This thread seems to be about good writing for math.
Okay, for some decades, I've read, written, taught, applied, and published, in total, quite a lot of math. Got a Ph.D. in applied math.
Yes, there are problems in writing math, that is, some math is poorly written.
But, some math is quite nicely written. (1) Of course, at least define every symbol before using it. (2) It helps to motivate some math before presenting it. (3) Sometimes intuitive statments can help.
For more, carefully reading some well-written math can help learning how to
write math well:
Paul R.\ Halmos,
{\it Finite-Dimensional Vector Spaces, Second Edition,\/}
D.\ Van Nostrand Company, Inc.,
Princeton, New Jersey,
1958.\ \
R.\ Creighton Buck,
{\it Advanced Calculus,\/}
McGraw-Hill,
New York,
1956.\ \
Tom M.\ Apostol,
{\it Mathematical Analysis:
Second Edition,\/}
ISBN 0-201-00288-4,
Addison-Wesley,
Reading, Massachusetts,
1974.\ \
H.\ L.\ Royden,
{\it Real Analysis:
Second Edition,\/}
Macmillan,
New York,
1971.\ \
Walter Rudin,
{\it Real and Complex Analysis,\/}
ISBN 07-054232-5,
McGraw-Hill,
New York,
1966.\ \
Leo Breiman,
{\it Probability,\/}
ISBN 0-89871-296-3,
SIAM,
Philadelphia,
1992.\ \
Jacques Neveu,
{\it Mathematical Foundations of the Calculus of Probability,\/}
Holden-Day,
San Francisco,
1965.\ \
This isn't just about good writing for math; the post author was trying to verify FLT as is developed in the literature, and along the way they discovered that a lemma underpinning a whole subfield is untrue, as was used. They nevertheless have confidence that the subfield is largely salvageable, by virtue of the faith that if it were bogus, someone would have already found negative results.
But now they had to find a suitable replacement to underpin the field.
Okay, for some decades, I've read, written, taught, applied, and published, in total, quite a lot of math. Got a Ph.D. in applied math.
Yes, there are problems in writing math, that is, some math is poorly written.
But, some math is quite nicely written. (1) Of course, at least define every symbol before using it. (2) It helps to motivate some math before presenting it. (3) Sometimes intuitive statments can help.
For more, carefully reading some well-written math can help learning how to write math well:
Paul R.\ Halmos, {\it Finite-Dimensional Vector Spaces, Second Edition,\/} D.\ Van Nostrand Company, Inc., Princeton, New Jersey, 1958.\ \
R.\ Creighton Buck, {\it Advanced Calculus,\/} McGraw-Hill, New York, 1956.\ \
Tom M.\ Apostol, {\it Mathematical Analysis: Second Edition,\/} ISBN 0-201-00288-4, Addison-Wesley, Reading, Massachusetts, 1974.\ \
H.\ L.\ Royden, {\it Real Analysis: Second Edition,\/} Macmillan, New York, 1971.\ \
Walter Rudin, {\it Real and Complex Analysis,\/} ISBN 07-054232-5, McGraw-Hill, New York, 1966.\ \
Leo Breiman, {\it Probability,\/} ISBN 0-89871-296-3, SIAM, Philadelphia, 1992.\ \
Jacques Neveu, {\it Mathematical Foundations of the Calculus of Probability,\/} Holden-Day, San Francisco, 1965.\ \