Here are some questions that I consider important, but not an exhaustive list. I don’t know the answers to any of them, although they are all things I’ve pondered long and hard and I have at least some thoughts about most of them. Perhaps one day I’ll even find time to write up those thoughts or even to find proper answers. I haven’t ranked them by importance, but I have at least collected them thematically:
 Why did animals and plants develop comparatively quickly after three billion years of microbial evolution?
 What caused the Upper Palaeolithic revolution after hundreds of thousands of years of technological stagnation?
 What are the possible failure modes of civilisations?
 What are the possible failure modes of states?
 What don’t historians see about their own societies?
 Which conditions are necessary for an industrial revolution?
 How stable is our society against perturbations?
 How can we bootstrap ourselves to a spacefaring civilisation, all the while making a profit along the way?
 Are there universal attractors in the development of society, technology and morality that transcend human parochialism?
 What are the longterm prospects for life in the universe?
 Why do we seem to be alone  is there a Great Filter?
 How does human thought work?
 What is the relationship of the world of matter and the world of qualia?
 What is the basis for moral reasoning and how does it relate to the world of matter?
 How do the worlds of qualia and morality relate?
 What is the nature of “meaning”?
 What matters to me?
 What constitutes a “fact”?
 Why do some people have religious faith?
 How can one live a good life?
 What is the best way to synthesize forms, and most especially to effectively develop software?
 Are thinking machines possible and can we invent them?
 How do we quantise gravity?
 Why is mathematics so effective in describing nature?
 Why is the search for beautiful theories such a powerful guideline in physics?
 How can we most effectively teach knowledge and thinking?


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To take a crack at one of those: "Why is mathematics so effective in describing nature?" At a guess, because we can keep playing with it until it fits. The most basic math was *invented* so that we could describe nature on a basic level (arithmetic and geometry). At intermediate levels, developments in mathematics such as calculus were motivated in large part by physical questions (planetary motion, describing the shapes of certain curves, predicting the behavior of light, and so on). So it's no surprise that basic and intermediate levels of math describe nature; that's what they were invented to do. We can count bears or gazelles or huckleberries using arithmetic because that's exactly what arithmetic was first made to do; we can describe planetary motion and ballistics with calculus because that's exactly what calculus was made to do. As for more advanced math and how it relates to more advanced descriptions of nature (as in relativity and tensors, or string theory and the highly advanced mathematics associated with it), I think the explanation is thus: Modern mathematics has questioned almost all the underlying axioms of 'conventional' mathematics, such as the ancient Greeks or the mathematicians of the Age of Reason would be familiar with. We can use it to describe virtually *anything*, because we can construct a mathematical description of any set of starting assumptions or conditions. Want to describe a universe shaped like a 5dimensional doughnut? Math can do that. Want to predict how an arbitrarily shaped blob of stuff will spread out through that space? Math can do that, too. Our mathematical toolkit is so broad that it's hard to specify anything we couldn't theoretically describe with it. So it may well be that we now have a description for every thing that the universe *could* be, simply because we've exhausted the possibilities by coming up with such an anarchically broad array of different mathematical techniques. 
bad not good sorry not enough questions