Since my own field is mathematics - at once the most self-contained and the most open-ended field of human inquiry, as well as the most hermetic from the outsider’s point of view - it would not be very useful for me to speculate on old and new questions that might fascinate mathematicians over coming decades.
The second question posed is of very general interest. My own answer is that western society and to some extent the world as a whole is mired in a dreadful paradox. As a species, we have created, over the aeons, an enormously powerful epistemological engine, capable of generating vast amounts of very reliable and extremely useful knowledge. This is modern science. On the other hand, we have a culture which has a hard time coming to grips with science and digesting what it tells us about the world. This difficulty produces a large spectrum of obtuse though passionate dogmas, from creationism to the widespread hysteria over genetically modified crops.
The problem that confronts us is to devise a pedagogy, in the broad sense, that will enable the population at large to deal with scientific matters with mature comprehension rather than fearful ignorance.
Norman Levitt is author of Prometheus Bedevilled: Science and the Contradictions of Contemporary Culture (buy this book from Amazon (UK) or Amazon (USA)), and coauthor of Higher Superstition: The Academic Left and Its Quarrels with Science (buy this book from Amazon (UK) or Amazon (USA)).