The rate of change of bubble volume. If this quantity is positive, the bubble will grow; if it’s negative, it will shrink. A constant that depends on the temperature and the specific gas in the foam. (The foam on top of a glass of Guinness lasts unusually long because Guinness uses nitrogen in addition to carbon dioxide in its beer. K is smaller for nitrogen, so the bubbles change size more slowly.) The sum of the lengths of the edges of the surfaces where the bubble intersects other bubbles. For an isolated bub...

MATH TREK: A claimed proof that P≠NP spurs a massive collaborative research effort.

To figure out how much we should spend fighting climate change, economists have some questions for you: How much would you be willing to spend now to make your child $100 richer in the future? What about your grandchild in the farther future, or your great-great-great-great-great-grandchild in the very distant future? The health of the planet may hinge on the answers. Most economic analyses of climate change have concluded that we should be spending only small amounts to combat climate change now, ramping up slowly over time. This conclusion mystifies most climate scientists, who argue that i...

The reclusive mathematician who proved the Poincaré conjecture may or may not claim his prize.