I'm trying to find the birth year for the mathematician Thomas Hales.
He is currently a professor at the University of Pittsburgh. He is
known for his work on the Kepler Conjecture. I believe his birth year
is 1958 but I am trying to find confirmation of that.

Dear mbhenry,

I have found only one source that mentions Thomas C. Hales' birth
year, but I have no reason to doubt that the information is correct.

On 5 July 2000, the German newspaper "Berliner Zeitung" published in
its science part an article on Thomas C. Hales who then had held a
speech at the important annual convention of the mathematical
departments of the Berlin and Potsdam universities. After a
description of Mr. Hales' scientific achievements, the article says:

"Thomas C. Hales wurde 1958 in San Antonio (Texas) geboren", which means:
"Thomas C. Hales was born in 1958 in San Antonio (Texas)".

Since I assume that the universities had sent press material with
biographical information on their famous guest or provided something
similar to the newspapers, I consider this date trustworthy.

Source:
Berlin Online: Text Archive Berliner Zeitung - Wissenschaft - "Er
knackte zwei Jahrhunderträtsel. Der Mathematiker Thomas C. Hales hielt
die renommierte Euler-Vorlesung in Potsdam"
http://www.berlinonline.de/berliner-zeitung/archiv/.bin/dump.fcgi/2000/0705/wissenschaft/0007/

Search terms used:
"thomas hales" 1958
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"thomas c hales" 1958
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"thomas  hales" "san antonio" born
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Hope this is what you were looking for!
Regards,
Scriptor

Great answer.