Many a mathematics or physics student will know the popular site Ask a Mathematician / Ask a Physicist. The main contributor of that blog is Seth Cottrell, "the physicist", who has however a mathematics degree in quantum information from NYU. In 2008 at the Burning Man festival (an annual experimental festival in the Nevada desert) he, together with a friend Spencer Greenberg "the mathematician", set up a little tent with a sign "Ask a Mathematician / Ask a Physicist", an experiment that was later repeated in public parks around New York City. The idea is that strangers can just ask any question about the physics of our universe, which the physicist and/or the mathematician try to answer as well as possible. Later (2009) this took the more convenient form of the previously mentioned blog on the Internet where "the physicist" is definitely more active than "the mathematician", or perhaps the physics questions are more popular. This book is a collection of some of the Q&A from that blog. Thus also here most of them are more physics-related than directly mathematics-related. It is however interesting to note that on the FAQ of the blog it is written:
It cannot be overemphasized how important math is. If you’re bad at math, then doing more math is the only way to get better. If you can’t get past something (looking at you, fractions), then admit it to your teachers (or anyone else who can help), ask lots of questions, and then: math, math, math. Math.
Cottrell admits that he started mathematics studies because of his interest in the physics and he needed mathematics to understand the physics. This book is a selection of the more extensive blog entries (there are now hundreds Q&A in the searchable blog archive).
The reader is warned by the author that some of the questions (and their answers) are controversial and may be subject to critique and neither "the mathematician" nor "the physicist" are infallible. The questions are however most interesting, and I can safely assume that most of you sooner or later in life have asked some of these and answering them is sometimes surprisingly nontrivial. Since inquirers are often students or certainly not specialists, the answer tries to balance between a proper (but deep and technical) answer and a superficial (with some hand-waving) reply that remains readable (at least to some extent) for the person who asked the question. As popularizing science texts usually are, the style is colloquial, entertaining, and even funny. A special warning is given when things become more technical. This more technical or more advanced material is placed at the end and gets a section-title "gravy".
The book has four parts called "Big Things" (about cosmology and the universe), "Small Things" (about atoms, particles and quantum physics), "In-Between-Things" (mostly about classical physics), and "Not Things" (about mathematical topics). The title of the book "Do Colors Exist?" is for example a question discussed in the "In-Between" part. Although we can define color by wavelength and we can take pictures beyond the human visual boundaries, what our eyes register are basically only three components from which our brain makes up a color. Some other questions here discuss why wet stones look different from dry stones, but also carbon dating, entropy, energy, plasma, etc, The cosmological questions are related to the obligatory big bang, relativity theory, dark energy, and expansion of the universe, but also: 'What if the Earth were a cube?' and 'What if we drill a tunnel though the Earth and jump in it?'. The description of what we would experience just before the Earth were hit by another celestial object of a similar size is mind-bogglingly frightening. The "Small Things" section answers questions about true randomness, or whether an atom is besides a few particles mostly empty space, furthermore quantum decryption, anti-matter, particle-spin, etc.
These is of course some mathematics involved already in answering some of the previous questions but the more "purely" mathematical section contains 11 questions, which form a curious collection. Some of them are classical topics in popularizing math books like why 0.999... = 1, and the problem of 1/0: stumble stones in undergrad mathematics. Others involve modern cryptography and the Enigma machine, transfinite numbers, the number pi, prime numbers, and chaos theory. Somewhat less obvious are a discussion of Fourier analysis, fractional derivatives, and a topological problem of knots in higher dimensions, and what the "Theory of Everything" (ToE) stands for.
All in all, an entertaining collection with some interesting physics questions. A skilled mathematician, may not be thrilled by the mathematical subjects, but I can imagine that many people are pleased with the mathematics answers as much as they are by the physics explanations. The whole book has some nice illustrations (sometimes more intended to be fun or just to be `illustrating' than they are explaining). Of course the "Ask a Mathematician/Ask a Physicist" site is not the only one of its kind. There are many similar initiatives, which is a blessing of the World Wide Web, but entails also the danger of innocent students being spammed by fake and incorrect information. Science in general and mathematics in particular is certainly happy with people such as Cottrell who take such initiatives to their heart and serve the interested and the curious only driven by their enthusiasm, with little or no financial support.
It is true that Cottrell is not really avoiding formulas, since there are quite a lot, perhaps more than what some people are prepared to swallow. On the other hand, if the readers had a phobia for formulas, they would probably not be asking the question. Most people will be more than satisfied with the answers provided. But be warned that to really understand the physics (or the mathematics), it will require a handbook to look up de details, although I must admit that for some explanations the answer will not directly be found there, and it will require to work up your way to a well founded answer starting from first principles. In that case Cottrell is your guide, pointing the way to follow.