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It is necessary to be clear about the relationship between creativity and genius - and the relationship between genius and breakthroughs.
The following are some of my definitions and assumptions:
1. Genius is creative - it is a mixture of creativity and high ability (mostly intelligence).
2. Creativity is an aspect of personality - creativity is indeed part of the cluster of personality traits discovered by HJ Eysenck and called Psychoticism. The Psychoticism trait-cluster also tends to include various 'antisocial' or socially disvalued personality traits such as lower than average conscientiousness, lower than average empathy/ agreeableness, impulsiveness, arrogance etc. - these are, in fact, necessary components of creativity.
3. Because intelligence and personality are mostly hereditary, so are the components of genius - but the necessary particular combination is rare.
4. Because intelligence and personality averages and distributions are different between human groups, so is the incidence of genius - some societies have a much higher percentage of geniuses than others; but this incidence is never very high, and may be zero.
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5. Because genius has been defined in terms of psychological attributes, the assumption is that these attributes will tend to lead to the achievements which are associated with genius - but not necessarily. A person may be a genius, but for various reasons (bad luck, inhospitable society, underdeveloped culture, illness, persecution etc) fail to make a major achievement.
5. On the other hand, I assume that ALL major achievement (all major breakthroughs) are made by a genius - whether correctly attributed to a specific genius person, or not. Apparent counter examples, e.g. when major breakthroughs are apparently made by people of high intelligence but low creativity (or to 'teams'), will (I believe) almost-always be found to depend on the work of an unattributed creative genius (or pair, or very small number) - and if that person cannot be identified, I assume that they nonetheless existed.
6. Therefore, without major geniuses, there are no major breakthroughs.
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But genius is relative - in the sense that creative people of lower ability, and less luck, may make important breakthroughs at a smaller societal scale, and perform as 'local geniuses' uniquely able to solve local problems (whether credited for doing so, or not).
I have (provisionally) termed these 'local geniuses' Patagonian Shakespeares.
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