Re: What scientist first used scientific method to solving problems?

That is a hard question. 

Firstly, there is a lot of controversy about just what the "scientific method" 
is. There is how scientists think they discover things, how they actually 
discover things, or how some philosophers think they need to discover things so 
that their knowledge will be logically valid. And different scientists and 
philosophers do not even agree about these things. Then there are different ways 
that scientists go about things in different areas of science.

The simplified story you get told about experiment, hypothesis, and testing, is 
partly true, but not totally realistic. If you really get interested in these 
questions, there is a book you should read in a few years when you have done more 
science and more studying generally: Henry Bauer: "Scientific Literacy and the 
Myth of the Scientific Method", University of Illinois Press, 2nd Ed 1992. I do 
not think he has all the right answers, but I do think he raises a lot of the 
right questions.

Probably the first time that anyone used something like what is now commonly 
called scientific method was in the stone age, when someone tried chipping 
different sorts of rock to see which would make the best sharp edges for tools. 
That must have had all the right ingredients -- try something, think critically 
about the results, and modify your next try accordingly. It is hard to think of 
any other way it could have been done.

The great Greek thinkers Plato and Aristotle had a view of nature that was 
directly opposed to what we would think of as scientific method. 

Plato believed that all of the great knowledge and true nature of things was in 
the world of thoughts and ideas, and that the physical world was only an 
imperfect expression of abstract ideas. For example, in the world of ideas a line 
runs perfectly straight and has no thickness. But in the physical world all lines 
have a thickness, and their straightness is not perfect.

Aristotle believed that to study nature was to contemplate the world as we find 
it, without interfering with it in any way. Any form of experiment was therefore 
not part of the study of "nature", because it involved interfering with the world 
and making things behave in an "unnatural" way.

The ideas of these two thinkers, coupled with the strong influence of a dogmatic 
approach to religion and some cultural superstitions, dominated European thought 
for two thousand years. It was not really until the Renaissance in the 1400s and 
1500s that things changed.

Three (very different) scientists that you should look at in more detail are
 
Roger Bacon, 1220-1292

Philippus Aureolus Theophrastus Bombastus von Hohenheim, better known as 
Paracelsus, 1493-1541

Galileo Galilei, 1564-1643

check them out at 
Encyclopedia Britannica
or from  
Carmen Giunta's Classic Chemistry Page

Here is an interesting quote from Paracelsus that shows a new attitude to 
science:

"People have neglected to study the secret forces and invisible radiations. They 
have been satisfied with relating miraculous facts. Nature has within itself 
forces visible and invisible, and all are natural."