Don't dig new trenches: Complement your creative work by writing openly and understandably about mathematics

Writing about mathematics offers freedoms of explanation that complement the dense texture of meaning captured by mathematical symbols. 

                                                                                              Mircea Pitici, 2014.

Mathematicians are innovators, tinkerers and thinkers. They typically represent their ideas, definitions, algorithms and proofs in condensed formulations and symbol-loaden notations. In his Introduction to The Best Writing On Mathematics, 2013 (Princeton University Press, 2014), editor Mircea Pitici argues for the “inestimable educational and social value” of “talking plainly about mathematics.” He writes that mathematicians should seek validation outside their discipline and narrow community. Pitici explains: 

Mathematics and its applications are scrutable only as far as mathematicians are explicit with their own assumptions, claims, results, and interpretations. When these elements of openness are missing mathematicians not only fail to disrupt patterns of entrenched thinking but also run the risk of digging themselves new trenches.