When examining the role of The House of Wisdom in mathematics I have found it to be very important to consider what the role of this place was in relation to anything. First, The House of Wisdom was founded by a man by the name of Caliph Harun al-Rashid. Now this is a guy who was pretty darn powerful in his day. He was intellectually, politically, and militarily resourceful, which is the exact way that many modern liberals would describe the late "Dubblya Bush." Further his surname translates to "the just," "the upright" or "the rightly-guided," which just further demonstrates the correlation made above. To get more to the point, and the value of the actual situation, this was a man who valued intellectuality and the discoveries that came along with it. He founded The House of Wisdom to be a place where intellectuals of many different disciplines could come together to research, explore, and translate ideas in the areas of science, mathematics, astronomy, medicine, alchemy and chemistry, zoology, geography and cartography. A good way to look at this place would be to think of it as a room where all of the best and brightest could come together to share their wisdom, learn from one another, and put their ideas into text of many languages, sort of like a coffee shop where people discuss the novels they are writing, but actually doing it.
Anyhow, how does this apply to the current state of mathematics? Given that the best and brightest were all gathered in this place, ideas could truly be explored and either proved or put to rest. This was a place where mathematicians could collaborate with other mathematicians and intellectuals to discuss problem points with whatever it was that they were exploring. I think that some of the greatest strides in mathematics came from collaboration and still do. How many people did it take to prove or disprove any point of discrete mathematics? Five line geometry? Any of Euclid's theorems? It takes often takes many people to work through a given math problem and The House of Wisdom was a place where people could do that. Not only did the work through the mathematics to come up with something that was valid and trustworthy, they translated those works into other languages so that the ideas could spread. Without this type of translation, many modern math strategies and formulas and theorems would not have been used, or maybe not discovered in certain cultures until years later. Maybe never. The sharing of ideas is incredibly important to the spreading of knowledge. The House of Wisdom is the hub of knowledge spread-ation, if you will. Like a raptor chases down its prey, displays every aspect of predation and devours that prey, so the spread-ation of mathematics hunts down the minds of skeptics and devours them into parabola shaped smile of discovery.