There are hundreds of Child genius reported every year, yet little evidence of new Einsteins, Mozarts, Shakespeares, da Vinci's, etc. Why is this?

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That sort of genius is usually recognized posthumously. Society’s attention span is smaller than the possibility space that genius can operate in. If someone doesn’t come across a genius’ works and then promote it in such a way that it becomes viral, that genius will never become famous. The reality