Why Your Calculator Is (Slightly) Lying to You—And Why That's OK

Presented by Tobin Driscoll

We trust computers to follow the rules of arithmetic. But even expensive scientific software can fail to uphold the basic principle \((a+b)+c = a + (b+c)\). This is not a glitch—it's a clue to a deep tension between the perfect world of mathematics and the practical world of computation. In this talk, we'll take a journey through the numbers we think we know—from whole numbers to fractions, and onward to the supposedly "imaginary" number \(\sqrt{-1}\). While these abstract ideas have become indispensable tools, their digital simulations are full of surprising compromises. The climax of our journey will be a mathematical mystery: a simple approximation that fails because of an invisible barrier that lurks in the imaginary direction. This surprising connection is spurring advances in the practical challenge of representing mathematical functions on computers. I will show how both new and old ideas continue to drive new breakthroughs, making these methods faster and more powerful than ever before.