jQuery and Php form doesn't send email

Question

I have a problem with a form. Submition seems to work (the fading animation works) but I don't receive emails. Is there any error in the following code?

<div id="section-4"> 
        <div class="twelve columns">
        <h3>Would you like to cooperate?
        Get in touch</h3>
        <p></p>
<div id="success">
    <span class="green textcenter">
        <p>Your message was sent successfully! I will be in touch as soon as I can.</br><a href="http://www.ewelinawoloszyn.com">Refresh the page here.</a></p>
    </span>
</div>

<div id="error">
    <span>
        <p>Something went wrong, try refreshing and submitting the form again.</p>
    </span>
</div>

                <form id="contact" name="contact" method="post" novalidate="novalidate">
    <fieldset>

        <label for="email" id="email">Email<span class="required">*</span>
        </label>
        <input type="text" name="email" id="email" size="30" value="" required="">
        <label for="Message" id="message">Message<span class="required">*</span>
        </label>
        <textarea name="message" id="message" required=""></textarea>
        <label for="Answer" id="answer">Name the small house pet that says “<i>meow</i>“<span class="required">*</span>
        </label>
        <input type="text" name="answer" value="" required=""></br>
        <input id="submit" type="submit" name="submit" value="Send">
    </fieldset>
</form></div>
</div>

        <hr/>
<footer>
All rights reserved.
</footer></div><script src="http://cdnjs.cloudflare.com/ajax/libs/jquery.form/3.32/jquery.form.js"></script>
<script src="http://cdnjs.cloudflare.com/ajax/libs/jquery-validate/1.11.1/jquery.validate.min.js"></script>
<script type="text/javascript">
jQuery.validator.addMethod('answercheck', function (value, element) {
        return this.optional(element) || /^\bcat\b$/.test(value) || /^\bkitten\b$/.test(value) || /^\bkot\b$/.test(value) || /^\bkotek\b$/.test(value);
    }, "Type the correct answer ;)");

// validate contact form
$(function() {
    $('#contact').validate({
        rules: {

            email: {
                required: true,
                email: true
            },
            message: {
                required: true
            },
            answer: {
                required: true,
                answercheck: true
            }
        },
        messages: {

            email: {
                required: "No email, no message"
            },
            message: {
                required: "Please write something to send this form.",
                minlength: "This message is too short."
            },
            answer: {
                required: "Sorry, wrong answer!"
            }
        },
        submitHandler: function(form) {
            $(form).ajaxSubmit({
                type:"POST",
                data: $(form).serialize(),
                url:"process.php",
                success: function() {
                    $('#contact :input').attr('disabled', 'disabled');
                    $('#contact').fadeTo( "slow", 0.15, function() {
                        $(this).find(':input').attr('disabled', 'disabled');
                        $(this).find('label').css('cursor','default');
                        $('#success').fadeIn();
                    });
                },
                error: function() {
                    $('#contact').fadeTo( "slow", 0.15, function() {
                        $('#error').fadeIn();
                    });
                }
            });
        }
    });
});
</script>

Here's Php code:

<?php

    $to = "youremail@gmail.com";
    $from = $_REQUEST['email'];
    $headers = "From: $from";
    $subject = "You have a message.";

    $fields = array();

    $fields{"email"} = "email";
    $fields{"message"} = "message";

    $body = "Here is what was sent:\n\n"; foreach($fields as $a => $b){   $body .= sprintf("%20s: %s\n",$b,$_REQUEST[$a]); }

    $send = mail($to, $subject, $body, $headers);

?>

Any suggestions are more than welcome. I'm using Html, jQuery, and Php (Php just for the form).I have the problem since I've changed host. I've tried a few solutions from similar submitions without luck. Perhaps I need to update jQuery?

Regards, Neko