Hewlett-Packard scientists have announced a new electronic component which they say is a fundament on a par with the transistor and resistor.
According to the Herald article, it was theorised by Leon Chua [in 1971] that there should be a fourth element to a passive circuit (one in which the components consume but do not produce electricity): to go with the resistor, inductor, and transistor, there should also be a memory resistor.
This latter is something that couldn't be derived from any combination of the other three. This component "remembers" the direction of current flow, and "expands in that direction to improve the flow". This last bit I'm not sure how much I understand, but the discovery team leader (Stanley Williams) says it has implications for a computer to be able to remember its state. In other words, it could retain state when power is off, and reboot instantly.
It has also been said that such a [two-terminal] component could be configured in combination to replace a transistor, being smaller and so taking up less space. (This is well beyond my second-year undergraduate electronics, so I can only report it as it's said.)
The team has developed both a mathematical model for this, and a physical example. Published in the 30 April 2008 edition of the journal Nature.