Fix SSE server bug with uncaught TypeError

src/mcp/server/fastmcp/server.py

@@ -423,9 +423,9 @@ class FastMCP:
     async def run_sse_async(self) -> None:
         """Run the server using SSE transport."""
         from starlette.applications import Starlette
-        from starlette.routing import Route
+        from starlette.routing import Route, Mount
 
-        sse = SseServerTransport("/messages")
+        sse = SseServerTransport("/messages/")
 
         async def handle_sse(request):
             async with sse.connect_sse(
@@ -437,14 +437,11 @@ class FastMCP:
                     self._mcp_server.create_initialization_options(),
                 )
 
-        async def handle_messages(request):
-            await sse.handle_post_message(request.scope, request.receive, request._send)
-
         starlette_app = Starlette(
             debug=self.settings.debug,
             routes=[
                 Route("/sse", endpoint=handle_sse),
-                Route("/messages", endpoint=handle_messages, methods=["POST"]),
+                Mount("/messages/", app=sse.handle_post_message),
             ],
         )
 

src/mcp/server/sse.py

@@ -11,7 +11,7 @@ Example usage:
     # Create Starlette routes for SSE and message handling
     routes = [
         Route("/sse", endpoint=handle_sse),
-        Route("/messages", endpoint=handle_messages, methods=["POST"])
+        Mount("/messages", endpoint=handle_messages, methods=["POST"])
     ]
 
     # Define handler functions