Trying to Submit and Email a contact form using jquery-validation. Passes validation, but no mail is received
<p>I am attempting to learn how to create a form, validate the input, sanitize that data, and email it to myself. I began by creating the HTML form and integrating the <a href="https://github.com/jzaefferer/jquery-validation" rel="nofollow">jquery-validation plugin from here.</a></p>

<p>The client-side validation seems to be working great, not allowing the user to "submit" unless my rules are specified. However, I am having a hard time understanding actually <i>how to process and mail</i> this form to myself. From what I can tell, the ajax is successfully passing data to my PHP processing page, but I never receive any data in my email.</p>

<p><strong>HTML Form :</strong></p>

<pre><code>&lt;form id="contact-form" role="form" enctype="multipart/form-data" method="post" action=""&gt;
&lt;input type="text" placeholder="First Name *" name="firstName" id="firstName"&gt;
&lt;input type="text" placeholder="Last Name *" name="lastName" id="lastName"&gt;
&lt;input type="text" placeholder="Street Address *" name="address" id="address" &gt;
&lt;select name="state" id="state" &gt;
    &lt;option value="" disabled selected style="display:none;"&gt;State *&lt;/option&gt;
    &lt;option value="AL"&gt;Alabama&lt;/option&gt;
    &lt;option value="AK"&gt;Alaska&lt;/option&gt;
    &lt;option value="AZ"&gt;Arizona&lt;/option&gt;
&lt;/select&gt;
&lt;input type="text" placeholder="Zip *" name="zip" id="zip" &gt;
&lt;input type="tel" placeholder="Phone Number *" name="phone" id="phone"&gt;
&lt;input type="email" placeholder="Email Address (optional)" name="email" id="email"&gt;                         
&lt;textarea rows="3" placeholder="Additional Message (optional)" name="message" id="message"&gt;&lt;/textarea&gt;    
&lt;input type="submit" id="submit-button" value="Send Message"&gt;
&lt;/form&gt;
&lt;script src="http://ajax.aspnetcdn.com/ajax/jquery.validate/1.15.0/jquery.validate.min.js"&gt;&lt;/script&gt;
&lt;script src="http://ajax.aspnetcdn.com/ajax/jquery.validate/1.15.0/additional-methods.min.js"&gt;&lt;/script&gt;
&lt;script src="js/validation.js"&gt;&lt;/script&gt;
</code></pre>

<p><strong>Validation.js :</strong></p>

<pre><code>$(function() {

$("#contact-form").validate({
    rules: {
        firstName: {
            required: true
        },
        lastName: {
            required: true
        },
        address: {
            required: true
        },
        state: {
            stateUS: true,
            required: true
        },
        zip: {
            zipcodeUS: true,
            required: true
        },
        phone: {
            phoneUS: true,
            required: true
        },
        email: {
            email: true
        },
        method: {
            lettersonly: true,
            required: true
        }
    },
    messages: {
        email: {
            email: 'Please enter a valid email address.'
        }
    },
    submitHandler: function(form) {
        $.ajax({
            type: "POST",
            url: "/test/mail.php",
            data: $(form).serialize(),
            timeout: 3000,
            success: function() {alert('works');},
            error: function() {alert('failed');}
        });
        return false;
    }
});
});
</code></pre>

<p><strong>mail.PHP :</strong></p>

<pre><code>&lt;?php

    $firstName = $lastName = $address = $state = $zip = $phone = $email = $method = $message = "";
    $email_subject = $email_message = $headers = "";
    $email_to = "matt@gmail.com";

    $firstName = test_input($_POST["firstName"]);

    $lastName = test_input($_POST["lastName"]);

    $address = test_input($_POST["address"]);

    $state = test_input($_POST["state"]);

    $zip = test_input($_POST["zip"]);

    $phone = test_input($_POST["phone"]);                                                               

    $email = test_input($_POST["email"]);

    $message = test_input($_POST["message"]);

    $email_subject = "New Meeting Request - ".$name;        
    $email_message = "Details below:\n\n";                                                      
    $email_message .= "First Name: ".$firstName."\n\n";
    $email_message .= "Last Name: ".$lastName."\n\n";
    $email_message .= "Address: ".$address."\n\n";
    $email_message .= "State: ".$state."\n\n";
    $email_message .= "Zip Code: ".$zip."\n\n";
    $email_message .= "Phone Number: ".$phone."\n\n";
    $email_message .= "Email Address: ".$email."\n\n";
    $email_message .= "Additional Message: ".$message."\n\n";

    $headers = 'From: PHP Form'."\r\n".
    'Reply-To: N/A'."\r\n" .
    'X-Mailer: PHP/' . phpversion();
    @mail($email_to, $email_subject, $email_message, $headers);  

    return true;

    function test_input($data) {
       $data = trim($data);                 //trims whitespace on both ends
       $data = stripslashes($data);         //removes extra slashes
       $data = htmlspecialchars($data);     //converts special characters to HTML equivalents
       return $data;                        //returns cleaned data
    }

?&gt;
</code></pre>