I would say "neither" - and by that, I mean that it seems my love of math was largely self-generated. I've always been entranced by the precision, symmetry and beauty of it all. However, the home environment helped to cement my love of the subject.
I was certainly encouraged/enabled by my parents, who would get me any math book I wanted. This is why I was able to master basic differential and integral calculus by the age of 12 with self-study, about 4 years before it was taught at school.
Certain experiences helped to cement my love of math. When I was about 9, I had self-taught myself basic algebra (it wouldn't be covered in school for another 3 years). I had no clue about the theory of quadratic equations at this point, yet for some silly reason, fixated upon this equation (I still remember it!): x^3 = 5x - 5, which I'd come up with off the top of my head. I didn't know it was called a cubic, and I had no clue how to solve it. But a visitor with a computing background and a slight knowledge of math told me what sort of equation it was. So I knew to search for "cubic equations". This was in the era before the Internet was a global resource, so I buckled down and looked through the Encyclopaedia Brittanica (which my father had previously purchased) and learned about Niccolo Tartaglia, Girolamo Cardano, and the theory of solution of cubic and quartic equations. Of course, I quickly learned to solve quadratics along the way, and I preferred to complete the square because it is assured to give an answer, and it seemed cooler than memorising a formula. Later on, I discovered that a good bit of the theory of cubics and quartics had already been elucidated by the ancient Indians, my ancestors.
Another example of a significant formative experience is when my family was visited socially by a gentleman by the name of Gopal Prasad. Some of you may know him - he's a prominent mathematician working in abstract algebra at U. Michigan. I was about 13 at this time, I think. I had been playing around with an idealised "multiplying rabbits" problem (again, I'd just been thinking about this idly), and had come up with a simple geometric series (I didn't know that that was the right name!), then generalised it symbolically. However, I didn't have the insight to add it up to get an elegant expression, and had left it in sigma notation. Dr Prasad showed me how to write the progression twice aligned vertically, multiply the top by the common ratio, "frame shift" by one term, then subtract term-by term, and finally divide by (common ratio - 1) to get a neat expression for the sum (identical to the one school would teach me years later). I was thunderstruck when I saw what he'd done, and I immediately set about manipulating other series in similar ways, and that led me to a wondrous journey through Analysis. (I later found out from school that I'd somehow skipped over a more elementary series - the Arithmetic series and gone straight to the Geometric series, but such lack of systematicity is one of the perils of being an autodidact).
In the same visit, Dr Prasad introduced me to his field of Group Theory, and tried to explain the basic concept to me (of a closed set of elements under an operator), but I found it all a little too abstract at the time. He gave me a "first print" of a paper of his, entitled "Volumes of S-arithmetic quotients of semi-simple groups". Of course, I found it impossible to understand, and I still can't follow it (despite having learned rudimentary abstract algebra along the way), but the paper still takes pride of place in my math papers and books collection (yes, I have one!
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Well, those are the seminal events that come to mind when I think about what influenced my love for the subject. I guess most of them happened at home, but it seems like the interest in math has always been intrinsic to my personality. It wasn't really due to any member of my immediate family - my dad (coincidentally, also named "Dr Prasad"!
) is a medical doctor, and although I consider him generally brilliant, he isn't that keen on advanced math. I do have him to thank for providing resources to me to enrich myself in my interests. He still felt that Medicine was the safer choice, which is why I ended up doing it for a career, but (as should be obvious), I still have a very keen interest in math, which I pursue as an amateur whenever I find the time.
Apologies for the long post. I just felt I had to get this all out.
