The question is based on what defines great genius. The degree to which metrics of genius can be objective seems limited. The first basic problem with “genius” is that it could be broadly defined as encompassing two types of people. A genius could be one with holistic abstract intelligence, and a genius could be someone who leads discovery in specific domains of knowledge. Early philosophers are known for their broad domain of knowledge, while current “geniuses” are most often recognized for discoveries within specific branches of science.
But, I’d much prefer to expand on areas of applications conscious that have been less thoroughly considered. Given a specific person, what is it they want in comparison to what is it that they achieve. Many geniuses are quite miserable because they expect much more than they accomplish. For each complex problem domain space, how efficient is the person at solving each of those problem domains? For problem domains involving factors of uncertainty or confidence, how accurately can a person make predictions within each of those problem domains?
Genius implies specific goals in specific problem domains that are metrics that can be measured with such concepts as an IQ test. However, if a genius is miserable, you have to ask the question, “If you’re such a genius, why can’t you resolve your own misery?”. That is why genius splits into holistic intelligence and specific domain intelligence.
Specific problem domains seem to take precedence, in which case “genius” is a biased version of intelligence. For example, the people who can memorize phone books may not considered as genius as the people who memorize and apply physics formulas even if the memorization takes the same level of complexity.
Next, you have information capabilities of a human brain. Some people have the ability to watch two TV shows at once. Comparing this to someone who can memorize a phone book, you are not comparing apples to apples. But by necessity, you may need to find a way to compare apples to oranges to compare two people’s holistic intelligence. The challenge would be akin to saying “is this apple better at being an apple than this orange is at being an orange”?
“Genius” is also very closely tied with “intelligence”. Do you wish to define genius as being a certain magnitude of intelligence? Or, does genius instead require a specific subset of intelligence as a quality?
Finally, I’d note that qualities having little to do with a human brain’s calculation ability such as patience, persistence, and even tolerance could be factors of genius. There are many different factors which go beyond “book smarts” which cause people to discover new science. Someone’s ability to learn from others as a social skill could come into play for example. Interesting question!