Natural numbers, one, two, three and onward, are the counting numbers, the most basic number system mathematics is built on, used originally for the simplest possible task, counting distinct, whole things. Every richer number system that came afterward, integers including negative numbers, rational numbers including fractions, real numbers including numbers that can't be written as any fraction at all, was constructed specifically to answer a mathematical question the natural numbers alone genuinely couldn't handle.
Each extended number system was built to fix a specific operation the previous one broke
Natural numbers alone can't represent the answer to a subtraction like three minus five, since no natural number describes a genuinely negative quantity, which is exactly the gap integers were introduced to close. Integers alone still can't represent the answer to a division like one divided by three, since no integer captures that in-between value exactly, which is exactly the gap rational numbers were introduced to close. And rational numbers alone still can't represent certain lengths that arise naturally in geometry, the diagonal of a unit square, which is exactly the gap real numbers were eventually introduced to close.
This layered construction means every richer number system quietly contains the earlier ones
Each of these successive extensions was built specifically to contain the previous, more limited system intact while adding exactly the new numbers needed to make the problematic operation actually work, meaning every natural number is also an integer, every integer is also a rational number, and every rational number is also a real number, nested layers rather than separate, competing systems. This nested structure is exactly why mathematicians can move fluidly between these different number systems depending on what a given problem actually requires, confident that whatever holds true for natural numbers still holds true once they're viewed inside any of the larger systems built on top of them.
What we're still unsure about
That natural numbers form the foundational base each successively richer number system was built to extend, closing a specific operational gap the previous system left open, is well established, rigorously formalised mathematics confirmed since the late nineteenth century's careful axiomatic treatment of number systems. What's more genuinely a matter of ongoing foundational and philosophical interest is exactly what natural numbers themselves fundamentally are, whether they're best understood as sets, as purely formal symbols manipulated by fixed rules, or as something else again, and philosophers and foundational mathematicians continue to debate exactly which formal characterisation best captures what a natural number genuinely is, rather than that foundational question being fully settled.
This sits inside Natural Numbers & Number Systems, one of seven topics in Arithmetic, one of seven domains in Mathematics, one of seventeen subjects the app can quiz you on.