Very true, these books are qualitative. There's a bit of basic math around delta-G for reactions and Chi-sq tests for genetic associations, but the conventional undergraduate introductory biology course is 99% descriptive.
There are reasonable arguments for taking that approach. These courses are foundations for subsequent study, with the intended outcome that students have a broad but shallow understanding of core basic ideas. Lots of biology makes intuitive, mechanistic, and visual sense, much like introductory computer science and introductory chemistry.
Obviously applied math plays a key role in biology but it tends to address specific needs like protein structure prediction, dynamic modeling of transcription/translation and metabolism, inferring phylogeny, high-throughput 'omics analysis, network simulation of epidemic outbreaks, and so on. These are great to study, but without the broader context the understanding would be relatively fragmented, lacking the big picture.
Rereading OP's question:
> good modern starting points to someone who would want to learn more about how living beings work (from bottom up)?
I interpret that as wanting a general understanding, starting with chemistry and working upwards towards evolution and populations. That's all in the standard two-semester introductory course, hence my book recommendation.
If that's wrong and OP wants a math-centric approach, here are a few gems:
Physical Biology of the Cell, Phillips, et. al
An Introduction to Systems Biology, Alon
Evolutionary Dynamics, Nowack