Can I make a path variable optional?

No. In spring MVC path variables are mandatory, however, we may have two controller methods that call the same service code:

@RequestMapping(value="/module/{path}", method=RequestMethod.GET)
public @ResponseBody String mapRequest(HttpServletRequest req, @PathVariable String path) {
        return processRequest();
}

@RequestMapping(value="/module", method=RequestMethod.GET)
public @ResponseBody String mapRequest(HttpServletRequest req) {
       return processRequest();
}

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