How to start and stop/pause setInterval?

The reason you're seeing this specific problem:

JSFiddle wraps your code in a function, so start() is not defined in the global scope.

Moral of the story: don't use inline event bindings. Use addEventListener/attachEvent.

Other notes:

Please don't pass strings to setTimeout and setInterval. It's eval in disguise.

Use a function instead, and get cozy with var and white space:

var input = document.getElementById("input"),
  add;

function start() {
  add = setInterval(function() {
    input.value++;
  }, 1000);
}

start();

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<input type="number" id="input" />
<input type="button" onclick="clearInterval(add)" value="stop" />
<input type="button" onclick="start()" value="start" />

See Working Demo on jsFiddle: http://jsfiddle.net/qHL8Z/3/

$(function() {
  var timer = null,
    interval = 1000,
    value = 0;

  $("#start").click(function() {
    if (timer !== null) return;
    timer = setInterval(function() {
      $("#input").val(++value);
    }, interval);
  });

  $("#stop").click(function() {
    clearInterval(timer);
    timer = null
  });
});

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<input type="number" id="input" />
<input id="stop" type="button" value="stop" />
<input id="start" type="button" value="start" />

As you've tagged this jQuery ...

First, put IDs on your input buttons and remove the inline handlers:

<input type="number" id="input" />
<input type="button" id="stop" value="stop"/>
<input type="button" id="start" value="start"/>

Then keep all of your state and functions encapsulated in a closure:

EDIT updated for a cleaner implementation, that also addresses @Esailija's concerns about use of setInterval().

$(function() {
    var timer = null;
    var input = document.getElementById('input');

    function tick() {
        ++input.value;
        start();        // restart the timer
    };

    function start() {  // use a one-off timer
        timer = setTimeout(tick, 1000);
    };

    function stop() {
        clearTimeout(timer);
    };

    $('#start').bind("click", start); // use .on in jQuery 1.7+
    $('#stop').bind("click", stop);

    start();  // if you want it to auto-start
});

This ensures that none of your variables leak into global scope, and can't be modified from outside.

(Updated) working demo at http://jsfiddle.net/alnitak/Q6RhG/