Firstly, you have specified a relative directory to the file "contact.php" in your jQuery code. This means you must be executing the code from a URL stating the same directory as the anticipated location of contact.php. For instance, executing your code on the following URLs would have the respective effect;
/wordpress/index.php => /wordpress/contact.php
/wordpress/contact => /wordpress/contact/contact.php
So you need to verify that your contact.php file is located within the same directory as the file generating the request.
As pointed out by Jai in a comment, you are sending data via jQuery AJAX in the POST method, but your php script is anticipating (listening for) the GET method. This will be problematic as your backend script will not interpret the data you are sending to it.
If you are sending the data as a POST request, then you should use $_POST to retrieve it, otherwise if you're sending the data as a GET request, use $_GET to retrieve it. You can use a more ambiguous method of retrieving the data by using $_REQUEST, however this is not usually the best way of doing things.
You may want to use encodeURIComponent for certain fields using non-alphanumeric characters (for instance, your message variable) this will ensure the data is transmitted correctly between your front and back end code.
Furthermore, you might want to check out the OWASP top 10 list as your script is vulnerable to CSRF attacks, and can be used as an email relay. Check it here
Lastly, it is common practice to use some form of CAPTCHA verification on data forms requiring no previous form of bot filtering / user validation. This prevents bots using your script as a relay to send out malicious or spam emails.
type :'post'in ajax and you are using$_GET[]in php.