Now for scientific:
Boiling wort is normally required for the following reasons:
1. Extracts, isomerizes and dissolves the hop α-acids
2. Stops enzymatic activity
3. Kills bacteria, fungi, and wild yeast
4. Coagulates undesired proteins and polyphenols in the hot break
5. Evaporates undesirable harsh hop oils, sulfur compounds, ketones, and esters.
6. Promotes the formation of melanoidins and caramelizes some of the wort sugars (although this is not desirable in all styles)
7. Evaporates water vapor, condensing the wort to the proper volume and gravity (this is not a primary reason, it's a side effect of the process)
A minimum of a one hour boil is usually recommended for making quality beer. When making all grain beer, a boil of 90 minutes is normal for many commercial brewers, with the bittering hops added during the last hour. One exception to boiling was historically used to brew the Berliner Weisse style. Here, the hops were added to the mash tun, and the wort is cooled after sparging and then fermented with a combination of lactobacillus from the malt and an ale yeast.
Boiling for less than one hour risks under-utilization of hop acids, so the bitterness level may be lower than expected. In addition, the head may not be as well formed due to improper extraction of isohumulones from the hops. A good rolling boil for one hour is necessary to bind hop compounds to polypeptides, forming colloids that remain in the beer and help form a good stable head. An open, rolling boil aids in the removal of undesired volatile compounds, such as some harsh hop compounds, esters, and sulfur compounds. It is important to boil wort uncovered so that these substances do not condense back into the wort.
Clarity will be also be affected by not using at least a full hour rolling boil, as there will not be a adequate hot break to remove the undesired proteins. This will also affect shelf life of the bottled beer, since the proteins will over time promote bacterial growth even in properly sanitized beer bottles. The preservative qualities of hops will also suffer greatly if the wort is not boiled for one hour, as the extraction of the needed compounds will be impaired.
Boiling wort will also lower the pH of the wort slightly. Having the proper pH to begin the boil is not normally a problem, but if it is below 5.2, protein precipitation will be retarded and carbonate salt should be used to increase the alkalinity. The pH will drop during the boil and at the conclusion should be 5.2-5.5 in order for proper cold break to form and fermentation to proceed normally. Incorrect wort pH during the boil may result in clarity or fermentation problems.
The effects of boiling on the wort should match the intended style. It is often desirable to form melanoidins which are compounds produced by heat acting on amino acids and sugars. These add a darker color and a maltier flavor to beer. When desired, an insufficient boil will not form enough melanoidins for the style. Boiling the initial runnings of high gravity wort will quickly caramelize the sugars in the wort. This is desired in Scottish ales, but would be inappropriate in light lagers.
Vigorously boiling wort uncovered will evaporate water from the wort at a rate of about one gallon per hour, depending the brewing setup. In order to create a beer with the appropriate target original gravity, changes in the wort volume must be taken into account. Longer boil times or additions of sterilized water may be required to hit the target gravity.
