diff --git a/CHANGELOG.md b/CHANGELOG.md
index 54ebd13..18456f0 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -76,9 +76,12 @@ and this project adheres to [Semantic Versioning](http://semver.org/spec/v2.0.0.
 
 ### Fixed
 
-* Hexadecimal is never an empty string; fixed in [#593](https://github.com/ramsey/uuid/pull/593).
+* Allow brick/math version `^0.13`; fixed in [#589](https://github.com/ramsey/uuid/pull/589).
 * Update call to `str_getcsv()` to avoid deprecation notice in PHP 8.4; fixed in [#590](https://github.com/ramsey/uuid/pull/590).
+* Hexadecimal is never an empty string; fixed in [#593](https://github.com/ramsey/uuid/pull/593).
 * Update docblocks for `Uuid::fromBytes()`, `Uuid::fromString()`, `Uuid::fromDateTime()`, `Uuid::fromHexadecimal()`, and `Uuid::fromInteger()` to note that each can throw `InvalidArgumentException`, addressing PHPStan errors occurring at call sites; fixed in [#552](https://github.com/ramsey/uuid/pull/552).
+* `getVariant()` for `MaxUuid` now correctly returns `Uuid::RESERVED_FUTURE`, as specified in [RFC 9562, section 5.10](https://www.rfc-editor.org/rfc/rfc9562#section-5.10).
+* `getVariant()` for `NilUuid` now correctly returns `Uuid::RESERVED_NCS`, as specified in [RFC 9562, section 5.9](https://www.rfc-editor.org/rfc/rfc9562#section-5.9).
 
 ### Deprecated
 
diff --git a/composer.json b/composer.json
index bff4edb..21ea6d9 100644
--- a/composer.json
+++ b/composer.json
@@ -11,7 +11,7 @@
     "require": {
         "php": "^8.2",
         "ext-json": "*",
-        "brick/math": "^0.11 || ^0.12"
+        "brick/math": "^0.11 || ^0.12 || ^0.13"
     },
     "require-dev": {
         "captainhook/captainhook": "^5.25",
diff --git a/composer.lock b/composer.lock
index 43fa360..3b37a5e 100644
--- a/composer.lock
+++ b/composer.lock
@@ -4,29 +4,29 @@
         "Read more about it at https://getcomposer.org/doc/01-basic-usage.md#installing-dependencies",
         "This file is @generated automatically"
     ],
-    "content-hash": "1dd714ad3bd396f8cb8d4e0b5227acd7",
+    "content-hash": "d8c670f63b96a7f61d29da1702892f34",
     "packages": [
         {
             "name": "brick/math",
-            "version": "0.12.3",
+            "version": "0.11.0",
             "source": {
                 "type": "git",
                 "url": "https://github.com/brick/math.git",
-                "reference": "866551da34e9a618e64a819ee1e01c20d8a588ba"
+                "reference": "0ad82ce168c82ba30d1c01ec86116ab52f589478"
             },
             "dist": {
                 "type": "zip",
-                "url": "https://api.github.com/repos/brick/math/zipball/866551da34e9a618e64a819ee1e01c20d8a588ba",
-                "reference": "866551da34e9a618e64a819ee1e01c20d8a588ba",
+                "url": "https://api.github.com/repos/brick/math/zipball/0ad82ce168c82ba30d1c01ec86116ab52f589478",
+                "reference": "0ad82ce168c82ba30d1c01ec86116ab52f589478",
                 "shasum": ""
             },
             "require": {
-                "php": "^8.1"
+                "php": "^8.0"
             },
             "require-dev": {
                 "php-coveralls/php-coveralls": "^2.2",
-                "phpunit/phpunit": "^10.1",
-                "vimeo/psalm": "6.8.8"
+                "phpunit/phpunit": "^9.0",
+                "vimeo/psalm": "5.0.0"
             },
             "type": "library",
             "autoload": {
@@ -46,17 +46,12 @@
                 "arithmetic",
                 "bigdecimal",
                 "bignum",
-                "bignumber",
                 "brick",
-                "decimal",
-                "integer",
-                "math",
-                "mathematics",
-                "rational"
+                "math"
             ],
             "support": {
                 "issues": "https://github.com/brick/math/issues",
-                "source": "https://github.com/brick/math/tree/0.12.3"
+                "source": "https://github.com/brick/math/tree/0.11.0"
             },
             "funding": [
                 {
@@ -64,7 +59,7 @@
                     "type": "github"
                 }
             ],
-            "time": "2025-02-28T13:11:00+00:00"
+            "time": "2023-01-15T23:15:59+00:00"
         }
     ],
     "packages-dev": [
diff --git a/src/Rfc4122/VariantTrait.php b/src/Rfc4122/VariantTrait.php
index 65862ef..50f1324 100644
--- a/src/Rfc4122/VariantTrait.php
+++ b/src/Rfc4122/VariantTrait.php
@@ -49,8 +49,18 @@ trait VariantTrait
             throw new InvalidBytesException('Invalid number of bytes');
         }
 
