/sci/ - Science & Math

>physicist

anyone?

The thing with stuff like this is that the machinery and abstraction may seem terrible, but when the preliminary work is done, they start spitting out results with minimal work. I haven't yet looked into operads enough to say anything about them, but the whole field of algebraic topology should be a good motivator for you.

You should look at it from a model making physicist's perspective. To get a functioning model that isn't too painful to use, one must remove unnecessary information. When modeling a car going on a road, not every single little crack in the asphalt can be taken into account. The use of such constructions in mathematics is similar. There is a lot of redundant stuff shrouding the essential properties. When things are generalized, they are translated into another language/formalism in a way that inessential stuff gets lots in the translation.

I hope you can get some motivation from this viewpoint.

>>8404698
Thanks for the general motivational approach. I was more looking for what they are useful in general, other than classifying stuff in topology for the sake of classifying stuff.

>>8405523
Well, consider this: if there is some useful property related to the operads, classifying spaces with respect to equivalence in terms of operads allows one to reduce may problems solvable using operads to the simple case.

You mentioned homotopy theory, so I will give an example out of there regarding the usefulness of classifying spaces. A torus with one point removed looks scary, but it is really just homotopy equivalent to the wedge of two circles. Now, every homotopy invariant property of these two spaces is the same, so instead of popping holes in one's donut, one can consider a space more accessible. Similarly, properties invariant under operad isomorphisms (whatever they are called) will be the same for any two spaces with isomorphic operad systems.