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In pure math, equations aren't often named. For instance, we might define that $f$ is a (real) polynomial function iff there exists a finite sequence of real numbers $a_i$ such that $$f(x)=a_0 + a_1 x + \cdots a_n x^n.$$

Notice, though, that we haven't defined an equation, but rather a kind of function.

Furthermore, we might define that a solution multiset of a polynomial function $f$ is a multiset of real numbers $x$ such that $f(x)=0$, with the additional requirement that the multiplicities are correct. Again, note that we've defined a way of getting a multiset from a function; technically, this is another function! Its certainly not an equation.

However, in applied math, I've noticed a lot more naming of equations / syntactical objects. Like, a text might define that a polynomial equation is an equation of the form $$a_0 + a_1 x + \cdots a_n x^n = 0.$$

Why is this the case?

goblin GONE
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    I don't think the name "polynomial equation" belongs to applied math with any kind of exclusivity. – hmakholm left over Monica May 12 '13 at 15:36
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    I suppose applied math puts the stress on the equations because that's the link with the application. For instance, Newton's second law leads to an equation. But you can look at that equation as a simple ODE, or you can cast it in the more general context of the theory of manifolds involving all kinds of tangent spaces and what you have... You can use the language of vectors or tensor calculus. Depending on these choices, the mathematics will be different but the underlying equation is still Newton's 2nd law. – Raskolnikov May 12 '13 at 15:41

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Your question is a little confused & confusing.

I would say that applied mathematics is generally more concerned with model building, so there are large numbers of things which in some way describe either a particular model or class of models, or a method of solution of models.

Since solutions can generally be written as thing you care about = function of input, and since models are generally described by a governing equation in applied mathematics, this means you might end up with a fair few equations named after people.

In pure mathematics, you tend not to have governing equations so much (due to the absence of physics, such as time evolution), and tend not to be so intently focused on getting out quantities as answers. Even when one does come across formulae, pure mathematicians tend to call them identities or refer to them as theorems. There are huge numbers of named theorems in pure mathematics.

Anyhow, I think this is not a very deep observation. It's just a convention for nomenclature, and a suggestion of where the emphasis lies in each of these (vague) subdivisions of mathematics.

not all wrong
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Applied mathematicians need more help remembering things than pure mathematicians do.

marty cohen
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