He invented dozens of different systems of logical syntax, including a syntax based on a generalization of de Morgan's relative product operation, an algebraic syntax that mirrored Boolean algebra to some extent, a quantifier-and-variable syntax that (except for its specific symbols) is identical to the much later Russell-Whitehead syntax.
An example of such an algebraic encoding is the Lindenbaum-Tarski algebra, a Boolean algebra corresponding to classical propositional logic.
When, in the nineteenth century, algebra and analysis took precedence over geometry, the rectilinear coordinate system of algebraic geometry came to be called "Cartesian coordinates" in honor of Descartes' discovery.
Another general algebraic notion which applies to Boolean algebras is the notion of a free algebra.
Yet those who have heard of her praised her highly – her work in abstract algebra and theoretical physics led Einstein to call her "a creative mathematical genius", and mathematician Norbert Wiener wrote that she was "the greatest female mathematician who has ever lived".
Nor are the rules of algebra governed by social conventions: a gawky 14-year-old who clams up in interviews can still do well.And pure mathematics, at least, needs no fancy facilities like particle accelerators or wind tunnels.
THE roots of algebra, as John Derbyshire tells us, go back to the ancient world: the Babylonians left cuneiform tablets showing simple algebraic problems.
Some 26% of the state's adults smoke, and 35% of its high-school pupils puff while studying their algebra.
Whereas 30% of campus students passed an entry-level algebra course, 18% of those studying online did and the gap widened as material became more complex.
The version of economics advanced here has nothing to do with algebra or interest rates.
The first is that formal methods do not scale up: it takes a whole page of algebra to prove that a three-line program works properly, yet many programs now run to millions of lines of code.
