Science has proven to be very forthright about correcting mistakes in this field. It's quite easy to get a grasp of the fundamentals of carbon dating. Also, you may find that reading about the different strata of rocks, and how scientists arrive at the age of mountain ranges and such, is indeed. interesting, and just makes lot of sense to the average person whose willing to take a bit of time and study up on the subject.
As a general comment, I get the point about 'pure' science. I instantly thought of this;`
Tesla = profound curiosity, genius and the passion to *discover* and *share* ('pure' science)
Edison = brilliant, perhaps, but corrupted by self-interest ('not-so-pure' science)
..............
Sheesh, where would we be without people who questioned the current norm? And as for Mathematics being 'cut and dried' and 'easily taught' ........ ahaha, you have just betrayed a profound ignorance of the ART of higher mathematics.