Re: How seriously do you take mathematics?
- From: "Nora Baron" <norabaron@xxxxxxxxxxx>
- Date: 19 Apr 2005 14:15:33 -0700
Mike H wrote:
> I have psychotic depression right now. I am so sad about having no
friends
> and no girlfriend that only fascinating things continue to interest
me. I am
> talking about little equations like e^(i*Pi) = -1 and other
mysterious (and
> uneasily proved) facts.
>
Mike,
I am sorry to learn that you are depressed. I would have to say that
feeling bad in that way is ordinarily a very serious impediment to
doing mathematics, and I admire the strength of your spirit, that
even though feeling down, you find some solace in math.
> Do any mathematics professors take their subject as seriously as they
> possibly can?
Motivations vary all over the map. The main motive for some
mathematicians is professional advancement, which is obtained by
getting stuff published. Others would be drawn to doing math even
if they were stranded on a desert island and there was no way that
doing it would benefit their career. Some have a huge natural
talent for it - hard to explain, because in human evolution, it
probably had little survival value. Some people do math mostly
for recreation. Most math professors will say they take their
subject seriously, but that should be questioned.
>Do you mainly stick to your field, or do you memorize all the
> axioms of set theory and philosophize about the continuum hypothesis?
I don't memorize much of anything. I have not spent much time
on the continuum hypothesis. My own areas of interest are fairly
broad - topology, algebra, statistics, analysis - but not all that
deep, with a few exceptions. I think of math as an empirical
science, like physics - what we call axioms are analogous to what
physicists would call basic physical laws (e.g., the inverse
square law for gravitational attraction) and ultimately they
are based on *observation* - we note that 1 object plus 1
objects equals 2 objects, and we abstract that. Mathematical logic
is, I think, the least intuitive of the branches of mathematics,
and (for me) harder than most.
> I ask
> this because I am a resolute Platonist that believes that
mathematical truth
> is hidden within the written symbols on paper.
>
There may be two kinds of mathematicians: those who think very
symbolically and manipulate symbols according to rules, and those
who think primarily physically and intuitively. I am very
definitely in the second group. I think there is *physical* truth
behind written symbols on paper.
> I am taking axiomatic set theory seriously right now, and as much as
I am
> fascinated by the continuum hypothesis, all the little work involving
> quantifiers can be a pain in the neck. As much as I love mathematics
I feel
> that in the end I must regard it as merely useful and not
fascinating.
That's too bad. I would not recommend axiomatic set theory as a
way to get started in math. Rather I would suggest basic number
theory or geometric topology or applied math.
> I
> know that happiness has to do with neurotransmitters so I one day
hope to
> study chemistry. :) If you don't mind my asking, in what sense do you
enjoy
> mathematics as a profession, knowing that it is your job?
I like to solve problems that are just hard enough to be
challenging to me. Set theory and logic are a bit too dry and
do not seem to turn on any creative impulses for me. What I
consider a great theorem is something like the Borsuk-Ulam
theorem or the Fundamental Theorem of Algebra or parts of
Galois theory. I would like to (but have not) study the proof
of Dirichlet's great theorem on primes in arithmetic progression.
You can get so quickly into very hard problems where I at least
have no clue how to start - for example, are there infinitely
many primes of the form n^2 + n + 1 ?
Nora B.
.
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- How seriously do you take mathematics?
- From: Mike H
- How seriously do you take mathematics?
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