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 d0591716924..fbba3a3b2c1 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 4aa1adff507..29e85299707 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
@@ -2087,6 +2087,30 @@ 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");
diff --git a/spring-core/src/test/java/org/springframework/util/backoff/ExponentialBackOffTests.java b/spring-core/src/test/java/org/springframework/util/backoff/ExponentialBackOffTests.java
index 39ea225f2ed..01517e0216f 100644
--- a/spring-core/src/test/java/org/springframework/util/backoff/ExponentialBackOffTests.java
+++ b/spring-core/src/test/java/org/springframework/util/backoff/ExponentialBackOffTests.java
@@ -79,7 +79,17 @@ class ExponentialBackOffTests {
 	}
 
 	@Test
-	void maxAttemptsReached() {
+	void maxIntervalReachedImmediately() {
+		ExponentialBackOff backOff = new ExponentialBackOff(1000L, 2.0);
+		backOff.setMaxInterval(50L);
+
+		BackOffExecution execution = backOff.start();
+		assertThat(execution.nextBackOff()).isEqualTo(50L);
+		assertThat(execution.nextBackOff()).isEqualTo(50L);
+	}
+
+	@Test
+	void maxElapsedTimeReached() {
 		ExponentialBackOff backOff = new ExponentialBackOff(2000L, 2.0);
 		backOff.setMaxElapsedTime(4000L);
 
@@ -90,6 +100,19 @@ class ExponentialBackOffTests {
 		assertThat(execution.nextBackOff()).isEqualTo(BackOffExecution.STOP);
 	}
 
+	@Test
+	void maxAttempts() {
+		ExponentialBackOff backOff = new ExponentialBackOff();
+		backOff.setInitialInterval(1000L);
+		backOff.setMultiplier(2.0);
+		backOff.setMaxInterval(10000L);
+		backOff.setMaxAttempts(6);
+		List<Long> delays = new ArrayList<>();
+		BackOffExecution execution = backOff.start();
+		IntStream.range(0, 7).forEach(i -> delays.add(execution.nextBackOff()));
+		assertThat(delays).containsExactly(1000L, 2000L, 4000L, 8000L, 10000L, 10000L, BackOffExecution.STOP);
+	}
+
 	@Test
 	void startReturnsDifferentInstances() {
 		ExponentialBackOff backOff = new ExponentialBackOff();
@@ -143,16 +166,6 @@ class ExponentialBackOffTests {
 		assertThat(execution.nextBackOff()).isBetween(4275L, 4724L);
 	}
 
-	@Test
-	void maxIntervalReachedImmediately() {
-		ExponentialBackOff backOff = new ExponentialBackOff(1000L, 2.0);
-		backOff.setMaxInterval(50L);
-
-		BackOffExecution execution = backOff.start();
-		assertThat(execution.nextBackOff()).isEqualTo(50L);
-		assertThat(execution.nextBackOff()).isEqualTo(50L);
-	}
-
 	@Test
 	void toStringContent() {
 		ExponentialBackOff backOff = new ExponentialBackOff(2000L, 2.0);
@@ -174,17 +187,4 @@ class ExponentialBackOffTests {
 		assertThat(execution).asString().isEqualTo("ExponentialBackOffExecution[currentInterval=4000ms, multiplier=2.0, attempts=2]");
 	}
 
-	@Test
-	void maxAttempts() {
-		ExponentialBackOff backOff = new ExponentialBackOff();
-		backOff.setInitialInterval(1000L);
-		backOff.setMultiplier(2.0);
-		backOff.setMaxInterval(10000L);
-		backOff.setMaxAttempts(6);
-		List<Long> delays = new ArrayList<>();
-		BackOffExecution execution = backOff.start();
-		IntStream.range(0, 7).forEach(i -> delays.add(execution.nextBackOff()));
-		assertThat(delays).containsExactly(1000L, 2000L, 4000L, 8000L, 10000L, 10000L, BackOffExecution.STOP);
-	}
-
 }