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H. Timothy Choi

At the Honda Center

Department of Mathematics
University of California, Irvine
Irvine, CA 92697-3875
or
http://math.uci.edu/~tchoi
RH 540M
(949) 824-5390

I am a candidate for the Ph.D. program. I graduated from UCSD (2002) with B.A. degree in mathematics. I am studying number theory and a part of UCI Number Theory group.
   Number theory is a branch of mathematics which studies integers with whatever tools available in mathematics. Their problems, whether solved or unsolved, often look naively easy to understand so that anyone with sound math background can start working on some cases to verify validity of the assertions, but it, most of time, is pretty scary how complicated their development towards the solutions become or will become.
   However, not every number theory problem requires the most sophisticated arguments in mathematics. P. Erdös' proof of the theorem regarding counting prime numbers is such an example for which he only used elementary methods to prove. By the way, my Erdös number is 3.
   Among some mathematicians number theory is believed to be the queen of mathematics, which was once quoted by the prince of mathematics, C. F. Gauss. My personal interest includes parables told by Jesus among other things, and my hobby is to study differential geometry.

A variant of an old math joke and its moral

One day a nonzero constant function k, an exponential function e^x, and 'his friend' were walking on a street. Soon turning around a corner, k noticed a guy walking towards them and became pale-faced.

   e^x: "What's wrong?"

   k: "That guy is a differential operator. He will differentiate me. Then I will vanish to zero! I am out of here!"

and he ran away.

   e^x: "I ain't afraid of him. I am an exponential function."

When they confronted each other, e^x introduced himself to the guy.

   e^x: "I am an exponential function e^x."

   Guy: "I am d/dy."

   e^x: "Oh no!"

But he was saved because 'his friend' with him was a change of variable.

Note that the joke finishes with a happy ending contrary to the original joke where e^x ends his life with a tragic vanishing to zero. The moral of the joke is that "let's be a friend who can help friends in need."

Pascal, Blaise (1623-1662)

We arrive at truth, not by reason only, but also by the heart.
Pensees. 1670.

Unknown

If you think that you can, then you can.
If you think that you cannot, then you are right.

* A poem written by my ancestor

Here is a beautiful picture of Dokdo. Dokdo (Lonely Island) is an island in Korea.

Erdös, Paul

Imagine an alien force,
vastly more powerful than us landing on Earth
and demanding the value of R(5, 5)
or they will destroy our planet.
In that case, we should
marshal all our computers and all our mathematicians
and attempt to find the value.
But suppose, instead, that
they asked for R(6, 6),
we should attempt to destroy the aliens.

Book I Ode XI, Quintus Horatius Flaccus

Ask not - we cannot know - what end the gods have set for you, for me;
nor attempt the Babylonian reckonings Leuconoë.
How much better to endure whatever comes,
whether Jupiter grants us additional winters or whether this is our last,
which now wears out the Tuscan Sea upon the barrier of the cliffs!
Be wise, strain the wine;
and since life is brief, prune back far-reaching hopes!
Even while we speak, envious time has passed:
pluck the day, putting as little trust as possible in tomorrow!

* A translation of the quotation on http://math.uci.edu/~gpatrick.

Camus, Albert

There is but one truly serious philosophical
problem, and that is suicide.
Judging whether life is or is not worth living
amounts to answering
the fundamental question of philosophy.
All the rest
—whether or not the world has three dimensions,
whether the mind has nine or twelve categories—
comes afterwards.

You can tell whether a man is clever by his answers.
You can tell whether a man is wise by his questions.

Dosan

Despair is death of young men,
and when young men die, the nation dies.