Matt Mizuhara ‘12

Mathematics Major

Hometown: Allentown, PA

*What writing project(s) are you working on right now?*

I have been spending
the past academic year completing an honors thesis in the Mathematics Department.
I spent parts of the summer and the majority of the fall semester conducting
research on a problem in an area called group theory. A group is a
fundamental object in mathematics that captures the essential properties of
symmetry. Groups arise naturally in the physical sciences: chemists study
the symmetries of crystal structures and physicists verify conservation laws by
observing symmetries of space-time. Groups themselves contain symmetry in
the form of special functions called automorphisms. Many mathematicians
have conducted research in order to understand the structure of these
automorphisms in order to more fully understand the underlying groups themselves.
The project on which I have been focusing deals with a special class of
automorphisms, called nearly-inner automorphisms, in order to understand how
common an occurrence they are.

After discovering
some interesting results, my thesis adviser and I have been writing a formal
report to the Honors Council so as to share our work with the greater
mathematical community. This report is theoretically self-contained,
requiring minimal formal mathematical knowledge, however quickly builds the
requisite tools to state and prove our main result.

*What do you love about it?*

I love the feeling of
conducting independent research, which, very fortunately, leads to new
results. It's an incredibly unique and rewarding sense of
accomplishment. This has been the most demanding and frustrating venture
I have attempted in academia; however, the end result is something of which I
am very proud.

*What about it (if anything) is driving you nuts?*

Accepted language and
syntax is very distinct in mathematics, and is something I am still
developing. I owe a lot to my adviser, Professor Pete Brooksbank, for his
patience and support. As the thesis reports were due April 1st, we had several
busy weeks of intensive writing and editing. My inability to succinctly and
accurately describe certain aspects of our mathematics was quite
frustrating. However, Professor
Brooksbank's advice and mentorship guided our project from imprecise writing to
a properly formatted report.

*How would you describe your writing process?*

For me, it is most
important to understand the organization of the mathematics. Writing
general ideas and broad schemes is most important so that I introduce all
relevant information in the most succinct and natural manner possible.
Once a first draft is written, my edits serve several purposes. I aim to
streamline the exposition as well as rewrite the mathematics in the most
"balanced" way possible. It is important to find a balance
between writing too many and too few details. In the former case, the
reader can be bogged down by trivialities which can cause him/her to lose track
of the overall ideas. In the latter case, the reader could be left
confused and uninspired.

*What kind of feedback on your writing do you find most helpful?*

Generally, it is easy
for me to lose track of those aspects that need explanation. After a year
of study, many concepts become natural to a researcher while they remain
esoteric to even their most qualified peers. As such, it is often requisite to
develop mathematical intuition and ideas slowly in one's writing. The
most useful feedback to me is when people simply explain at which points of a
paper they become less comfortable with the information or they feel I have
explained a concept too quickly (or perhaps too slowly). In that sense,
the most useful feedback is more global, rather than local. The
overarching flow and rhythm of my writing is more difficult to judge and write,
while the specific details are much easier to modify independently.

*What would you like your peers to know about you as a writer?*

Mathematics is hardly
as exotic and inaccessible as popular culture or

perceptions
imply. The same thought process which allows a computer scientist to
write a program, a philosopher to conjecture a new idea, or a Spanish major to
learn a new language is precisely that which allows mathematicians to discover
new and exciting results. Math research is as alive and varied as any
other science, and the results are, in some instances, more groundbreaking and
beautiful than any physical experiment or art form. Problems can go
unsolved for hundreds of years, only to be cracked by an enlightened new
approach by a fresh mind, and once a result is proved, it will remain so
forever. As Hardy said, mathematical results are, in some sense, the closest
form of immortality that we mortals can attain. Further,

*Times*magazine once wrote of a mathematical novel that "to read it is to realize that there is a world of beauty and intellectual challenge that is denied to 99.9 percent of us who are not high-level mathematicians." In my mind, it is unfair that not everyone can share this same passion and understanding of mathematics. It takes some time to understand the language of mathematics, but I only ask that everyone at least devote some patience to unravel its mysteries and to give it a try before turning up their noses at a rewarding and beautiful art.
OH Yeah!

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