Say I know that on the web there are 50 academic papers which prove
some mathematical statement to be true.

In this case I was trying to prove (unsuccessfully) that 
Y= 2 + d + ((2+d)/d)^d is always greater than or equal to 0 for delta
between 0 and 1.

Now I don't need or expect an answer to this problem, but I want
information generally on is there a smart way to search for math
formulae on the internet.

The first problem is that it will likely be either
1a) formatted in a PDF not as pure text or
1b) as text split over multiple lines which makes it 'visually' easy
to read but unsearchable
also
The second problem is
2) It is quite likely that someone else may have proved it and just
named the variables differently.

I want information and ideas (perhaps from someone with experience
with these types of searches) on how to effectively search the
internet for a mathematical formula or proof.

Hi ponderer,

As you have found, it is usually difficult to locate a mathematical
formula using an internet search engine.

You have pointed out a number of reasons why this is so. In addition,
it is made more difficult by the way in which the search engine
processes the text of a web page before indexing it.

During the process of indexing the web, the search engine transforms
the text by discarding symbols (such as "="), removing formatting
(such as superscripts and subscripts), transforming words to their
case-insensitive form, combining repeated single letters, etc. The
same transformations are applied to the search query that you type in,
before the search engine reports matching pages.

The effect of these transformations can be seen by searching for the
your equation, surrounded by quote marks:

"Y= 2 d ((2 d)/d)^d"
://www.google.com/search?q=%22Y%3D+2+d+%28%282+d%29%2Fd%29%5Ed%22

The one document returned does have an equation featuring the symbols
"Y, 2, d, 2, d, d, d" in that order - but it's a completely different
equation.

There is a symbol-based equation search engine on the web, but it's
mostly loaded with physics equations:

EQNDB
http://www.eqndb.com/

If you type into the "Symbol" search box the following text

   pi rho

you will receive a list of equations that include the symbols pi and
rho.

There are also a number of specialized mathematical search engines,
although they are primarily designed to help with mathematical
research:

Google Web Directory: Science -> Math -> Publications -> Search
Engines
http://directory.google.com/Top/Science/Math/Publications/Search_Engines/

So what's the best way to locate a mathematical formula or proof? You
need to know its name, or its field of applicability. Then, you will
get useful search results from queries like these:

"proof of pythagoras theorem"
://www.google.com/search?q=%22proof+of+pythagoras+theorem%22

"equation of a plane"
://www.google.com/search?q=%22equation+of+a+plane%22

"how to apply stokes theorem"
://www.google.com/search?q=%22how+to+apply+stokes+theorem%22

Notice the use of quote marks in the search queries. These ensure that
the quoted words appear together in the documents located by the
search engine. See also how additional words like "proof of" and "how
to apply" can help to narrow down the search results.

Supposing you don't know the name of the equation that you want to
locate? Then, you need to start at a general math site. A good
starting point for students is Math Forum:

The Math Forum Home Page
http://mathforum.org/

From here you can search math sites

Math Forum Search Page
http://mathforum.org/grepform.html

or browse and search the "Internet Mathemetics Library"

Math Forum Internet Mathematics Library
http://mathforum.org/library/

or visit "Ask Dr. Math"

The Math Forum - Ask Dr. Math
http://mathforum.org/dr.math/

where you can browse previous answers and post your own questions.
Doctor Math answers questions in a very readable way and can help to
make complex topics much more approachable. The Dr. Math Frequently
Asked Questions list is a place to find answers to all those niggling
math concepts that you never quite fully understood:

The Math Forum - Ask Dr. Math FAQ
http://mathforum.org/dr.math/faq/

If you're seeking something a little more interactive, Discovery
School's Webmath has an interactive problem solver. You key in your
problem, and are presented with a worked solution, step-by-step. There
are solver applications for numbers, measurement, geometry,
trigonometry, calculus, statistics, algebra and more. For example, you
could select "Solving Linear Equations" and ask for a worked solution
to "4m+3m-8=4n+5n-15", solved for 'm' or 'n':

Webmath offers math homework help ...
http://school.discovery.com/homeworkhelp/webmath/index.html

If you need to broaden your search further, there are some more great
math sites listed in the Google Web Directory - just start at the
following entry:

Google Web Directory: Science -> Math
http://directory.google.com/Top/Science/Math/


Google search strategy:

"math search"
://www.google.com/search?client=googlet&q=%22math%20search%22


Regards,
eiffel-ga

Thanks for your help, good thoughts and ideas - what I was looking. 
Interesting about how the search engine transforming the text before
indexing it.  Quite thorough.

If you can't prove that "Y= 2 + d + ((2+d)/d)^d is always greater than
or equal to 0 for delta between 0 and 1." on your own you are going to
have a difficult time understanding any other proof.  You probably
need to get some basic calculus books and start looking over some
proofs there.  If you insist on searching the web, search by a topic
not by a formula, you can usually find a related proof that can used
to find the proof you are looking for.

Dear math_man,

Showing that 2 + d + ((2+d)/d)^d is always greater than or equal to 0
for delta between 0 and 1, turns out to be a much more difficult
problem than one might expect.

I am completing graduate studies in econometrics, and was trying to
help out my colleague with a PhD in mathematics to show this.  We
spent 6 hours on it unsuccessfully.  We have something now that is
quite nasty, 3 separate proofs for 3 different ranges of delta
spanning 0-1.  It is easy to verify it is true for any particular
delta between 0 or 1, but the derivative isn't able to be easily
signed either.

Its clearly true, as can be seen by plotting the graph, but that
unfortunately is not a mathematical proof...

Dear ponderer-ga, 

The proof of this problem is direct since all terms in the right hand
side are positive, which can be proved from their definitions. The
most advanced one is about the definition of the exponential, which
can be found in elementary mathematics books.

If you have more questions, please let me know.


Just4look
A person has one Ph. D in math, 2 master degrees in math and applied
math(statistics and operations research). A person who had taught in
universities for about 15 years.

OK math_man I owe you an apology... I just read just4look's comment
and realised that I misrecalled the problem here, its been a few days
since I spent the whole night working on it in frustration.

I should have said Y = 2 + d - ((2+d)/d)^d

No wonder math_man looked at the problem and considered it obvious... 
as just4look points out, it would be elementary as originally posted,
since all the terms would obviously be positive by inspection.

Sincerely,
ponderer

Then the question becomes a little more difficult, but I can solve it.

I am curious that how you determine the price. Do you think that a
solution which you and your colleague with a PhD in mathematics
couldn't figure out in six hours only worth $5?

Just4look

just4look,
Re: the price

Well actually I never intended to actually post the question itself
(just the searching query), it was just that math_man commented that
it was easy/obvious, which I thought was a strong claim considering
the amount of time I had spent on it.

So I thought what the heck if he thinks its _obvious_ then i'll post
it as a $5 question and see if he can answer it.  Of course as it
turned out, I had posted the question incorrectly, which explained why
he had said it was obvious.  Because it WAS obvious as originally
posted.  So once I realised my mistake I was going to close the
question (not expecting anyone to solve it), but it was locked and
then before I knew it... there was an answer.

Regards,
Ponderer