Why is PHP form not sending email

Question

I am trying to send email using jquery and PHP but somehow I am not receiving emails even when PHP executes successfully.

This is my javascript code:

<script type='text/javascript'>
    $("#formoid").submit(function(event) {
        event.preventDefault();
        var $form = $(this),
            url = $form.attr('action');
        var posting = $.post(url, {
            name: $('#name').val(),
            email: $('#email').val(),
            message: $('#message').val()
        });
        posting.done(function(data) {
            $("#result").empty().append('Thank you for contacting. Will get back to you as sson as possible.');
        });
    });
</script>

My PHP looks like this:

<?php 
    if(isset($_POST['submit'])){
        $to = "[email protected]"; // this is your Email address
        $from = $_POST['email']; // this is the sender's Email address
        $name = $_POST['name'];
        $email = $_POST['email'];
        $subject = "Portfolio form submission";   

        $message = $name . " " . $email . " wrote the following:" . "\n\n" . $_POST['message'];    

        $headers = "From:" . $from;
        $headers2 = "From:" . $to;
        mail($to,$subject,$message,$headers);
    }
?>

When I submit the form, and inspect the dom, I see the results are good. In the XHR details, it shows:

statusText: "OK"

Am i doing something wrong here?

Edit: Adding HTML as requested:

<form class="no-bottom" id="formoid" action="contact.php" title="" method="post">
    <label for="name" class="sr-only">Name</label>
    <input type="text" class="underline" name="name" id="name" placeholder="Your name..." required>
    <label for="email" class="sr-only">Email</label>
    <input type="email" class="underline" name="email" id="email" placeholder="Your email..." required>
    <label for="message" class="sr-only">Message</label>
    <textarea class="underline" name="message" id="message" cols="30" rows="6" placeholder="Here goes the message..." required></textarea>
    <div class="margin-1"></div>
    <input type="submit" value="Send it">
</form>

Answer 1

isset($_POST['submit']) is checking if the key submit is present in the date Posted from the client.

However, the data sent from client does not include it.

var posting = $.post(url, {
    name: $('#name').val(),
    email: $('#email').val(),
    message: $('#message').val()
});

To make it work, you can either add it in POST data or check another key in the server.

var posting = $.post(url, {
    name: $('#name').val(),
    email: $('#email').val(),
    message: $('#message').val(),
    submit: 'anythingTruthyHere' // Added `submit` key
});

OR, you can check if the email is present in the POST data

if (isset($_POST['email'])) {
    // send mail code here