Another quote from Bill Thurston, this with an arresting image of mathematical communication:
We have an inexorable instinct to convey through speech content that is not easily spoken. Because of this tendency, mathematics takes a highly symbolic, algebraic, and technical form. Few people listening to a technical discourse are hearing a story. Most readers of mathematics (if they happen not to be totally baffled) register only technical details – which are essentially different from the original thoughts we put into mathematical discourse. The meaning, the poetry, the music, and the beauty of mathematics are generally lost. It’s as if an audience were to attend a concert where the musicians, unable to perform in a way the audience could appreciate, just handed out copies of the score. In mathematics, it happens frequently that both the performers and the audience are oblivious to what went wrong, even though the failure of communication is obvious to all.” (Thurston 2011, page xi)
William P. Thurston : Foreword. The Best Writing on Mathematics: 2010. Edited by Mircea Pitici. Princeton, NJ, USA: Princeton University Press.
"Bill Thurston, mwanasayansi wa sayansi ya hesabu, aliandika hivi: ""Tuna kichocheo cha kuwasiliana kupitia maneno ambayo hayawezi kusemwa kwa urahisi.""" Kwa sababu ya mwelekeo huo, hesabu huchukua umbo la mfano, la aljebra, na la kiufundi. Ni watu wachache wanasikiliza hotuba ya kiufundi wanaposikia hadithi. Wasomaji wengi wa hisabati (kama wao kutokea si kuwa kabisa baffled) kumbukumbu tu maelezo ya kiufundi <unk> ambayo ni kimsingi tofauti na mawazo ya awali sisi kuweka katika hotuba ya hisabati. Maana, ushairi, muziki, na uzuri wa hesabu kwa ujumla hupoteza. Ni kana kwamba watazamaji wangehudhuria maonyesho ambapo wanamuziki, wasioweza kufanya kwa njia ambayo watazamaji wangeweza kuthamini, walitoa tu nakala za muziki. Katika hisabati, ni mara nyingi hutokea kwamba wote waigizaji na watazamaji ni oblivious kwa nini akaenda vibaya, hata ingawa kushindwa kwa mawasiliano ni dhahiri kwa wote. <unk> (Thurston 2011, ukurasa xi) William P. Thurston: Preface. "Mwaka 2010 ""Mwaka wa Maandishi Bora ya Hisabati""" Ilikaririwa na Mircea Pitici. Princeton, NJ, Marekani: Chuo Kikuu cha Princeton Press.