Two corollary explanations come to mind. First, writing uses a wider variety of registers and styles than spoken language. Forms and usages that would sound exaggerated or affected in spoken language are socially appropriate in writing. Writing is constructed over time and predominately “for the record,” so it uses precise, unforgiving language that suits the specific context of the writing. This is why the first line of a Wikipedia article on some topic in math, poetry, or physics is often indecipherable to a lay reader, even an educated one, without further reading. Spoken language, on the other hand, is first and foremost a form of communication from a speaker to a listener, and is composed and interpreted in real time, even if it’s guided by notes. This makes it more fluid and colloquial, and more likely to employ a register that the speaker and listener will both understand readily. Since successful writers use the more precise, ossified language and successful speakers use the more fluid one, they diverge through memetic evolution, as suggested.
The second explanation has more to do with the way writing is taught. I don’t know how much it applies to technical writing, maybe somebody can share their experience on that point. Since the Victorian era, prose has embraced brevity. The briefest explanation that still conveys the broad meaning of an author’s idea is usually treated as the best stylistically. This sacrifices precision for a kind of clarity, but in a field like mathematics, precision is clarity. Typical admonitions about brevity of style, then, render useless attempts to explain big, scary concepts. Lecturers, however, have the opportunity to pursue digressions and explain minutiae in half-organized ways and still hold the attention of an audience because the lecturer can easily signal the importance of a difficult intermediate step to the wider narrative in a way that would be clunky and perhaps abrupt in writing.
Two corollary explanations come to mind. First, writing uses a wider variety of registers and styles than spoken language. Forms and usages that would sound exaggerated or affected in spoken language are socially appropriate in writing. Writing is constructed over time and predominately “for the record,” so it uses precise, unforgiving language that suits the specific context of the writing. This is why the first line of a Wikipedia article on some topic in math, poetry, or physics is often indecipherable to a lay reader, even an educated one, without further reading. Spoken language, on the other hand, is first and foremost a form of communication from a speaker to a listener, and is composed and interpreted in real time, even if it’s guided by notes. This makes it more fluid and colloquial, and more likely to employ a register that the speaker and listener will both understand readily. Since successful writers use the more precise, ossified language and successful speakers use the more fluid one, they diverge through memetic evolution, as suggested.
The second explanation has more to do with the way writing is taught. I don’t know how much it applies to technical writing, maybe somebody can share their experience on that point. Since the Victorian era, prose has embraced brevity. The briefest explanation that still conveys the broad meaning of an author’s idea is usually treated as the best stylistically. This sacrifices precision for a kind of clarity, but in a field like mathematics, precision is clarity. Typical admonitions about brevity of style, then, render useless attempts to explain big, scary concepts. Lecturers, however, have the opportunity to pursue digressions and explain minutiae in half-organized ways and still hold the attention of an audience because the lecturer can easily signal the importance of a difficult intermediate step to the wider narrative in a way that would be clunky and perhaps abrupt in writing.