Don't believe me?
You never do.
Well, let's think this through. What problems have occurred since the development of nukes? And how have they been solved?
War: See Hiroshima and Nagasaki. World War II ended shortly afterwards. Nukes solve. All the other wars weren't significant enough to warrant a nuking. I mean, they were nowhere near big enough! Come World War III, the only weapon used will be nukes.
Energy: We have harnessed the energy of a nuke and transformed it into a nuclear reactor. Don't worry. This energy is 100% safe. The nuke won't go off unless a Transformer comes from Hoover Dam and tries to kick it across the Atlantic. Then it's Europe's problem, not ours.
(And what do we do with the giant robot? Nuke it.)
Poverty: If the humans don't exist to be impoverished, there can't be poverty. Simple.
Environment: Yes, nukes save the environment too. And not just by nuking factories which spew out chemicals and pollutants. What shape do nukes take when they explode? A mushroom (It's not called a mushroom cloud for nothing!). What do mushrooms do? Intake carbon dioxide, and release oxygen. What does a giant mushroom do? Intake lots of carbon dioxide, and release lots of oxygen. What do nukes make? Giant mushrooms. Not just the cloud, either. I'm sure you've heard of all the (Perfectly safe) genetic mutations which radiation can generate. Well, plants have been shown by this study (Which I cannot link to, due to it's lack of existence) which shows that plants in the aftermath of a nuke intake 200% the normal carbon dioxide. The only question here is....why haven't we nuked all the plants of the world?
Politics: Nuke the politicians.
Natural Disaster: See this. Yeah. You read that right. We're going to fucking nuke that oil spill! We're going to nuke it out of existence! Yeah, eat nuke, oil spill! That'll teach you to be....erm....oily!
Now, you might ask why we didn't nuke Katrina, or the Haitian earthquake. Well, there are perfectly valid reasons. For the earthquake, our underground nuke-bot had temporarily broken down, so we couldn't prevent the quake. And as for Katrina, we could've nuked her into the spring breeze, but Bush was too much of a pansy to risk losing Louisiana in the blast radius of the nuke.
So the next time you have a problem, nuke it. And if that doesn't work, nuke it again. And again. And again!