Intelligent designers: move to Texas!

Texas on the news again: They are considering a bill to protect creationists from discrimination. I heard about it last Friday from a postdoctoral student of our department and checked it out. There is an article about it in Mother Jones. Using the language and rationale of political correctness, the author of the bill, Republican state representative Bill Zedler proposes:

HB 2454, Section A51.979.A:
A PROHIBITION OF DISCRIMINATION BASED ON RESEARCH RELATED TO INTELLIGENT DESIGN.
An institution of higher education may not discriminate against or penalize in any manner, especially with regard to employment or academic support, a faculty member or student based on the faculty member's or student's conduct of research relating to the theory of intelligent design or other alternate theories of the origination and development of organisms.

Texas is the state where the major proponent of creationism/intelligent design, William Dembski, teaches: He is professor at the Southwestern Baptist Theological Seminary in Ft. Worth, he conducts research in theology by means of creationism/intelligent design, and desperately tries to use pseudo-mathematics in support of his theological claims. Dembski did a PhD in mathematics but he immediately switched to theology. He is not alone in Texas. There are many creationist pseudoscientists there who can find lots of money by religious fundamentalists; the latter will happily fund the former in order that they use pseudo-science and pseudo-mathematics to "prove" theological claims, ranging from denial of evolution to belief that the Earth is a few thousand years old.

Now the state of Texas is trying to pass the aforementioned bill. In my opinion, this will have at least two effects:

1.  If a faculty member in a Texas university cannot do serious mathematics or science then he or she can turn to creationism and publish papers in pseudo-scientific creationistic journals.  He or she then will ask to be tenured and, based on the above law, he or she should not be discriminated against.
2.  Funding for creationism will have to be considered as academic funding. The law justifies creationism as an academic field of study.
3. Academics with creationistic tendencies will seek jobs in Texas universities.

I have served in Texas as a faculty member and know the mentality. Although there are many academics who will be angry at such a bill, there are several others, academics or not, religious fundamentalists, who will espouse this bill and use it for theological purposes.

A new very short proof of the fundamental theorem of algebra

I've always been intrigued by the fundamental theorem of algebra (every nonconstant polynomial with complex coefficients has a root), not least because I don't know any proof which uses algebra only. Earlier, I posted an easy proof in this blog, one that uses Cauchy's theorem.There is a recent proof (Oswaldo Rio Branco de Oliveira, Mathem. Intellig., March 2011), which is almost trivial. It goes as follows (and this is a chance for me to see if the embedded LaTeX script works...):

Let $P(z)$ be a polynomial of degree $n$. Since $|P(z)|$ is a nonnegative continuous function, tending to $\infty$ as $|z|$ tends to $\infty$, it has a minimum at some point $z_0$:

$|P(z)| \ge |P(z_0)|$, for all $z$.

By division of $P(z)-P(z_0)$ by $z-z_0$, write

$P(z) = P(z_0) + (z-z_0)^k Q(z-z_0),$

where $Q(0) \not = 0$. Since $P(z)$ is nonconstant, the integer $k$ is $\ge 1$.
Therefore

$|P(z_0) + (z-z_0)^k Q(z-z_0)|^2 \ge |P(z_0)|^2$, for all $z$,

and, expanding the square,

$|z-z_0|^{2k} |Q(z-z_0)|^2 + 2 \Re \{ (z-z_0)^k Q(z-z_0) \overline{P(z_0)}\} \ge 0$, for all $z$.

Let $z=z_0 + r e^{i \theta}$, divide by $r^k$, and let $r$ tend to $0$. We obtain

$\Re \{ e^{i k \theta}  Q(0) \overline{P(z_0)}\} \ge 0$,  for all real $\theta$.

It is an easy exercise in algebra that, if $\alpha$ is a complex number such that $\Re \{ e^{i k \theta} \alpha\} \ge 0$ for all $\theta$, then $\alpha=0$. Hence $Q(0) \overline{P(z_0)}=0$. Since $Q(0) \neq 0$, we obtain $P(z_0)=0$.