I would like to see some proof that radiometric dating is fallable. I recall reading a study by the Lamont-Doherty Geological Laboratory of Columbia University at Palisades, N.Y. which indicated that some early carbon-14 dating techniques had a potential margin of error of up to 3,500 years. I think this is WELL within a 1% margin of error for 4,540,000,000 years...which is the current estimate of the age of our planet.
In any case, accurate tree ring records of age are available for a period extending more than 9,000 years into the past...do Christians doubt tree ring dating as well? How about the fact that the Chinese were making beer from rice at roughly that same time (7,000 BCE). This was...of course...2,000 years AFTER the Egyptians and Mesopotamians were brewing beer (9,000 BCE). That's just the history of beer...I can get other examples we have proof of (from written records) if you'd like.
Of course, there is also the age of the Universe itself we should be looking at...considering that God made the Universe and the Earth in the same week. Current estimates place the age of the Universe at 13,750,000,000 years (+/- 1.2%). That number is based on many things...least of which is the assumption that a Creator wouldn't have created a Universe with light and other forms of radiation from distant stars and phenomenon ALREADY in transit to earth...for example, on 23 April 2009 a gamma-ray burst was detected which was later confirmed at being over 13 billion years old. Background radiation and expansion rate measurements are based on the assumption that the "Big Bang" occurred...I'm sure you are fully prepared to ignore all scientific proof of that "theory", so no further explanation is really worthwhile.
Or, some contradictory books written by outcasts and recluses between 3,000 and 1,700 years ago could provide a true account of the history of humanity. Either way, right?
You call yourself a man of science and faith....to be a man of science means that you embrace...not any particular scientific theory...but the scientific method itself. This method seeks to explain the events of nature in a reproducible way, and to use these findings to make useful predictions. Taken in its entirety, the scientific method allows for highly creative problem solving whilst minimizing any effects of subjective bias on the part of its users. How can you do that and stay true to your faith, when your faith requires that you believe regardless of any and all proof (or lack thereof)?