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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
by vouaobrasil 2y ago
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.
- analog31 2y agoClassical 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.
- vouaobrasil 2y ago> 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.
- 867-5309 2y agothat's like studying medicine then not becoming a doctor
- AnimalMuppet 2y agoNot becoming a patient-treating doctor. Research doctors still matter a great deal in the field of medicine.
- orochimaaru 2y agoI 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.
- analog31 2y agoMath 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.
- chris_wot 2y agoWhich is exactly what Hardy said himself.
- tikhonj 2y agoso like studying (human) biology and becoming a biologist
- LPisGood 2y agoThere are lots of medical researchers who don’t treat patients.
- liontwist 2y agoUtility is not the ultimate goal of math, understanding is.
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- vouaobrasil 2y agoI think that would also be rewarding. I have no desire to become a doctor but I'm interested in how medicine works.
- OJFord 2y agoOn the contrary, it's more like studying medicine and then remaining in medical research in a purely academic (non-clinical) setting.
- lsharkey602 2y agoJohn Keats, Osamu Tezuka, Somerset Maugham, Hector Berlioz. Studied medicine but did not practice (Keats did for a little while). Just for interest.
- lsharkey602 2y agoAlso, Che Guevara.
- woopsn 2y agoThat'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.
- Koshkin 2y agoMathematics has, and has always had, applications within itself.
- vouaobrasil 2y agoObviously. I only meant applications to the real world. Don't care about those.
- OJFord 2y agoI 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!
- tomatocracy 2y agoAbsolutely - 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.