Gregor Mendel, an Augustinian monk working through the 1850s and 1860s, worked out the basic rules of inheritance by carefully cross-breeding thousands of pea plants and meticulously counting the traits that showed up in each generation, well before anyone had ever seen a gene or a chromosome. Mendelian inheritance holds that each parent contributes one of two gene copies to an offspring at random, and a Punnett square is the diagram biologists still use today to lay out every possible combination of those copies, predicting the exact probability that each possible trait will show up in the resulting offspring.
Mendel's counting revealed predictable ratios hiding underneath apparent randomness
Mendel bred pea plants with different, clearly distinguishable traits, purple versus white flowers, tall versus short stems, and traced how those traits reappeared across successive generations, finding that specific, reliable numerical ratios kept showing up no matter which trait he was tracking. Those consistent ratios were the real clue: they revealed that each parent plant was passing on just one of two possible hereditary "instructions" at random, an insight Mendel reached purely from counting outcomes, decades before genes or chromosomes were physically identified as the biological structures carrying that information.
A Punnett square turns that random-selection rule into a concrete probability calculation
A Punnett square arranges one parent's two possible gene copies along one edge of a grid and the other parent's two possible copies along the other edge, filling in each resulting cell with the specific combination an offspring would inherit if that particular pairing happened. Because each parent contributes their copy at random, each cell in the grid represents an equally likely outcome, which turns Mendel's abstract inheritance rule into a concrete, checkable prediction: count how many grid cells produce each possible trait combination, and that fraction is the actual probability of seeing that combination in the next generation.
What we're still unsure about
That Mendel's basic inheritance ratios and the Punnett square method for predicting them are correct for traits governed by a single gene is extremely well established, confirmed by well over a century of subsequent genetics research. What's more genuinely a matter of ongoing complexity is exactly how many real traits actually work this cleanly, since a great many traits are influenced by multiple genes interacting together, or by environmental factors layered on top of genetic inheritance, and a simple Punnett square, built for one gene with two clean alternative versions, doesn't capture that added complexity on its own, which is exactly why more advanced genetics has had to build additional tools on top of Mendel's original single-gene framework rather than that framework covering every case by itself.
This sits inside Mendelian Inheritance & Punnett Squares, one of eight topics in Genetics, one of six domains in Biology, one of seventeen subjects the app can quiz you on.