What name is given to the statistical phenomenon in which a trend that holds true within every subgroup of data reverses once those subgroups are combined?

Math

In a classic Simpson's Paradox case like hospital survival-rate data, what can happen even though Treatment A outperforms Treatment B in every individual subgroup?

The Simpson's Paradox flips outcomes: Treatment A beats B in every subgroup, yet B wins overall—a real phenomenon hospitals face with survival rate statistics.

Math

In the Birthday Paradox, how many people must be in a room for there to be roughly a 50% chance that two share a birthday?

Birthday Paradox reveals only 23 people needed in a room for 50% odds two share a birthday—our brains wildly underestimate how fast probabilities compound.

Math

In the classic three-door Monty Hall problem, what is the win probability for a contestant who keeps their original door choice?

The Monty Hall Problem stumped mathematicians for years: switching doors after one opens increases your win odds from 33% to 67%, yet most people's brains reject this.

Math

In what year did Robert Recorde introduce the equals sign (=) to mathematics?

The equals sign (=) didn't exist until 1557 when Robert Recorde invented it—mathematicians literally wrote out 'is equal to' before then.

Math

According to architectural historians, which ancient Greek temple is most famously (and controversially) said to embody the golden ratio in its proportions?

The golden ratio φ appears in the Parthenon's dimensions, but this was likely architectural intuition, not deliberate Platonic design as romanticized in legend.

Math

Which ancient Greek mathematician calculated bounds for pi using inscribed and circumscribed polygons around a circle?

Archimedes calculated pi so accurately in 250 BC that his bounds weren't beaten until 1000 years later, using only geometry and patience.