
Ask HN: What does it mean to have a attack on a problem - quietthrow
I was reading Richard Hammings lecture - “you and your research” where he mentions about having “an attack on a problem”. He mentions he didn’t work on time travel , antigravity etc because he did not have an attack on that problem. And because he didn’t have an attack on the problem they were not important problems.<p>What does it mean to have a attack on a problem?
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SamReidHughes
It means you have some path you can take to make progress on the problem. For
example, suppose I want to compute the sum for n = 1 to infinity of 1/n^2.

I can't think of any way to solve it. But one day you discover that you can
calculate 1-1/2+1/3-1/4+..., by sticking x^n terms on it: sum(x^n *
-(-1)^n/n), differentiating, giving you sum((-x)^(n-1)), recognizing that's a
geometric series for 1/(1+x), which clues you in to see if the initial series
was a Maclaurin series for log(1+x), and so it is, the sum is log(2).

This gives you a new attack on the problem: Try parameterizing the series on a
variable, like the sum{x^n/n^2}, or sum{1/(nx)^2}, or what-have-you, perform
some manipulations, and see what happens.

If that doesn't work out, another attack is to compute an approximation of the
sum on a computer, by adding up the first hundred million terms, and seeing if
it approaches a value you recognize. Knowing the actual value might give you
clues about the solution technique (if you want to prove the answer).

Before the age of computers, you might approximate it with the integral 1/x^2
from k+0.5 to infinity, with the first k terms added. Or you might develop
general techniques to approximate the sum f(n) more exactly, using the
derivatives of f(x) to adjust for the errors that basic integral approximation
gave.

If you find out that it's approximately X, then maybe the series is related to
some other formula that is known to give you X. Then by performing some
manipulations, you might show the two are equivalent. That's another attack on
the problem.

And then any time you see a formula with 1/n^2's in it... maybe you could
somehow connect that to the series.

~~~
quietthrow
Thanks for the answer with the examples. I am not much of a math person so am
not following the math example but I think I (at least) directionally get what
you are saying.

Follow up question:

Based on what you are saying does it mean that forming different hypothesis on
ways to solve the problem can be considered an attack on the problem OR it has
to be more than a hypothesis whereby you might have a general approach to
solving that class of problem but the detailed steps for solving a particular
instance of that problem needs to be figured out and tested?

~~~
SamReidHughes
Either.

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muzani
It's more that you have something to start on.

We can tackle problems like building a Mars colony. We can make rockets, we
can do life support, we can scout the area, calculate trajectories, figure out
how to make rockets that land.

However, we can't do time travel because there's nothing to start on.

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hieloz
Richard Hamming wrote that serious scientists should have a list of problems
that they would like to work on, but they can't work on all of them at the
same time, and some are off the active list because there is no attack
available. An attack is "a good starting place, some reasonable idea of how to
begin."

This is an article that will help you understand "attack" . [http://www.the-
rathouse.com/2013/Fanaticism.html](http://www.the-
rathouse.com/2013/Fanaticism.html)

