Combinatorial Explosion
Etymology
From "combinatorics," the mathematics of counting combinations (Latin "combinare," to join two by two), plus "explosion" for runaway growth. It names how possibilities multiply out of reach as variables accumulate. The phrase is descriptive, not eponymous.
noun phrase · /kom-bih-nuh-TOR-ee-ul ik-SPLOH-zhun/
The way the number of possible combinations balloons astronomically as you add even a few more variables.
What it names
A handle for why some problems are hopeless to brute-force: adding options multiplies rather than adds, so checking "every possibility" quickly exceeds any computer or lifetime — the reason we need heuristics, not exhaustive search.
Example
Personalizing the menu for every diet, allergy, and portion size hit a combinatorial explosion no kitchen could stock for.
Related idea
Sharper than plain nonlinearity: combinatorial explosion is the specific case where outcomes scale multiplicatively with the number of choices, so the count outruns intuition almost immediately.