-        if ($this->isMax() || $this->isNil()) {
-            return Variant::Rfc4122;
+        // According to RFC 9562, sections {@link https://www.rfc-editor.org/rfc/rfc9562#section-4.1 4.1} and
+        // {@link https://www.rfc-editor.org/rfc/rfc9562#section-5.10 5.10}, the Max UUID falls within the range
+        // of the future variant.
+        if ($this->isMax()) {
+            return Variant::ReservedFuture;
+        }
+
+        // According to RFC 9562, sections {@link https://www.rfc-editor.org/rfc/rfc9562#section-4.1 4.1} and
+        // {@link https://www.rfc-editor.org/rfc/rfc9562#section-5.9 5.9}, the Nil UUID falls within the range
+        // of the Apollo NCS variant.
+        if ($this->isNil()) {
+            return Variant::ReservedNcs;
         }
 
         /** @var int[] $parts */
diff --git a/tests/ExpectedBehaviorTest.php b/tests/ExpectedBehaviorTest.php
index 8210eed..a9cf02e 100644
--- a/tests/ExpectedBehaviorTest.php
+++ b/tests/ExpectedBehaviorTest.php
@@ -303,7 +303,7 @@ class ExpectedBehaviorTest extends TestCase
     public static function provideFromStringInteger(): array
     {
         return [
-            ['00000000-0000-0000-0000-000000000000', null, 2, '0'],
+            ['00000000-0000-0000-0000-000000000000', null, 0, '0'],
             ['ff6f8cb0-c57d-11e1-8b21-0800200c9a66', 1, 2, '339532337419071774304650190139318639206'],
             ['ff6f8cb0-c57d-11e1-9b21-0800200c9a66', 1, 2, '339532337419071774305803111643925486182'],
             ['ff6f8cb0-c57d-11e1-ab21-0800200c9a66', 1, 2, '339532337419071774306956033148532333158'],
@@ -336,7 +336,7 @@ class ExpectedBehaviorTest extends TestCase
             ['ff6f8cb0-c57d-01e1-db21-0800200c9a66', null, 6, '339532337419071698752551071748029454950'],
             ['ff6f8cb0-c57d-01e1-eb21-0800200c9a66', null, 7, '339532337419071698753703993252636301926'],
             ['ff6f8cb0-c57d-01e1-fb21-0800200c9a66', null, 7, '339532337419071698754856914757243148902'],
-            ['ffffffff-ffff-ffff-ffff-ffffffffffff', null, 2, '340282366920938463463374607431768211455'],
+            ['ffffffff-ffff-ffff-ffff-ffffffffffff', null, 7, '340282366920938463463374607431768211455'],
         ];
     }
 
