The most important subjects are ai research and fusion research, assuming that they will ever pay off. The human condition is limited by the human body - it's lifespan, need for calories, obsession with reproduction, hence ai would change the whole world. As for fusion, oil, coal, solar wind, geothermal, nuclear, tidal and biomass do not have enough EROI to run a carbon capture machine at a carbon profit and natgas is very expensive to ship without it escaping into the atmosphere.
The biggest thing that will affect the history of the next century is whether or not fusion and real ai are invented, and if so, where and when.