It's not like its relation to some abstract form.

And there was a little an interesting theory about abstraction.

In abstract algebra, field extensions are the main object of study in field theory.

In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring.

And here we see Galois starting to develop a language to see the substance of the things unseen, the sort of abstract idea of the symmetry underlying this physical object.

Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces.

And one of the art forms that elicited the interest of the agency, and had thus come under question, is abstract expressionism.

The last step is not so hard, but that middle step going from the abstract description to the folded shape that's hard.

And the power of Galois' mathematical language is it also allows us to create symmetrical objects in the unseen world, beyond the two dimensional, three dimensional, all the way through to the four or five or infinite dimensional space.

Can NATO survive defeat in Afghanistan? The question is far from abstract.

The analysis of SDSs uses techniques from combinatorics, abstract algebra, graph theory, dynamical systems and probability theory.

Now to put some neurobiological meat on this abstract model, we constructed a simple one dimensional world for our favorite subject, fruit flies.

But this language allows us to say that they are representations of the same symmetrical abstract object, which we call 4 4 2.

And here we see Galois starting to develop a language to see the substance of the things unseen, the sort of abstract idea of the symmetry underlying this physical object.

In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative.

Any design for enhancing the effectiveness of the Security Council therefore cannot just be based on abstract wisdom concerning the requisites of the international order.

Even in the 1930s, my colleagues that were trying to put together an abstract art show had all of these works stopped by the customs officers that decided they were not art.

Now to put some neurobiological meat on this abstract model, we constructed a simple one dimensional world for our favorite subject, fruit flies.

The first step is to select material with abstract content to challenge students' logic, and that will therefore have different meaning to different students, in order to aid discussion.

And the power of Galois' mathematical language is it also allows us to create symmetrical objects in the unseen world, beyond the two dimensional, three dimensional, all the way through to the four or five or infinite dimensional space.

Alaskan food web since they eat several kinds of animals but nothing eats them, at least not on this chart.

They all look very different. But this language allows us to say that they are representations of the same symmetrical abstract object, which we call 4 4 2. Nothing to do with football, but because of the fact that there are two places where you can rotate by a quarter of a turn, and one by half a turn.