diff --git a/package-lock.json b/package-lock.json
index 184851c..12e660a 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -9,15 +9,15 @@
       "version": "0.1.0",
       "dependencies": {
         "clsx": "^2.1.1",
-        "flexsearch": "^0.7.43",
+        "flexsearch": "^0.8.212",
         "github-slugger": "^2.0.0",
         "gray-matter": "^4.0.3",
-        "katex": "^0.16.11",
+        "katex": "^0.17.0",
         "mermaid": "^11.15.0",
         "next": "^15.1.0",
         "next-mdx-remote": "^5.0.0",
-        "react": "^19.0.0",
-        "react-dom": "^19.0.0",
+        "react": "^19.2.7",
+        "react-dom": "^19.2.7",
         "rehype-autolink-headings": "^7.1.0",
         "rehype-katex": "^7.0.1",
         "rehype-pretty-code": "^0.14.0",
@@ -29,7 +29,7 @@
       },
       "devDependencies": {
         "@types/node": "^22.7.5",
-        "@types/react": "^19.0.0",
+        "@types/react": "^19.2.17",
         "@types/react-dom": "^19.0.0",
         "autoprefixer": "^10.4.20",
         "eslint": "^9.17.0",
@@ -2142,9 +2142,9 @@
       }
     },
     "node_modules/@types/react": {
-      "version": "19.2.15",
-      "resolved": "https://registry.npmjs.org/@types/react/-/react-19.2.15.tgz",
-      "integrity": "sha512-eRwcGNHve+E8qtEQSSRl6urh+rFop4v8gm6O8rGv25CodbvFdLjA1vVQ1KkiFE0w0UPOnb8tDiFKL5lp0rtY5Q==",
+      "version": "19.2.17",
+      "resolved": "https://registry.npmjs.org/@types/react/-/react-19.2.17.tgz",
+      "integrity": "sha512-MXfmqaVPEVgkBT/aY0aGCkRWWtByiYQXo3xdQ8r5RzuFrPiRn8Gar2tQdXSUQ2GKV3bkXckek89V8wQBY2Q/Aw==",
       "license": "MIT",
       "dependencies": {
         "csstype": "^3.2.2"
@@ -5355,9 +5355,31 @@
       "license": "ISC"
     },
     "node_modules/flexsearch": {
-      "version": "0.7.43",
-      "resolved": "https://registry.npmjs.org/flexsearch/-/flexsearch-0.7.43.tgz",
-      "integrity": "sha512-c5o/+Um8aqCSOXGcZoqZOm+NqtVwNsvVpWv6lfmSclU954O3wvQKxxK8zj74fPaSJbXpSLTs4PRhh+wnoCXnKg==",
+      "version": "0.8.212",
+      "resolved": "https://registry.npmjs.org/flexsearch/-/flexsearch-0.8.212.tgz",
+      "integrity": "sha512-wSyJr1GUWoOOIISRu+X2IXiOcVfg9qqBRyCPRUdLMIGJqPzMo+jMRlvE83t14v1j0dRMEaBbER/adQjp6Du2pw==",
+      "funding": [
+        {
+          "type": "github",
+          "url": "https://github.com/ts-thomas"
+        },
+        {
+          "type": "paypal",
+          "url": "https://www.paypal.com/donate/?hosted_button_id=GEVR88FC9BWRW"
+        },
+        {
+          "type": "opencollective",
+          "url": "https://opencollective.com/flexsearch"
+        },
+        {
+          "type": "patreon",
+          "url": "https://patreon.com/user?u=96245532"
+        },
+        {
+          "type": "liberapay",
+          "url": "https://liberapay.com/ts-thomas"
+        }
+      ],
       "license": "Apache-2.0"
     },
     "node_modules/for-each": {
@@ -6639,9 +6661,9 @@
       }
     },
     "node_modules/katex": {
-      "version": "0.16.47",
-      "resolved": "https://registry.npmjs.org/katex/-/katex-0.16.47.tgz",
-      "integrity": "sha512-Eeo8Ys1doU1z+x8AZsPpQu+p/QcZBI5PeOo7QGQdy2x2m0MU/hYagBbGOmXwr5KVbEfVuWv9LpnQWeehogurjg==",
+      "version": "0.17.0",
+      "resolved": "https://registry.npmjs.org/katex/-/katex-0.17.0.tgz",
+      "integrity": "sha512-Vdw0ATsQ9V+LuegM/BTwQqV/6cTl5lbGcIrU+BCgLxyf6bo38ybOr372tuSIxir3CN720flu1meYR6XzNMwQnw==",
       "funding": [
         "https://opencollective.com/katex",
         "https://github.com/sponsors/katex"
@@ -7179,6 +7201,22 @@
         "uuid": "^11.1.0 || ^12 || ^13 || ^14.0.0"
       }
     },
+    "node_modules/mermaid/node_modules/katex": {
+      "version": "0.16.47",
+      "resolved": "https://registry.npmjs.org/katex/-/katex-0.16.47.tgz",
+      "integrity": "sha512-Eeo8Ys1doU1z+x8AZsPpQu+p/QcZBI5PeOo7QGQdy2x2m0MU/hYagBbGOmXwr5KVbEfVuWv9LpnQWeehogurjg==",
+      "funding": [
+        "https://opencollective.com/katex",
+        "https://github.com/sponsors/katex"
+      ],
+      "license": "MIT",
+      "dependencies": {
+        "commander": "^8.3.0"
+      },
+      "bin": {
