I have reviewed Graham Farmelo’s new book for Nature.
You can find the full review here.
Mathematics, physics and the relationship between the two is a fascinating topic which sparks much discussion. The review only came out this morning and has already sparked a flurry of emails. Generally I’d prefer it if the discussion were to be held in the comments here rather than my inbox.
As you can probably tell from the last sentence of my review, I’m a strong believer in the primacy of data for progress in physics. I do worry sometimes that experiment becomes collateral damage in heated discussions about theory and maths. But hey, read the review for more from me, and the book for more from Graham.
Graham has also conducted a series of interviews around the book. The first, with theoretical physicist Nima Arkani-Hamed, is well worth a listen. The second, with mathematician Michael Atiyah was posted a few days ago and I haven’t had chance to listen yet but plan to do so soon. They will I presume all be linked up here eventually.
25/5/2019 The book is also reviewed by Peter Woit on his blog.
Life and Physics 
To your almost final comment that “The standard model is a complex, subtle and immensely successful theoretical structure that leaves significant questions unanswered”, I wonder whether Farmelo has anything compelling to say about which questions are significant?
To your final sentence, “The Universe might speak in numbers, but it uses empirical data to do so”, with which as an empiricist I absolutely agree, for any finite set of numbers there are arbitrarily many formalisms that could be tinkered with to produce those numbers or convincingly close statistics for those numbers. In judging the lineup of those formalisms, however, it is for me as much the most tractable and most useful of them for engineering that eventually will out as it is the prettiest.