###parsing integers
The function `convert()` calls `parseInt()` with no second parameter (i.e. [***radix***][1]). The MDN documentation states one should "_**Always specify this parameter** to eliminate reader confusion and to guarantee predictable behavior_"<sup>[1][1]</sup>. So that call should have `10` added as the second parameter. And that function doesn't get re-assigned, so `const` can be used instead of `var`.

	const convert = function(a){
	    return parseInt(a.val(), 10);
	}

###Caching DOM references
I agree with [kingdao's answer](https://codereview.stackexchange.com/a/188707/120114): DOM references should be cached, though they should be cached once per page load instead of each time the function runs. So in the example code, `$newAge` and `$retireYear` should be declared outside the `result` function, and inside the [DOM-ready callback](http://api.jquery.com/jQuery/#jQuery3) (i.e. [`$(function(){ ...})`](http://api.jquery.com/jQuery/#jQuery3)). 

Also, the names might be a little misleading. For example, the jQuery function (i.e. [`$(selector)`](http://api.jquery.com/jQuery/#jQuery1)) returns a jQuery object referencing DOM elements. Thus an appropriate name might be `newAgeElements` instead of `$newAge` (though you can use the `$` if you want). Also, cache the currentYear elements in a constant too.

	$(function() {	//DOM ready callback
		const newAgeElements = $(".newAge");
		const retireYearElements = $(".retireYear");
		const currentYearElements = $(".currentYear");
		//other variables/constants declaration: like currentYear, convert()
		
		const result = (a, b) => {

		  currentYearElements.text(currentYear)
		  if (b > a) {
			newAgeElements.text(b - a)
			retireYearElements.text(currentYear + (b - a))
			message1.dialog("open")
		  } else {
			newAgeElements.text(a - b)
			retireYearElements.text(currentYear - (a - b))
			message2.dialog("open")
		  }
		}
	});

For more information about why caching DOM elements is important, read [this article](https://ilikekillnerds.com/2015/02/stop-writing-slow-javascript/). I know it is a few years old and bashes jQuery but it is still relevant and useful.
	
 [1]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/parseInt#Parameters