The story in question featured, as the vague title suggests, a "space mission" that is really a cover for forcing a bunch of really smart people to be in close proximity to each other for long enough that they can truly evolve their collective intelligence. I recall them developing new maths and, e..g, "farseeing" and eventually figuring out that while there was no planet at the end of their journey as they were told, they were able to construct one for themselves.
The novel Starburst matches your description. I think it's a rework or expansion of The Gold at Starbow's End, but can't verify this.
Starburst, by Frederik Pohl, tells the story of Dr. Dieter von Knefhausen and the starship he built to take eight Americans to the planet Alpha-Aleph, in orbit around Alpha Centauri. The story is told from the points of view of Knefhausen, a product of the Hitler Youth movement during World War II, and the passengers of the Constitution, the ship which was designed to make the voyage.
Early in the novel, Pohl reveals that Alpha-Aleph doesn't really exist and Knefhausen's real goal is to advance humanity's knowledge of the universe by placing eight highly intelligent humans in a situation in which they have no distractions.
The astronauts end up making their way back to Earth in the end, and Knefhausen has to confront them. The United States has been fragmented, and the world in general is pretty bad off. I don't remember if they stay on Earth or not, but I do remember the I Ching is part of the plot.
I suspect it may be Frank Herbert's Destination: Void.
In the future, humankind has tried to develop artificial intelligence, succeeding only once, and then disastrously. A transmission from the project site on an island in the Puget Sound, "rogue consciousness!", was followed by slaughter and destruction, culminating in the island vanishing.
The current project is being run on the moon, and the book tells the story of the seventh attempt in a series of experiments. For each attempt the scientists raise a group of clones. These clones are kept isolated and raised to believe that they will be the crew of a spaceship that will colonize a planet in another solar system. The spaceship will take hundreds of years to reach the system and the crew will spend most of their time in hibernation. Along with the crew of six, the ship carries thousands of other clones in hibernation, intended to populate the new colony and, if necessary, provide replacements for any crew members who die along the way.
The crew are just caretakers: the ship is controlled by a disembodied human brain, called "Organic Mental Core" or "OMC", that runs the complex operations of the vessel and keeps it moving in space. But the OMC becomes catatonic, and its two replacements suffer similar fates. The crew are faced with a choice: turn around, or build an artificial consciousness that will enable the ship to continue. The chances of survival if they attempt to turn back are very low.
The clones have been bred and carefully selected for psychological purposes to reinforce each other, as well as to provide various specialized skills that will give them the best chance of success. The crew includes a chaplain-psychiatrist, Raja Flattery, who knows their real purpose, and that the breakdown of the "OMC"s was planned. He's aware that several ships have gone out before theirs, each one failing. He understands the nature of the test: create a high pressure environment in which brilliance may break through out of necessity, and create in the safety of the void what humans couldn't safely create on Earth.