This is from someone presumably smart enough to know better Exponential curves feel gradual and then sudden:
After the fact, exponential curves look relatively smooth. When you are in the midst of them, however, they feel like they are divided into two stages: gradual and sudden.
Exponential curves are always exponential. Consider the outputs of 2^x:
Every adjacent pair is a doubling. If you you begin at x=0,1, it feels just as ‘fast’ as it does should you began at x=20,21
generalize: e^(x*a)/e^((x-1)*a) and you have the ratio e^a . For the above example, a=ln2
Shortly after, he announced he was going to stop blogging and use Twitter instead. Wise move. If you’re liable to hanging yourself by your own stupidity, you may as well give yourself as little rope as possible.
And an article from Bloomberg that went viral A Mathematician’s Secret: We’re Not All Geniuses
I’m not saying we shouldn’t have high hopes and standards for our children. But by focusing our attention on the kids who get the top SAT scores, we reinforce the fixation on genius to the detriment of everyone else
No amount of idealism will change the fact that mathematicians , with virtual certainty, tend to score very high on such tests. To find the next generation of mathematician, look to kids who are getting ceiling scores on the math part of the SAT at the age of 13. Sometimes ‘late boomers’ exist, but still they exhibit preciosity at youth and then later decide to turn to mathematics and learn the material very quickly due to having a high iq. If genius is defined by having a high IQ (which according to the Stanford Binet Intelligence scale it is) and standardized test scores, virtually all mathematicians are geniuses, regardless of how much recognition they later get in their careers.
Spatial ability test scores in high school predict STEM achievement a decade later: Spatial Ability for STEM Domains: Aligning Over 50 Years of Cumulative
Psychological Knowledge Solidifies Its Importance
Here is a TedX talk that shows how IQ (and its proxy the SAT) predicts creativity.
But future mathematical ability can be predicted even earlier life, even in 1-year-olds Lessons from a 45-Year Study of Supersmart Children.