Since 2002, the USAMO has been a six-question, nine-hour mathematical proof examination spread out over two days. (The IMO uses the same format.) On each day, four and a half hours are given for three questions.
Maybe the high school math curriculum is way different in the US, but as a Canadian in second year of university studying math, I had never written a single proof until my first year calculus and algebra courses. I have a hard time believing any kid, no matter how smart, could qualify through that exam without opening a math textbook and only doing homework on normal math problems from high school.
You haven't shown it is 'preposterous' at all. You haven't shown anything. You have presented a single outlier and interpreted it poorly.
A meta-analysis of broad statistical analyses of a large number of people controlling for genetics and shared environment that looks into house after house after house and concludes that on average 50% of the variance of individual psychological traits is genetic, 1% ~ 2% is attributable to shared environment and the rest is attributable to non-shared environment isn't magically negated by one outlier appearing.
For starters in both cases the girls share 50% of their DNA. Your data point just isn't making the case you think it is. To figure out the variance attributable to shared environment you have to get a statistically significant result with the right controls in place in a well designed study. And then that has to be replicated across many studies to be considered reliable.
It doesn't make the case that siblings turn out much more similar than that in the general population due to being raised in the same home and/or going to the same school. The claim doesn't even suggest that you will never see a household where two siblings are very similar.
It's not at all obvious that if Richard Williams never handed them a tennis racquets that they wouldn't have won Wimbledon. You can't possibly make the claim there was a ZERO percent chance they wouldn't find tennis on their own or through school or through friends and get interested in it and become good. Or that they wouldn't find some other sport. Generalize the thought experiment across many many pairs of sisters where their father tries to coach them in something and what do you find? Does the conclusion you draw from a single data point have predicative power as it relates to what you would expect to see in the general population?
Is it equally as 'obvious' that if Roger Federer's parents never turned the on the TV where he saw tennis and became obsessed with it that he would never have become a tennis champion? His sister is a nurse too, not a tennis champion.
Robert Plomin, in Blueprint, makes the case that what our parents and schools do for us pretty much comes out in the wash as we make our way into adulthood and that throughout our lives our individual choices shape our environment greatly based on what we choose to spend our time doing and what who we choose to hang out with. And he states that our genetic propensities nudge us in the direction of making the choices that shape the environment that in turn shapes us. What parents and schools do has very little predictive power as to how their life will turn out.
Genetics may be a necessary condition to be a tennis champion but it definitely isn't sufficient. If Roger Federer had been kidnapped as a baby and raised by central African warlords, he would not have qualified for Wimbledon, let alone won it as many times as he has.
You've looked at a bunch of statistics and left your common sense at the door. People's lives are vastly more malleable through parenting than a mere 1-2%. Parents have the ability to give or take away any opportunity you could think of.
A kid with no known "piano playing genetics" (whatever that means) to speak of, adopted by a wealthy family that owns a grand piano and makes piano lessons mandatory for all of their children is going to be a hell of a lot better at piano than if Glenn Gould's (hypothetical) child were adopted by a poor family who could never afford lessons.
It's such an obvious claim that I feel almost embarrassed in making it, yet it's an important one. If Richard Williams had never handed his daughters tennis racquets, they would never have won Wimbledon. Similarly, it doesn't matter if your child scores 180 on an IQ test, if he never cracks open a math textbook in his life then there's no way he's winning an IMO gold medal.
Environment makes all the difference. Math textbook beats no math textbook every time. Same goes for tennis racquet and chessboard.