Seems that their 'invention' of algebra was a fluke given their love of personalistic and subjective logics.
Now we know why they invented the concept of 'zero'--they had to be able to describe the magnitude of their dedications and contributions to logic and world peace.
I hated algebra. Geometry rules!!
"Algebra" may be an Arabic word, but the Arabs learned it from the (Muslim) Moghuls, who learned it from their Hindu slaves. Likewise place value notation (that is, the zero).
These discoveries are historically called "Arabic" because the Europeans got them from the Arabs. Don't forget that Islam arose during the very low ebb of Western civilization known as the Dark Ages.
The struggle and cross-fertilization of the two cultures led to the revival of civilization in the West (the Renaissance). Islam on the other hand, after a brief flowering, sank back into the Dark Ages and stayed there.
They couldn't make any progress with the great philosophy they stole from the Eastern Church because it couldn't be squared with their irrational "revelation." It's no accident that Aquinas provided the great synthesis and not Avicenna or Averhoes.