I'm looking for the name and author of a first person story. It's about a man who gets recruited to join a secret society dedicated to improving their IQ, using more of their brain to develop telepathic powers and solve challenges of time and space travel. I had thought it was a Heinlein story/book but my research turned up nothing.
Often found in the same volume as Gulf, from Organic Marble's answer, the story 'Lost Legacy' (1941) also involves developing various mental abilities; they do join a secret society (although the goal isn't IQ enhancement) that attempts to disseminate this information to the rest of mankind.
I'm kind of wondering if you might be combining these stories (and possibly a few others) in your memory, and ending up with a single memory. If it helps, the two remaining stories in 'Assignment in Eternity' (where most people have read them) are 'Elsewhen', which involves a form of hypnosis being used to allow people to travel to alternate realities, and 'Jerry was a Man' (1947) which involves a genetically enhanced chimp (read as: enhanced intelligence) seeking human rights.
With those added -- does this sound familiar?
The Heinlein story Gulf (1949) describes how a man is recruited into a secret society of supermen who use more of their brain and develop telepathy. The elements you mention of time and space travel are not present, however (although there is a rather routine trip to the moon). It is also not written in the first person but rather from an omniscient-narrator perspective.
Have to throw it out there, but to me it sounds like "Mute" (1981), by Piers Anthony. Great book. Has all aspects - psionic ability, secret organisation, time travel...
Mute is science fantasy of mutation and psi: special mental powers. The protagonist, Knot, is a double mutant: He has a physical deformity, and the psi power to make others forget him. He’s satisfied with his life—until the lovely Finesse walks into his life to recruit him for a dangerous galactic mission. She is aided by two small animal mutants: a telepathic weasel and a clairvoyant crab. Knot tries to resist, aided by his psi, but the woman’s beauty and the animals’ powers doom him to a phenomenal adventure.
Could also be Heinlein's Time for the Stars (1956) in which the Long Range Foundation hires (identical?) twins who have the ability to communicate telepathically - one twin stays on earth and the other goes aboard a "torchship" journeying to the stars.
LRF is a not-for-profit organisation, but not a secret society as far as I remember.
Travel to other planets is a reality, and with overpopulation stretching the resources of Earth, the necessity to find habitable worlds is growing ever more urgent. With no time to wait years for communication between slower-than-light spaceships and home, the Long Range Foundation explores an unlikely solution--human telepathy.
Identical twins Tom and Pat are enlisted to be the human radios that will keep the ships in contact with Earth. The only problem is that one of them has to stay behind, and that one will grow old while the other explores the depths of space.