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> At thirteen he read Kant, just for the fun of it. And before he was fifteen he had taught himself differential and integral calculus.
by chrisco255 4y ago
> At thirteen he read Kant, just for the fun of it. And before he was fifteen he had taught himself differential and integral calculus.
- Sai_ 4y agoFifteen is also around the time students get introduced to calc, isn’t it? In India, fifteen is around tenth or eleventh year of education and while I’m too old now to recall when we started diff calc, it definitely wasn’t in the 12 or later years of education. In that light, this particular achievement of Einstein’s doesn’t seem very impressive.
- Izkata 4y agoHigh school in the US (~ages 14-18) doesn't have one track, and calculus isn't required to graduate. There were around 800 students in my year, and I'd guess only around 100-200 took the class, and it was usually in the final year. So of the other group, the ones that went straight into working instead of college never had it. Edit: to clarify, mine was in the mid-2000s, don't know if there have been changes with things like Common Core, but from what I've seen/heard that seems focused on much earlier years so I don't think it would have affected this part of math education.
- SkyBelow 4y agoIt would depend upon the details of what is meant by learning calculus. Learning enough to pass the average high school class on it isn't much. Above average at math, but nothing very impressive. But the same language could also describe learning it at something closer to the level of analytics, having a much deeper understanding than the average class produces. The deeper the understanding, the more impressive the achievement, yet it would still be described in layman terms as "learning calculus".
- Sai_ 4y agoIf true, this makes so much more sense and is in line with whatever else we know of Einstein’s genius. If not, it sounds like resume padding by someone who wanted to make Einstein seem even more impressive than he is.
- yamtaddle 4y agoCalculus was introduced around ages 17/18 (senior year, i.e. the last year of high school, aka 12th grade, or the 13th year of formal primary and secondary education that most complete, including kindergarten) at the locally-regarded-as-very-good US high school this "elder" millennial attended, and only for those seeking the variant of our high school diploma that was supposed to get us college-ready. But it may have changed since then.
- chaxor 4y agoEinstein still got quite a bit of help from Noether when developing his general relativity because his math skills needed some touching up here and there. Maybe he was on to something about imagination being a bit more important, if you can use your academic community to polish the formalisms up a tid bit.
- chrisco255 4y agoHaving imagination doesn't matter if you don't understand what geniuses came before you and what they interpreted and misinterpreted about the world. His theory upended Newtonian physics on some level, which is the practical basis for Calculus in the first place. You have to understand those concepts on a deep and abstract level to be able to challenge a dominant, centuries long, paradigm like that. Imagination without complex, higher order, mental models is useless for discoveries like Einstein's.
- syzarian 4y agoIt’s not that his math skills needed brushing up. Noether’s Theorem was proven as a result of the need to for conservation laws in his theory of general relativity. She discovered (invented?) the mathematics that demonstrated the existence of conservation laws. Needing mathematics that hadn’t been discovered yet does not count as an example of his math skills needing to be touched up here or there.
- chaxor 4y agoI'm talking about her contribution towards general theory of relativity itself, not her other creation of Noether's theorem