Ultimately brewing is about enzymes, plain and simple. All enzymes are proteins and all proteins have specific pH ranges and temperatures in which they operate most efficiently. That applies to malting, mashing, boiling, and fermentation. Hitting specific pH ranges at certain points are like critical control points from a quality point of view. If you hit those points your chances of ending up with a great beer in the end is better than brewing blindly and getting lucky. I'm not saying everyone needs high precision instruments and pH meters but if you can figure out what you're working with you will be much better off.
We're not talking the application of the scientific method in brewing (unless we're talking tweaking recipes, then dependent and independent variables can and should be used). It's about utilizing and understanding the science behind what happens and why it happens. If you can teach yourself or learn some of the basic and more moderately advanced scientific principles of brewing, it will help out with the artisanal aspect of brewing. For example aged hops smell pretty awful on their own. After boiling, however, and a lenghty fermentation with brett the bound aroma compounds contained in the hops become a very citrusy aroma and flavor component. Prior to that biological impact from the yeast's glycosides they smelled like cheesy feet with an athlete's food problem. If you didn't know that someone looking to make a lambic may NEVER try aged hops because the smell bad. Another example is pitching rates. High pitch rates, to an extent, reduce ester development. However too high a pitch rate can make it just as estery (but in a different way) as too low a pitch rate. That's because metabolically the yeast doesn't have to reproduce and the Acetyl CoA (an enzyme) will be directed to making flavor rather than more yeast. This is why brewing new wort and blindly pitching on an entire yeast cake is ill advised. That's WAY too much yeast. Plus as you move forward trying to reuse the yeast the viability drops significantly because the yeast aren't reproducing they're just consuming sugar and shutting down. So as you reduce the replications necessary to attenuate your wort you have old yeast lying around in the fermentor with no nutrient and reduced glycogen to make new yeast resulting in a crappy culture. There are plenty of examples but I don't want to bore anyone more than I already have.
One of the things that bugs me is that homebrewers make statements based on something they read that someone else said. So then that statement is picked up by 5 more people and its repeated and next thing you know there's 300 homebrewers on this site alone that holds that original claim as true even if it isn't 100% correct. The other thing I see happen is a homebrew "celebrity" does something one way and so that becomes the accepted way and a preached technique. The technique could be terrible, specific to their brewing system, but because "insert name here" said so people tell others to do the same thing. So it could be wrong from the start and with no understanding beyond what they heard, bad information or techniques spread. This doesn't happen all the time but it does happen often enough.
An example of this herd mentality is with lactobacillus. Sure the commonly available cultures of lactobacillus are not hop tolerant. They're very sensitive to hops actually, well WL and Wyeast cultures are. However, when I make the claim that lacto soured a 35ibu 8%abv beer I made, people have told me I'm crazy. I have pdfs of academic papers working with hop tolerance in lactobacillus that further discusses how they even "trained" the bacteria to have stronger tolerance to hops in a short amount of time (its all about genes and protein synthesis). Again, I'm not saying you we need to all read academic papers, but instead be quiet enough to accept information contrary to strongly held homebrewing belief. I think there are many homebrewers that like to be an authority on certain things they read and its apparent on this website. There's a certain "this way or the highway" tone to some people's posts. That kind of attitude can scare someone away from homebrewing, and we don't want that. Ultimately people can do what they want, but there are bad, good, better, and best practices. I think our goal is to eliminate the bad practices work towards the best practices.
The meshing of science and art is important from the start. It begins with extract and just snowballs into full on grain brewing. Extract brewing is like making soup. Add ingredients boil, and ferment. However science still applies in that most basic type of brewing because you still have to worry about yeast and that yeast cannot be thrown in 180F wort and expect it to live and ferment. That's because the proteins (stupid proteins again) in the yeast denature and the yeast dies at that high temperature, if it was a thermophillic bacterium it'd probably be find at 180f, but we don't make beer with them. Also cold break is fine in the fermentor, all of it is fine in the fermentor. Most commercial breweries chill on the way to the fermentor during knockout and that means cold break is forming in the wort transfer line due to the heat exchanger.
When moving to grain brewing one should have an understanding of pH, and water chemistry to some extent to make the best beer one can make. If you have very soft/acidic water you are not going to make a very good stout because your mash pH will be too low. Same goes for trying to brew a pilsner using very alkaline water except in this case your mash pH will be too high. Sure you can just dump water in a mash tun and brew blind, it works for many people.
I am not suggesting we all become a science is the only way robot. There certainly is an artisanal aspect to brewing. That comes with knowing the flavors of your ingredients, the flavors the yeast produce, and imaging how they will combine to make a beer. I do draw the line at claiming it is art though. I claim its a merely a craft. If you ask me, Art is meant to be displayed and collected, something a craftsmen makes is consumed or used. You can refer to it as an art but I am not going to claim that I am an artist like some pompous American brewers that charge 4x per ounce compared to their import counterparts. Either they're horribly inefficient and have to charge to make up for that, or they're gouging considering you have less middlemen taking a cut.
Anyway that's my take, I'll shut up now.