**MATHEMATICAL WRITING**

1.
The role writing plays in the field
of mathematics. There are several types of writing, all very important to the
survival of the discipline of Mathematics itself

o
Research writing – journal articles
that advance the knowledge in the field by

a)
solving existing open problems;

b)
creating new directions of
investigation;

c)
writing creating interdisciplinary
bridges towards traditional allies of Mathematics such as Theoretical Physics
(Quantum Gravity/Black Holes, Solid State Physics), Computer Science, Computer/Electrical
Engineering, Cryptography, Algorithms, etc.

d)
introducing interesting analogues of
existing problems;

e)
providing new approaches for
previously solved problems;

f)
resurrects in a new light older
problems and methods (some more than 100 years old).

o
Expository writing:

a)
Provide concise summaries of areas
of research (some for experts, some others for the general public).

o
Writing of an educational/scholarly
nature

a)
Presents research problems in an
illuminating way for the benefit of future professional mathematicians that are
currently representing the younger generation – students;

b)
Presents techniques not currently
included in the standard curriculum (special methods of calculating integrals,
studying exotic math objects like fractals – all at an undergraduate level);

c)
Presents math problems that may
prove useful at various stages of math development (middle/high school,
undergraduate);

d)
Presents solutions to problem
assigned in various math journals or national/regional math competitions.

o
Magazine – style writing.

a)
Writing on various
pure/applied/interdisciplinary topics or new developments that are of interest
to the larger community (and enjoyable by persons without a math background).
Making them enjoyable and interesting to basically everybody is an art.

b)
Writing about the history of
Mathematics in various areas of the world, people of Mathematics, women in
Mathematics, etc.

2.
Difficulties that arise when trying
to become published.

o
In pure Mathematics, they are not
different than those encountered by, say, an author of literary work (fiction,
poetry, etc.). Publication is, like in literature, an existential thing.
Publish to remind yourself that you exist as a mathematician. Whatever
difficulties arise, passion will overcome them all;

o
In applied Mathematics, an interest is
needed in an external area such as Physics, Computer Science, etc. Losing
contact with recent discoveries in said areas, or with people active in them
(that can present you with interesting questions) is definitely a problem;

o
However, writing in Applied
Mathematics often inspires and reinforces writing in Pure Mathematics, and vice
versa.

3.
How writing differs in the
mathematics field from other types of writing.

o
In the intense engagement of the
person in a specific

*apriori*quest for truth, discovery, creativity and authenticity, it is closest to Fundamental Physics and Computer Science, Music (which has a formal development) and some big Literature styles (essay, fiction).
o
Somewhat different from the soft
sciences (sociology, psychology, biology, data analysis, etc.) that thrive and
live on data collected from various places

*in the world*. The Mathematics’ big paradox: even if mathematics is, at its core, not overly concerned with the existence of*a world*in particular,
a)
Has an unreasonable effectiveness
when applied to the study of the real world;

b)
It is concerned, in a sense, with
the existence of all possible worlds (real, imaginary, computational)

4.
Issues in the mathematics community

o
The whole body of mathematical writing actively
reflects the life of the Mathematical community

o
Mathematical writing is also inspired by another
central element of the mathematical community: the conferences/meetings.
Mathematicians are people: they need to meet, discuss, and exchange ideas.