Sample Personal Statement for Mathematics
Imagination: 1.the act or power of forming mental images of what is
2.the act or power of forming a mental image of something not present
to the senses or not previously known or experienced.
---Webster’s New World College Dictionary 4th edition
In the foregoing definition of the word “Imagination”, the most
important aspect is undoubtedly creativity and originality. This was
precisely what I had in my mind when I used this word to name the folk
rock band that I launched in collaboration with two other
undergraduates when I was a sophomore and in which I was the bass
guitarist. For about one year, we composed our original songs and
lyrics and gave a total of 14 performances on and off campus. We
became the cover story of the magazine XX and were interviewed by the
XX Cable Television Network.
Although I had to disband the band so that I could indeed concentrate
on my studies when I became a junior student, this brief musical
career gave full vent to my passionate creativity and imagination. The
process of musical composition gave me the same pleasure as
undertaking mathematical induction and deduction. In creating my
music, I started with a motif, followed by a few segments to
succinctly present my musical ideas, and finally expanded them into
full-length structure with the rigorousness and harmony characteristic
of equation derivation. For me, musical creation and mathematic
exploration are not contradictory, but are essentially the same—they
are all about the underlying order, structure and beauty of the
seemingly random phenomena.
I displayed recognizable talents in mathematics after I entered XX
Middle School, where classes were conducted in a seminar-like
environment, it was I who was always the first to solve the questions
and to go to the blackboard to explain the steps whereby the solution
was obtained. The classical joke of the class was that I, instead of
Mr. XX our mathematics teacher, was the person who did the real
But the most defining experience occurred when I happened to read the
formula for calculating the area under the parabolic curve. I was
enamored by the formula and was eager to know how it was derived.
Failing to deduce the formula by myself, I raised this issue to Mr.
XX, who refused to give me any instruction, saying that it might
distract my attention and energy. But my stubbornness prevailed.
Without referring to any materials, I spent weeks deriving the formula
and after repeated failures my efforts paid off. I derived the
equation, which I was surprised to find during my undergraduate
education essentially similar to the Euclidean approach in the ancient
The impact of this experience proved profound. I started to realize
the importance of imagination to mathematics and recognize my talent
in this aspect. Before I completed my senior middle school, I had read
Polya’s How to Solve It and other classics of mathematics, which bred
in me the determination to take up mathematics as my major when I was
admitted into XX in 1999.
What is special about my undergraduate program is that, instead of the
usual 4-year duration, the students of XX up to the Grade 99 spend 5
years on their program. As a result, I have attended many more
courses, which are also more difficult, than students in the
succeeding grades. I have taken and am going to take 11 courses
specifically for graduates. Having completed more than 200 credits for
the first four years, I have laid a more solid foundation in my area
of specialization and been exposed to a much wider range of
specialized knowledge. My overall GPA, which is well over 3.0, has
shown sustained ascendancy as I gradually shifted my focus from
extracurricular activities in the first two years to formal academic
study ever since then. In terms of my major, my GPA was 3.68 and I
achieved the highest scores in the entire class in such courses as
General Topology, Advanced Number Theory and Linear Algebra II. I have
been awarded second-class scholarship once and among 50 students in my
class my ranking is top 10.
Looking back on my past academic pursuit in mathematics, I find myself
well grounded not only in classical Mathematics but also in specific
subjects of modern mathematics. Analytic Number Theory by Prof. XX
allowed me to master the fundamentals of Number Theory and to
understand the celebrated remarks with which Gauss emulated the Number
Theory. Prof. XX’ s course Communicative Algebra not only exposed me
to the ideology and methodology of Algebra but also ushered me to
contemporary mathematics and gave me introductive background to
Algebraic Number Theory and Algebraic Geometry. Algebraic Geometry
delivered by Prof. XX, made me really perceive the power and beauty of
modern approaches in uncovering the identical or similar
characteristics behind the apparently diverse issues. I am quite
familiar with classics of mathematics such as Fermat’s Last Theorem by
Edwards, Basic Number Theory by Andre Weil, Commutative Algebra by
Boulbaki, which I self-studied. Such a comprehensive curriculum and my
self-education have enabled me to master fundamental knowledge and
develop specialized mathematical thinking.
Not contented with grasping established conclusions and existing
knowledge taught in class and books, I have the habit of speculating
on the underlying implications of the known axioms and of testing the
known principles through different mathematical approaches. I also
like to apply the knowledge of one subject to the solution of problems
in another subject, like what I did in using the techniques of Matrix
theory to simplify and work out a problem in Algebraic Number Theory.
In addition, while working on difficult problems, I made it a point
not to consult any hints in order not to be confined by established
conventions. In this way, I have repeatedly tasted the joy of
exploring new territories and letting my imagination soar.
As an undergraduate, I am particularly proud of my two achievements.
The first is the Undergraduate Research Program of XX titled “XX” in
which a classmate and I came under the direction of Prof. XX. In this
privileged three-person environment, we had in-depth discussions on
several selected topics of Number Theory and had extensive exchanges
of views and skills with Prof. XX. We offered totally new approaches
to some problems in Algebraic Number Theory and my classmate and I
published two papers in a Journal of Mathematics of our department.
For this reason our group was awarded the honor Outstanding Student
Research Program and I was awarded the Silver Medal for National
Science Talents Base. In another development, Prof. XX, based on his
intimate understanding of my knowledge in Algebraic Number Theory,
invited me to give lectures for two weeks on the subject to graduate
students whom he was teaching the course Analytical Number Theory.
This was the first time in XX that an undergraduate gave lessons to
graduates and naturally it created quite a sensation.
I first learned about the University of XX in I Want to Be
Mathematician by P. XX, who talked about the academic atmosphere and
the academic achievements of the faculty there. When I tried through a
variety of channels to further know about your university, I came to
learn your school motto XXX. I became deeply impressed by it
represents the objective that I have always been pursuing. Your
program has a very strong faculty in the field of XX, a fact which is
acknowledged worldwide. I am particularly interested in XXXXX. Some of
my alumni have undertaken graduate programs at your university and
they have given unanimous and most enthusiastic praises of your
program. D. Hilbert once claimed, “I despise the mathematician who
studies a board with an auger in his hand and bores a hole in the
thinnest part.” I like to face challenges and take on difficult
undertakings by pursuing a Ph. D. program in pure mathematics. Ever
since then I have regarded your University, with a high ranking in the
field of mathematics among all the American universities, as my
In my proposed program, I like to concentrate on Algebra, Algebraic
Geometry and Algebraic Number Theory, three mainstream subjects of
mathematics. Specifically, I am interested in Elliptic Curves,
Cyclotomic Fields, and K-Theory. In choosing to study in XX, I wish to
learn the latest developments in interdisciplinary studies in the
fields that I am interested in. I can also keep informed of the major
research findings in recent years. After completing your Ph. D.
program, I plan to take up a teaching and research career in a major
Chinese university, perhaps my Alma Mater. I will feel satisfied only
when I have made fruitful achievements in my scholarly pursuit.