This was the second book in the series I read about a decade or two ago.
The colony experience a famine after terrorist blew up a factory. The protagonist is on some spiritual journey and was modified to look like a neanderthal. There is also a riddle on how to catch a bird without clipping it's wings. The spaceships are also completely made out of diamond. At some point the protagonist looks at his thoughts on a screen and amuses an audience by thinking of a theorem.