Proposal edit
This is a proposal for a WikiProject to improve articles covering mathematical concepts by making them more accessible to readers without an advanced mathematical background. De-abstraction in this case does not mean removing the formal mathematical definitions of these concepts, but rather providing additional information in layman's terms which give a practical understanding of the purpose and meaning of the concepts.
Diagrams can also be useful in achieving this goal, but they are not a panacea to the problem which this project would aspire to solve. For example, the animated diagram at the top of pi is itself an excellent presentation of the concept of pi, but a reader who was not familiar with the concepts of circumference and diameter would benefit if the description below the image mentioned that the circumference was displayed in red and that the distance between the blue lines was the diameter. This is just an example of course; concepts like pi are not the focus of this proposal.
These are a few articles (off the top of my head) which I feel would benefit under this project:
Basic Tenets edit
I firmly believe that the vast majority of higher mathematical concepts can be understood, on at least a basic level, by the general public. Further, I believe that the vast majority of highly abstract concepts can be clarified (to the benefit of casual readers as well as experts in some cases) by examples, analogies, and illustrations. The current trend in academia is to present concepts with definitions clouded by many layers of abstraction. The result is that students often lose perspective on the meanings and applications of these concepts. It is my belief that perspective is an impetus for progress.
Lastly, I have been saddened to see some articles lose some of their informal illustrations in the name of making Wikipedia more encyclopedic. It is important that we make WP's style clear and understandable, but to do so at the cost of educational value is a mistake.
Original Research edit
One of the most essential policies of Wikipedia is the no original research policy. It is not the purpose or intent of this proposal to call this policy into question. It is, however, necessary to discuss the definition of original research as it applies to the proposal, specifically regarding analogies. There have been cases of good analogies being removed from articles because a citation could not be found for them. This, I believe, is outside the spirit of NOR, because NOR is explicitly worded so that it applies to analysis which 'advances a position'. If an analogy is illustrative, and knowledgeable experts can agree that it characterizes the concept accurately without advancing an opinion, there should be no reason to apply the NOR policy to it. If, on the other hand, the analogy also advances a position, then NOR would certainly apply.
My feeling is that analogies, when applied to empirical concepts like those found in mathematics, are not research, but literary devices. If the analogy can help the reader better understand the concept, its removal under NOR is detrimental to the quality of Wikipedia.