diff --git a/tests/Guid/FieldsTest.php b/tests/Guid/FieldsTest.php
index 793ed9a..65963ef 100644
--- a/tests/Guid/FieldsTest.php
+++ b/tests/Guid/FieldsTest.php
@@ -208,7 +208,7 @@ class FieldsTest extends TestCase
             ['00000000000000000000000000000000', 'getTimeLow', '00000000'],
             ['00000000000000000000000000000000', 'getTimeMid', '0000'],
             ['00000000000000000000000000000000', 'getTimestamp', '000000000000000'],
-            ['00000000000000000000000000000000', 'getVariant', Variant::Rfc4122],
+            ['00000000000000000000000000000000', 'getVariant', Variant::ReservedNcs],
             ['00000000000000000000000000000000', 'getVersion', null],
             ['00000000000000000000000000000000', 'isNil', true],
             ['00000000000000000000000000000000', 'isMax', false],
@@ -222,7 +222,7 @@ class FieldsTest extends TestCase
             ['ffffffffffffffffffffffffffffffff', 'getTimeLow', 'ffffffff'],
             ['ffffffffffffffffffffffffffffffff', 'getTimeMid', 'ffff'],
             ['ffffffffffffffffffffffffffffffff', 'getTimestamp', 'fffffffffffffff'],
-            ['ffffffffffffffffffffffffffffffff', 'getVariant', Variant::Rfc4122],
+            ['ffffffffffffffffffffffffffffffff', 'getVariant', Variant::ReservedFuture],
             ['ffffffffffffffffffffffffffffffff', 'getVersion', null],
             ['ffffffffffffffffffffffffffffffff', 'isNil', false],
             ['ffffffffffffffffffffffffffffffff', 'isMax', true],
diff --git a/tests/Rfc4122/FieldsTest.php b/tests/Rfc4122/FieldsTest.php
index 9504980..50f88f0 100644
--- a/tests/Rfc4122/FieldsTest.php
+++ b/tests/Rfc4122/FieldsTest.php
@@ -208,7 +208,7 @@ class FieldsTest extends TestCase
             ['00000000-0000-0000-0000-000000000000', 'getTimeLow', '00000000'],
             ['00000000-0000-0000-0000-000000000000', 'getTimeMid', '0000'],
             ['00000000-0000-0000-0000-000000000000', 'getTimestamp', '000000000000000'],
-            ['00000000-0000-0000-0000-000000000000', 'getVariant', Variant::Rfc4122],
+            ['00000000-0000-0000-0000-000000000000', 'getVariant', Variant::ReservedNcs],
             ['00000000-0000-0000-0000-000000000000', 'getVersion', null],
             ['00000000-0000-0000-0000-000000000000', 'isNil', true],
             ['00000000-0000-0000-0000-000000000000', 'isMax', false],
@@ -221,7 +221,7 @@ class FieldsTest extends TestCase
             ['ffffffff-ffff-ffff-ffff-ffffffffffff', 'getTimeLow', 'ffffffff'],
             ['ffffffff-ffff-ffff-ffff-ffffffffffff', 'getTimeMid', 'ffff'],
             ['ffffffff-ffff-ffff-ffff-ffffffffffff', 'getTimestamp', 'fffffffffffffff'],
-            ['ffffffff-ffff-ffff-ffff-ffffffffffff', 'getVariant', Variant::Rfc4122],
+            ['ffffffff-ffff-ffff-ffff-ffffffffffff', 'getVariant', Variant::ReservedFuture],
             ['ffffffff-ffff-ffff-ffff-ffffffffffff', 'getVersion', null],
             ['ffffffff-ffff-ffff-ffff-ffffffffffff', 'isNil', false],
             ['ffffffff-ffff-ffff-ffff-ffffffffffff', 'isMax', true],
diff --git a/tests/UuidTest.php b/tests/UuidTest.php
index 1175a83..7b96532 100644
--- a/tests/UuidTest.php
+++ b/tests/UuidTest.php
@@ -1306,13 +1306,7 @@ class UuidTest extends TestCase
                 'urn' => 'urn:uuid:00000000-0000-0000-0000-000000000000',
                 'time' => '000000000000000',
                 'clockSeq' => '0000',
-                // This is a departure from the Python tests. The Python tests
-                // are technically "correct" because all bits are set to zero,
-                // so it stands to reason that the variant is also zero, but
-                // that leads to this being considered a "Reserved NCS" variant,
-                // and that is not the case. RFC 4122 defines this special UUID,
-                // so it is an RFC 4122 variant.
-                'variant' => Variant::Rfc4122,
+                'variant' => Variant::ReservedNcs,
                 'version' => null,
             ],
             [
@@ -1571,20 +1565,13 @@ class UuidTest extends TestCase
                 ],
                 'urn' => 'urn:uuid:ffffffff-ffff-ffff-ffff-ffffffffffff',
                 'time' => 'fffffffffffffff',
-                // This is a departure from the Python tests. The Python tests
-                // are technically "correct" because all bits are set to one,
-                // which ends up calculating the variant as 7, or "Reserved
-                // Future," but that is not the case, and now that max UUIDs
-                // are defined as a special type, within the RFC 4122 variant
-                // rules, we also consider it an RFC 4122 variant.
-                //
-                // Similarly, Python's tests think the clock sequence should be
+                // Python's tests think the clock sequence should be
                 // 0x3fff because of the bit shifting performed on this field.
                 // However, since all the bits in this UUID are defined as being
                 // set to one, we will consider the clock sequence as 0xffff,
                 // which all bits set to one.
                 'clockSeq' => 'ffff',
-                'variant' => Variant::Rfc4122,
+                'variant' => Variant::ReservedFuture,
                 'version' => null,
             ],
         ];