I read this book as a first-year undergrad. His style inspired me to go after rigour and proof and was a good start to serious mathematics. I always loved Hardy's work and Hardy and Wright's number theory text was also very nice through my PhD in algebra/number theory. I found Hardy's book much nicer than the contemporary calculus texts with irrelevant pictures and modern-day examples. Just straight math! Not for everyone, but it has classical, austere appeal for those who enjoy such things.
Classical and austere, but not stilted. For instance...
>>> We can state this more precisely as follows: if we take any segment BC on Λ, we can find as many rational points as we please on BC.
reads as a normal English sentence.
As a student, I also preferred straight math. Proofs were what made math come alive for me. For applications of math, I had plenty of other sources such as physics, electronics, and programming, where the examples weren't forced.
> As a student, I also preferred straight math. Proofs were what made math come alive for me. For applications of math, I had plenty of other sources such as physics, electronics, and programming, where the examples weren't forced.
I guess the difference between us then is that I didn't care about applications.
That's fair. Hardy himself was a zealot and in fact despised applications, writing that he hoped his work would never be put to extrinsic use, for then its value would become contingent on a particular stage of technological development.
Math can be an end unto itself. This can come as a bit of a surprise in our prevailing culture, which needs to justify the usefulness of everything. Also, it's possible for someone to study math as a liberal art, and develop the ability to do useful things with it on their own. My observation is that the people who grudgingly learned math as a means to an end, tend to forget most of it soon after graduating. This explains the widespread but paradoxical aversion to math among engineers.
I doubt you have pure research doctors. Medicine is a field that is so dependent on treatment outcomes. There will be doctors more focused on research. However, I doubt they will stop seeing patients.
I know for a fact that pediatric oncology and hematology is entirely driven out of a research hospital or university. But doctors there publish but also treat.
I read somewhere that this was Turing's preparation for the Cambridge entrance exam; so I read through it in sixth form before sitting the STEP exams (modern equivalent for mathematics or CS with, and perhaps other programmes depending on college). I failed them, but that's a review of my naïveté, not the work!
Absolutely - Hardy and Wright's An introduction to the theory of numbers is excellent but definitely doesn't need to be restricted to postgrads - its also fine for undergraduate level number theory (indeed it was a recommended textbook when I was an undergrad).
It is quite dense but at least personally I find that style of textbook much more useful than the American style enormous textbooks which takes a chapter to explain what could be said in a paragraph. You just need to know to expect it will take you quite a while to read each page.
