Graduate School Topic
Let me encourage you to think more broadly and longer term. Contributing to math and science, even in the purest of pure fields, is a contribution to humanity. The effects may not be seen for a long time, but they will come.
If you think too narrowly then you may choose a problem that is intractable and you won't find a solution (though something may come of it later, after you've left the scene).
The obvious answer to your direct question would be to study applied math and/or something in, say, zero emissions power generation. Nuclear Fusion power would be a benefit, of course, at the moment.
But longer term, think of the contributions of Newton and Leibniz to the creation of the Calculus. It was pretty useless at the time, but enables much of engineering today. I worked in a field like that. It was so esoteric that I predicted at the time that no one would ever find a practical use for it. Well, guess what? About ten years later someone told me that my thesis work had been applied.
My advice is to choose something interesting and do a good job of extending knowledge in that area. If it is applied in some way, fine. If not, then eventually it will be. And pick something for which you will get good faculty support as you get started.
Another example is the Standard Model in physics. Hardly anything is more pure or theoretical than that. There are a few known holes in it, which if plugged will give a better idea of how &quot;Life, the Universe, and Everything&quot; actually works. Over time, that should lead to tremendous advances in, well, life, the universe, and everything.
To continue my advice, in working on what you love, provided you have the opportunity, as not many do, and you find some opportunity to do something practical and short term with what you and your colleagues know, then take it on as a project, or encourage others to do so.