Here is a chart which shows that “proven reserves” is an economic concept instead of a geological or physical concept. In other words, there is no absolute “fixed amount” of resources over the long run; rather, as demand for a product increases, suppliers in a free (enough) economy will find ways to deliver additional supply to meet that demand. What we see is a stable equilibrium condition for “proven resources” over time, and there is no reason to expect that to change.
Bonus snippet: William Stanley Jevons thought we would run out of coal by the start of the 20th century (if I remember correctly). Spoiler alert: he was wrong.