Mr. Money Mustache explores the shockingly simple math behind early retirement — which relies on some shocking simplifications to arrive at it shocking simplicity:
If are spending 100% (or more) of your income, you will never be prepared to retire, unless someone else is doing the saving for you (wealthy parents, social security, pension fund, etc.). So your work career will be Infinite.
If you are spending 0% of your income (you live for free somehow), and can maintain this after retirement, you can retire right now. So your working career can be Zero.
In between, there are some very interesting considerations. As soon as you start saving and investing your money, it starts earning money all by itself. Then the earnings on those earnings start earning their own money. It can quickly become a runaway exponential snowball of income.
As soon as this income is enough to pay for your living expenses, while leaving enough of the gains invested each year to keep up with inflation, you are ready to retire.
If you drew this on a graph, it would not be a straight line, it would be nice curved exponential graph, like this one from the Early Retirement Extreme book:
