To make artificial general intelligence, or AGI, we have to realize that there are in fact nine different types of intelligence, not just one. Howard Gardner, Professor in Cognition and Education at Harvard, has summed this up nicely in the diagram below. In it are listed the types of intelligence we will have to create in silicon, if we are to design and build a generally intelligent system. These are logical, spatial, interpersonal, intrapersonal, physical, linguistic, musical, naturalist and existential.
Gardner has also written a number of best-selling books on the subject – I would suggest starting with his 2006 book, Multiple Intelligences. Of course, then we have to build a system where all nine intelligences are completely and seamlessly integrated, just as they are with humans.