("floatValue=0.0f/0.0f", "doubleValue=0.0/0.0");
+
+		attributes = Map.of(
+				"name", "test",
+				"floatValue", Float.POSITIVE_INFINITY,
+				"doubleValue", Double.POSITIVE_INFINITY);
+		mapping = MergedAnnotation.of(RequestMapping.class, attributes).synthesize();
+		assertThat(mapping).asString().contains("floatValue=1.0f/0.0f", "doubleValue=1.0/0.0");
+
+		attributes = Map.of(
+				"name", "test",
+				"floatValue", Float.NEGATIVE_INFINITY,
+				"doubleValue", Double.NEGATIVE_INFINITY);
+		mapping = MergedAnnotation.of(RequestMapping.class, attributes).synthesize();
+		assertThat(mapping).asString().contains("floatValue=-1.0f/0.0f", "doubleValue=-1.0/0.0");
+	}
+
 	@Test
 	void equalsForSynthesizedAnnotations() throws Exception {
 		Method methodWithPath = WebController.class.getMethod("handleMappedWithPathAttribute");