+        "katex": "cli.js"
+      }
+    },
     "node_modules/micromark": {
       "version": "4.0.2",
       "resolved": "https://registry.npmjs.org/micromark/-/micromark-4.0.2.tgz",
@@ -7388,6 +7426,22 @@
         "url": "https://opencollective.com/unified"
       }
     },
+    "node_modules/micromark-extension-math/node_modules/katex": {
+      "version": "0.16.47",
+      "resolved": "https://registry.npmjs.org/katex/-/katex-0.16.47.tgz",
+      "integrity": "sha512-Eeo8Ys1doU1z+x8AZsPpQu+p/QcZBI5PeOo7QGQdy2x2m0MU/hYagBbGOmXwr5KVbEfVuWv9LpnQWeehogurjg==",
+      "funding": [
+        "https://opencollective.com/katex",
+        "https://github.com/sponsors/katex"
+      ],
+      "license": "MIT",
+      "dependencies": {
+        "commander": "^8.3.0"
+      },
+      "bin": {
+        "katex": "cli.js"
+      }
+    },
     "node_modules/micromark-extension-mdx-expression": {
       "version": "3.0.1",
       "resolved": "https://registry.npmjs.org/micromark-extension-mdx-expression/-/micromark-extension-mdx-expression-3.0.1.tgz",
@@ -8760,24 +8814,24 @@
       "license": "MIT"
     },
     "node_modules/react": {
-      "version": "19.2.6",
-      "resolved": "https://registry.npmjs.org/react/-/react-19.2.6.tgz",
-      "integrity": "sha512-sfWGGfavi0xr8Pg0sVsyHMAOziVYKgPLNrS7ig+ivMNb3wbCBw3KxtflsGBAwD3gYQlE/AEZsTLgToRrSCjb0Q==",
+      "version": "19.2.7",
+      "resolved": "https://registry.npmjs.org/react/-/react-19.2.7.tgz",
+      "integrity": "sha512-HNe9WslTbXmFK8o8cmwgAeJFSBvt1bPdHCVKtaaV+WlAN36mpT4hcRpwbf3fY56ar2oIXzsBpOAiIRHAdY0OlQ==",
       "license": "MIT",
       "engines": {
         "node": ">=0.10.0"
       }
     },
     "node_modules/react-dom": {
-      "version": "19.2.6",
-      "resolved": "https://registry.npmjs.org/react-dom/-/react-dom-19.2.6.tgz",
-      "integrity": "sha512-0prMI+hvBbPjsWnxDLxlCGyM8PN6UuWjEUCYmZhO67xIV9Xasa/r/vDnq+Xyq4Lo27g8QSbO5YzARu0D1Sps3g==",
+      "version": "19.2.7",
+      "resolved": "https://registry.npmjs.org/react-dom/-/react-dom-19.2.7.tgz",
+      "integrity": "sha512-t0BRVXvbiE/o20Hfw669rLbMCDWtYZLvmJigy2f0MxsXF+71pxhR3xOkspmsO8h3ZlNzyibAmtCa3l4lYKk6gQ==",
       "license": "MIT",
       "dependencies": {
         "scheduler": "^0.27.0"
       },
       "peerDependencies": {
-        "react": "^19.2.6"
+        "react": "^19.2.7"
       }
     },
     "node_modules/react-is": {
@@ -8983,6 +9037,22 @@
         "url": "https://opencollective.com/unified"
       }
     },
+    "node_modules/rehype-katex/node_modules/katex": {
+      "version": "0.16.47",
+      "resolved": "https://registry.npmjs.org/katex/-/katex-0.16.47.tgz",
+      "integrity": "sha512-Eeo8Ys1doU1z+x8AZsPpQu+p/QcZBI5PeOo7QGQdy2x2m0MU/hYagBbGOmXwr5KVbEfVuWv9LpnQWeehogurjg==",
+      "funding": [
+        "https://opencollective.com/katex",
+        "https://github.com/sponsors/katex"
+      ],
+      "license": "MIT",
+      "dependencies": {
+        "commander": "^8.3.0"
+      },
+      "bin": {
+        "katex": "cli.js"
+      }
+    },
     "node_modules/rehype-parse": {
       "version": "9.0.1",
       "resolved": "https://registry.npmjs.org/rehype-parse/-/rehype-parse-9.0.1.tgz",
diff --git a/package.json b/package.json
index eaf4032..8aca128 100644
--- a/package.json
+++ b/package.json
@@ -17,15 +17,15 @@
   },
   "dependencies": {
     "clsx": "^2.1.1",
-    "flexsearch": "^0.7.43",
+    "flexsearch": "^0.8.212",
     "github-slugger": "^2.0.0",
     "gray-matter": "^4.0.3",
-    "katex": "^0.16.11",
+    "katex": "^0.17.0",
     "mermaid": "^11.15.0",
     "next": "^15.1.0",
     "next-mdx-remote": "^5.0.0",
-    "react": "^19.0.0",
-    "react-dom": "^19.0.0",
+    "react": "^19.2.7",
+    "react-dom": "^19.2.7",
     "rehype-autolink-headings": "^7.1.0",
     "rehype-katex": "^7.0.1",
     "rehype-pretty-code": "^0.14.0",
@@ -37,7 +37,7 @@
   },
   "devDependencies": {
     "@types/node": "^22.7.5",
-    "@types/react": "^19.0.0",
+    "@types/react": "^19.2.17",
     "@types/react-dom": "^19.0.0",
     "autoprefixer": "^10.4.20",
     "eslint": "^9.17.0",