The Sphinxes are a Legacy that deals with symbols and abstractions. To the Pathfinders, the important and most difficult part of problem-solving is gaining the knowledge required to solve it. Alexander's brutish solution to the Gordian Knot repulses them, because it sends the message that brute force can replace patience and understanding. Destructive magic can be countered, manipulative magic can be redirected, but magic that hides knowledge cannot stop a persistent and intelligent willworker.
To the mages who choose to follow this Legacy, the true magic of humanity is language. More to the point, it is the capacity for symbolic recognition, to see a gesture or a marking, hear a collection of sounds, and from that understand. Human beings are optimized, either by the design of a greater being or the rigors of evolution, toward speech and language, both anatomically and neurologically. But all of the biophysical adaptations of the human body toward speech mean nothing without the ability to understand symbols.
The Legacy teaches understanding without processing, learning truth without realizing fact. A Sphinx sees meaning everywhere - in the number of cracks in a sidewalk, in the seemingly random sounds from a baby's babbling, in the texture of a brick wall. Intrinsic in this ability to find meaning anywhere is the knowledge that this meaning comes from somewhere. Sphinxes who cleave to the Atlantean model of mystical understanding posit that this meaning might come from ancient masters sending information forward in time, in a much more subtle way than with the Ananke.