Yes, you need to spin up on foundational knowledge. You are not an exception.

by Justin Skycak (@justinskycak) on

Even Ramanujan self-studied.

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If Euler, Gauss, Maxwell, Ramanujan, etc., needed to spin up on foundational knowledge, then so do you. Yes, these people all produced plenty of original research at early ages, but they didn’t skip the foundations.

Even Ramanujan self-studied. He didn’t just sit there and think up math with no prerequisites in place. For instance, just one quote from his Wikipedia page:

  • "In 1903, when he was 16, Ramanujan obtained from a friend a library copy of A Synopsis of Elementary Results in Pure and Applied Mathematics, G. S. Carr's collection of 5,000 theorems.[26][27] Ramanujan reportedly studied the contents of the book in detail.[28]"

Keep in mind there were also far fewer prerequisites needed to make novel contributions to math back then, so a person could fill up their prereqs to cutting-edge math in a shorter time.

These individuals were presumably highly cognitively advantaged as well, with outsized learning rate and generalization ability, which would allow them to move faster through a curriculum, infer more knowledge beyond it, and infer more knowledge from self-directed experimentation. Basically, across all math learners, these individuals would be the most likely to have their prereqs in place.

In general, when it looks like someone progressed so fast they “must” have taken a shortcut, what really happened is they speed-ran the foundations by way of a more efficient training environment, advantageous individual differences leading to more rapid skill acquisition, or by allocating way more of their time into training than is typical. Elite performers typically emerge from a combination of all three of those things.

Take Euler for example.

  • Advantageous training environment? Check. Euler was taught by his father, who had studied under Bernoulli, and Euler enrolled in the University of Basel at 13 years old, where he also studied under Bernoulli and self-studied more advanced textbooks under Bernoulli's guidance.
  • Allocating way more of their time into training than is typical? Check. I mean, geez, what 13-year-old is taking university courses and self-studying even more math textbooks on top of that?
  • Advantageous individual differences leading to more rapid skill acquisition? I don't think there's any formal record, but you'll see Euler on pretty much any "highest estimated IQ of all time" list. It seems pretty safe to conclude he was running on some exceptional cognitive machinery.


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