The Age of Absurdity: Why Modern Life Makes It Hard to Be Happy, by Michael Foley (Simon & Schuster, £10.99)

Office life is horrible; shopping, gadgets and TV rot the brain; no one knows how to think, love, or be alone; everyone's scared of difficulty and death. Foley (a novelist and poet) has assembled an impressive list of reasons to be cheerless. Look at those young folk, zombiefying themselves with texting and videogames, and broadcasting their every sex act. ("Modern love is photographing yourself being sucked off and [. . .] immediately circulating the photograph to your large circle of friends." Is it? Perhaps David Bowie could write a song about that.)

Young himself in style, the author uses the word "ironic" almost exclusively in the Alanis Morrissette sense; but he does have a saving salt of self-deprecation, and is good on cant ("dynamic", "self-esteem"). There are some interesting juxtapositions (using Hannah Arendt to criticise Malcolm Gladwell), but the overall result can seem scattershot. I did like his idea that towns float enormous message balloons over the streets, reminding citizens that "Failure Is More Common than Success"; "Many Will Dislike You Whatever You Do"; and "The World Does Not Oblige".

Numbers: A Very Short Introduction, by Peter M Higgins (Oxford, £7.99)

Transcendence might be elusive in modern everyday life, as Foley fears, but at least there are still "transcendent" numbers. This cordial guide to number theory speaks of each number having "its own character", and introduces us to those that are "perfect", "amicable", "sociable", "abundant", and "weird". Numbers might even have feelings: as Higgins argues, our habituation to expressing a number in base 10 is really an "unfair" prejudice that risks "typecasting" it: describing it differently (eg as a square) could allow another "facet of its personality" to bask in deserved attention.

This anthropomorphising tendency enlivens the author's efficient explanations of prime numbers (and their use in cryptography), the Fibonacci sequence, different orders of infinity, imaginary numbers and so forth. (Readers need to be able to follow some algebra, but Higgins is generous in offering geometric illustrations as well.) By the end, one feels a renewed sense of what the author calls the "mystery" of numbers, and what they are doing there at all.

Hope, by Stan van Hooft (Acumen, £9.99)

A more quotidian mystery: when I am putting on my socks, as well as intending to put them on, do I also hope that I will be successful in putting them on? After all, muscle spasm or earthquake might intervene and frustrate my desire to be well-socked. Van Hooft thinks such hope must accompany even the most trivial action, at least "at an implicit and deep level". People with terminal diseases, he judges, should not indulge in the "vice" of unrealistic hope; but then, it is not clear when a hope is "realistic" (so as to be "authentic"), since "legitimate commitments", on his account, might not be "realistic" themselves.

I stared glumly at my half-on socks. Then I remembered Van Hooft explaining that, when he invokes obscure "levels" or a "deeper stratum" of our "subjectivity", he is not saying anything that "requires factual . . . evidence", just making a "'hermeneutic' claim" about the interpretation of reality. Hope explains religion, too, and "there is no fact of the matter" about whether atheists or believers are right: it's all just hermeneutics. I felt happily free to posit the existence of any old exotic psycho-flora or cosmo-fauna and, if challenged, retreat to my hermeneutic castle. It's very cosy in here. I don't even need socks.