Trauma
The novel explores the theme of trauma, particularly in the treatment of grief and recovery. The most obvious example is Ye Wenjie being radicalized by the death and chaos of the Cultural Revolution and its aftermath, and then mourning her daughter, who commits suicide as an indirect result of Ye’s actions. There are moments of recovery for Ye, like when her heart thaws during her time with the villagers in Qijiatun, or as she cares for her neighbors’ children; however, her moments of individual caring never eclipse the traumatic losses that inspired her to contact the Trisolarans.
Other characters grieve as well. Ding Yi is intensely bereaved after Yang Dong’s suicide; he can’t sleep and drinks heavily. Mike Evans, co-creator of the ETO, is so traumatized by the deaths of animal species that he basically decides to try to destroy the human race as a result. Interestingly, the protagonist Wang Miao doesn’t seem to have any grief or trauma in his life, before his sadness over Yang Dong’s suicide. His traumatic moments in the novel center around the stability of the universe, not any personal loss.
The novel’s treatment of trauma as a theme is not particularly hopeful; it instead investigates trauma as a motivator of behavior, and how moments of recovery—like Ye’s—can’t undo decisions made out of grief and rage.
Hope
One of the foremost themes in the novel is hope, and what, if anything, can be done to preserve it when a situation seems hopeless. Characters find and lose hope throughout: Ye Wenjie’s hope for humanity’s moral improvement is destroyed during the Cultural Revolution and its aftermath, though she still hopes that the Trisolarans will be able to save humanity from itself (maybe by willfully ignoring Mike Evans’s beliefs and behavior). Wang Miao loses hope at many crisis points in the novel. His hope is restored in a variety of ways, though most effectively by Shi Qiang’s pragmatic advice, like when Shi shows Wang and Ding Yi locusts at the end of the novel.
Hope is shown to be pivotal for survival. When Ye Wenjie’s hope for Trisolaran redemption is crushed, she goes silent and accepts that this is the “sunset for humanity.” Though the tone of the novel is not particularly hopeful on its own, as Liu explores human motivation in the context of despair, hope is an important component of the novel’s ethos.
The Unknown
The Three-Body Problem is a text obsessed with the unknown, as we watch Wang Miao attempt to solve the mystery of Trisolaran interference. Wang has to grapple with his worldview being shattered when Trisolaran interference seems to destroy his model of physics. Wang also just has to learn a lot of things he didn't previously know throughout the book, from the cosmic microwave background to the best technique to slice open a battleship. These frequent unknowns are explained using stories—Ding Yi uses a pool for his science demo, and Dai Shi uses a cigar; the Frontiers of Science itself uses stories to talk about types of unknowns, in the shooter and the farmer hypotheses.
Three Body itself is an example of using stories to explain the unknown. The video game is a fun mystery for the player, but it also reveals the Trisolaran situation in an accessible way.
Author Liu Cixin talks frequently about the power of the science fiction genre to introduce new ideas; as a novel, The Three-Body Problem makes a case for the power of stories to shine light into the unknown.
Survival
Survival is pivotal to the characters of The Three-Body Problem, whether they're academics or police officers, Adventists or Redemptionists, or not even human at all. Trisolarans are on their way to exterminate humanity so that their culture can survive. On the other side of that coin, humans are killing each other and themselves over how they think the upcoming invasion should be handled. Pan Han kills Shen Yufei for not being Adventist enough; Ye Wenjie has him killed for murdering Shen, as well as hiding communications with Trisolaris. There’s a Battle Command Center from the beginning of Part II, and the question “who are we at war with?” is one that Wang Miao is constantly asking. There's a faction of the ETO called, simply, the Survivors.
The theme of survival is most clearly explored in these fundamentals of the plot, but it happens in smaller moments, too: Wang struggles to survive having his worldview shattered; Ding Yi struggles to survive the loss of Yang Dong; Mike Evans, in the ETO’s origin story, is unable to go on with life until he learns about Trisolaris. Even the swallows that Mike Evans is trying to save are in a desperate struggle for survival. Because the novel features so many suicides (not to mention the Adventists trying to wipe out humankind), survival is presented as a choice, and one that a person, human or otherwise, needs to be constantly making.
Redemption of humanity
A principal question asked in the novel is whether redemption is possible. Humans abuse each other horribly—Ye Wenjie's suffering during the Cultural Revolution is undeniable—and destroy the environment and other living creatures. Whether humanity's redemption for past actions is even possible is central to the conflict between Adventists and Redemptionists: Adventists believe that humanity is irredeemable, and Redemptionists believe that humanity's actions, while horrific, can still be redeemed with Trisolaris's interference.
On a smaller scale, the reader can ponder whether particular characters can be redeemed. Ye Wenjie's actions have a clear motivation, but they still doom humanity; despite her shock at the true state of Trisolaris revealed by the Judgment Day communications, she's still a murderer who enabled Mike Evans for decades. Whether Ye Wenjie is redeemed by her reasons, her choices, or her regret is ultimately up to the reader to decide.
Curiosity
The theme of curiosity is explored in the novel through the lens of Wang Miao and Shi Qiang. Wang is kept alive partially by his variety of interests: his photography exposes him to the countdown in a relatively safe way; his practical research and work-life balance provide a concrete counterpoint to the extremely theoretical problems happening in particle physics; he's philosophical enough to have connections to the Frontiers of Science, so he can ask Shen Yufei for help, but he's not close enough to be devastated by the ETO's large ideas. Wang Miao is, in essence, a well-rounded man and an engaged thinker, willing to engage with new ideas without throwing himself into them.
In this regard, he has two foils: Yang Dong, who was so theoretical and single-minded that she couldn't stand living, and Da Shi, who has no curiosity about the natural world at all and absolutely no impulse to commit suicide. As he tells Wang Miao, if he looks up at the wonder of the night sky, a criminal escapes; how can he worry about humanity's potential for redemption when he has bills to pay? Despite Da Shi's lack of curiosity about life's mysteries, he's an extremely inventive thinker, approaching problems creatively (if rudely). In a way, Da Shi has extreme curiosity, in that he is singlemindedly driven to solve cases, including the mystery of the Battle Command Center; his curiosity just presents differently from Wang Miao's tempered interest in various things.
Foundation/Belief
The novel poses the question of what foundation or belief, if any, leads to the best result. The risk of a foundation-less life is obvious: Yang Dong, with her foundation of theoretical physics destroyed, can’t bear to keep living. Even Ye Wenjie shuts down when her foundation (faith in Trisolaris) is shattered.
Belief systems are shown to be mandatory parts of social life. The Red Guard are passionate believers, who are then mostly abandoned as Chinese culture shifts. The Frontiers of Science believe in the value of philosophically approaching science. The Redemptionists have a fanatical belief in the coming of the Lord, the Trisolarans, to redeem humanity of its sins. The Adventists act on an equally strong foundation of hatred for humanity and a desire to see humankind’s end. Da Shi claims to be so dumb that he doesn’t need a foundation, but even he has his ultimate rule: “Anything sufficiently weird must be fishy.”
Extrapolating any direct proof of whether Liu Cixin supports a particular belief from The Three-Body Problem is almost certainly not a fruitful endeavor. However, the theme of the importance of believing is central to the story: characters without a foundation die, while characters with strong foundations will survive to confront the possibility of the alien invasion.