>"How Much Inequality Is Fair? Mathematical Principles of a Moral, Optimal, and Stable Capitalist Society, [...] perfect inequality, which has a definite mathematical form."
Income inequality does not have a "perfect mathematical form."
Since the stoics, clever folks adept with maths have realized that 'math/stats is the best way to lie or convince people you are right.'
Why? Because people trust in the intellectual rigor of maths. But while the language of maths is fundamental to our universe, formulating an argument with maths does not necessitate correctneas. even the hugely-influential economist Keynes, and others, believed that 'human behavior cannot be reduced to mathematics.'
Economics is currently, and has been for a century, trying to formulate as much as possible in the language of math, but we're consistently in disagreement and wrong. That is because Economists are almost always without the virtue of being able to do controlled experiments.
If you wanted to know the 'definite mathematically ideal' amount of inequality, you would first need to put forward a hypothesis which also defines ideal. "X is ideal for maximizing aggregate utility" is a reasonable hypothesis. Then for your experiment you would need many planet earths, and some way to to precisely measure people's utility.
This is all impossible. And as such, we would be wise to treat the current state of economics like that of 19th century medicine: somewhere between interesting-possibly-helpful and hogwash.