I was wondering why there are so few trappists and how is it that from the eleven trappists 6 of them are from Belgium. Why aren't the breweries more spread over the world? Does it have something do to with what happened there in the history?
The Trappists are members of a Roman Catholic religious order. Trappists follow a rule of St. Benedict stating that they should "live by the work of their hands", which means many Trappist monasteries sell goods for income. The order has no particular prohibition against alcohol, so producing beer is an entirely reasonable profession for the monks.
The order is centuries old, and originated in France. However, many of the French breweries were destroyed during the French revolution (and later, the world wars). Fortunately for us today, the monasteries in the beer-loving Belgium survived (or in cases like that of the Rochefort Abbey, were restored).
Today, the "Authentic Trappist Product" logo, which defines a "real" Trappist beer, is owned by the International Trappist Association, an organization founded in 1997. The founding members include six abbeys from Belgium, one from the Netherlands, and one from Germany (which doesn't produce beer). It is only in very recent years that the ITA has expanded to recognize breweries aside from the original 7, the first "new" one being Stift Engelszell from Austria in 2012.
As the craft beer revolution pushes forward, I'd say we're likely to see more monasteries start their own beer production and apply for the logo. But right now, it's still mostly the original Belgians.
The Trappist designation is monitored by the International Trappist Association. Here are the criteria set forth by them for an abbey to maintain their Trappist label:
The beer must be brewed within the walls of a Trappist monastery, either by the monks themselves or under their supervision.
The brewery must be of secondary importance within the monastery and it should witness to the business practices proper to a monastic way of life
The brewery is not intended to be a profit-making venture. The income covers the living expenses of the monks and the maintenance of the buildings and grounds. Whatever remains is donated to charity for social work and to help persons in need.
Trappist breweries are constantly monitored to assure the irreproachable quality of their beers.