The idea of a ‘genius’ has fascinated generations of people and is described and reinforced in literature and media. The greatest of geniuses, like Albert Einstein, Thomas Edison, Leonhard Euler, Karl Friedrich Gauss, Terence Tao, and the most amazing genius of all, Srinivasa Ramanujan, has inspired countless people. However, they may have discouraged a disproportionate number of people as well.

The problem with the notion of ‘genius’ is that most people decide who’s a genius and who’s not based on 1% or less of the make-up of the person. As Albert Einstein said, “genius is 99% hardwork and 1% talent”, natural affinity should not be the deciding factor on whether someone is destined to be good at something or not. In fact, research shows the opposite (see the work of Angela Duckworth, her research is summarized here: https://sites.sas.upenn.edu/duckworth/pages/research.

There are now countless ways to ‘determine’ whether or not someone is a genius. Most ‘genius’ tests involve some sort of mathematical puzzle. This is analogous to determining whether a child will be a good football player or not based solely on the number of sit-ups they can do. It’s almost preposterous. For instance, a famous question to school-aged children asked by the late Paul Erdos, the most proliferate and by many accounts the most passionate mathematician of the 20th century, was the following:

Suppose that you are given a set such that . Prove that contains two integers that do not share any common factors except for 1.

During Erdos’s time, long before the age of the internet and wide accessibility of just about every piece of information (and mis-information) to just about everybody, this question genuinely gave children a good challenge and the most successful among them ought to feel proud. Now, not only is this question (and many others like it) in dozens of problem solving books, it’s also easily accessible via the internet. Thus, the original intention of the question which was to see which child shows promising problem solving ability, is now totally lost; it’s now a question of who read the answer beforehand.

The goal should not be encourage children to seek anointment as a ‘genius’. Indeed, most ‘geniuses’ including the greatest of them don’t see themselves that way. They see themselves as someone with maybe slightly above average dispositions who happened to work really hard to achieve what they have. That should be the value we instil into our young; not worshipping the ones who have ‘gifts’.

OProS={2,4,6,…4n} does not seem to satisfy the property.

prayersontestsPost authorYes you are correct, I updated the post with the correct statement of the result. Thanks!