即使检查通过，PHP电子邮件脚本也会拒绝输入

Question

I have written a PHP script for a contact form however it is not working, as when I press submit the message "Error with sending the message" pops up instead of the confirmation message (see at the end of the php code). I am at a loss here. The script and html are stored in a single file called "contact.php" The php script is as follows

<?php
    if($_POST["submit"]){
        $name = $_POST['name'];
        $email = $_POST['email'];
        $subject = $_POST['subject'];
        $message = $_POST['message'];
        $human = intval($_POST['human']);
        $to = '[e-mail]';

        $message = "From: $name
 E-Mail: $email
 Message:
 $message";
        // Check if name has been entered
        if (!$_POST['name']) {
            $errName = 'Please enter your name';
        }

        // Check if email has been entered and is valid
        if (!$_POST['email'] || !filter_var($_POST['email'], FILTER_VALIDATE_EMAIL)) {
            $errEmail = 'Please enter a valid email address';
        }

        if (!$_POST['subject']){
            $errSubject = 'Please include the subject of the message';
        }
        //Check if message has been entered
        if (!$_POST['message']) {
            $errMessage = 'Please enter your message';
        }
        //Check if simple anti-bot test is correct
        if ($human !== 5) {
            $errHuman = 'Your answer is incorrect';
        }

        if(!$errName && !$errEmail && !$errSubject && !$errMessage && !$errHuman){
            if (mail ($to, $subject, $message)) {
                $result='<div class="alert alert-success">Thank You! I will be in touch</div>';
            } else {
                $result='<div class="alert alert-danger">Error with sending the message</div>';
            }
        }
    }
?>

And my HTML for the form is:

<div class="container">
    <div class="row">
        <div class="col-md-6 col-md-offset-3">
            <h1 class="page-header text-center">Contact</h1>
            <form class="form-horizontal" role="form" method="post" action="contact.php">
                <div class="form-group">
                    <label for="name" class="col-sm-2 control-label">Name</label>
                    <div class="col-sm-10">
                        <input type="text" class="form-control" id="name" name="name" placeholder="First & Last Name" value="<?php echo htmlspecialchars($_POST['name']); ?>">
                        <?php echo "<p class='text-danger'>$errName</p>";?>
                    </div>
                </div>
                <div class="form-group">
                    <label for="email" class="col-sm-2 control-label">Email</label>
                    <div class="col-sm-10">
                        <input type="email" class="form-control" id="email" name="email" placeholder="[e-mail]" value="<?php echo htmlspecialchars($_POST['email']); ?>">
                        <?php echo "<p class='text-danger'>$errEmail</p>";?>
                    </div>
                </div>
                <div class="form-group">
                    <label for="email" class="col-sm-2 control-label">Subject</label>
                    <div class="col-sm-10">
                        <input type="text" class="form-control" id="subject" name="subject" placeholder="Subject" value="<?php echo htmlspecialchars($_POST['subject']); ?>">
                        <?php echo "<p class='text-danger'>$errSubject</p>";?>
                    </div>
                </div>
                <div class="form-group">
                    <label for="message" class="col-sm-2 control-label">Message</label>
                    <div class="col-sm-10">
                        <textarea class="form-control" rows="4" name="message"><?php echo htmlspecialchars($_POST['message']);?></textarea>
                        <?php echo "<p class='text-danger'>$errMessage</p>";?>
                    </div>
                </div>
                <div class="form-group">
                    <label for="human" class="col-sm-2 control-label">2 + 3 = ?</label>
                    <div class="col-sm-10">
                        <input type="text" class="form-control" id="human" name="human" placeholder="Your Answer">
                        <?php echo "<p class='text-danger'>$errHuman</p>";?>
                    </div>
                </div>
                <div class="form-group">
                    <div class="col-sm-10 col-sm-offset-2">
                        <input id="submit" name="submit" type="submit" value="Send" class="btn btn-primary">
                    </div>
                </div>
                <div class="form-group">
                    <div class="col-sm-10 col-sm-offset-2">
                        <?php echo $result; ?>  
                    </div>
                </div>
            </form> 
        </div>
    </div>
</div>   

To test the code I am using MAMP on windows (in case that is where the fault lays)