Where do socks go?!?

There's not just one big problem - there's millions (perhaps billions) of one big problems, depending on who's doing the asking and who's doing the answering. Sure, there are a few common problems that could be solved, but you have to figure out a way to ask the questions about the problems in such a way that the solution will be mutually agreeable to the largest number of people.

Energy, food, war, socks. All of these are big problems (OK, not so much with the socks) that won't be solved with one big solution. By the time you're done breaking them down into solvable units, some wierdo will come along and ask "So, what's the biggest problem?"

Cheap, clean energy.

Solve that, and virtually everything in almost every industry changes.

* Incurable diseases

* Mass killings of human beings by other human beings (whatever be the reason, whatever they are called)

* Mismanagement of global food inventory, as mentioned by others

* Inequality between women and men (and others). Existing solutions are not customized for cultures/communities.

Inequality and lack of social mobility.

It's mind boggling how uneven wealth distribution is in some countries.

Paraphrasing Jared Diamond, the biggest problem we face is thinking that we can fix just one problem and be OK.

Greed.

It's the only thing that destroys everything it touches. And it often has massive reach and repercussions.

Its equal access to opportunity. Population would not be a problem, given level of education has a direct correlation to number of children. And there is more than enough food to sustain the planet

population growth. It drives hunger, unemployment, pollution, resource exhaustion, political instability,.... In systems terminology it is a control variable with many output variables.

Food production. Even today there are people without enough food. The planet isn't getting any bigger while the population grows each day.

I would make a slight correction to this. There is enough food. It is just in the wrong places. It is a cost / distribution problem.

Food, cheap but nutritious engineered food which can be produced/grown in diverse geographic areas in large quantities/density.

unethical businesses - Why? Because they do anything for money. They don't care about effects to the environment, they don't value human life and they treat employees as slaves (might not be same everywhere).

War & hunger.

Aging.

climate change