First approach: DENY
(Example: That's not a woolly mammoth! That's just an ordinary elephant with a few abnormalities!)
Second approach: LIE
(Example: Sure, it's a woolly mammoth, but it walked the earth less than 6000 years ago!)
I'm sick of this. Sick of the lying and denying because Jews should be above such shenanigans, and also because if you look back less than 200 years you can find a far more satisfying solution.
Yisroel Lipschitz of Danzig (1782-1860) was the author of Tiferes Yisroel, the popular commentary on the Mishnayos which can be found in almost every Shul. In the back of Sanhedrin, you'll find a long essay of his called "Derush Ohr HaChayim” (Homily on the Light of Life) Struggle though several difficult pages on the origin of the soul and you'll arrive at a facinating discussion of paleontology. Money quote:
In the year 1807... they found in Siberia... a great elephant... whose skelteon now stands in the Zoological Museum in Petersburg... We already know of a giant creature found in... the city of Baltimore... bones of this creature have been found in Europe, too. This creature had been named mammoth... they have found... iguanodon... whose height was 15 feet, and whose length was as much as 90 feet...there is yet another creature called megalosaurus... from all this it is clear... [citing kabbbalists, Gemarahs, Rabaynu B'chaya, the Ramban, and Ibn Ezra] that the world has been destroyed and renewed over and over again as many as four times...One of the kabbalists he cites has a formula, using this idea of cycles, that suggests the universe is several billion years old. His own writing suggest he thought each of those 4 cycles was at least 7000 years, and perhaps as many as 49,000 years. Another calculates the age of the universe at as much as 1.5 billion years
Lesson: Did the Tiferes Yisroel lie or deny? Did he act like Ed, who himself claims to act in the name of so-called gedolim? No, he did not. Instead he faced the facts, with open eyes.
Yoinoson Schreiber: DovBear, Tiferes Yisroel and the Woolly Mammoth
DovBear: 5000 years old? Not according to Chazal