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the author's counterparts claim that mammoths were still around until just a few thousand years ago. The author's claim mammoths were overhunted to extinction may also be exaggerated, in light of the numerous animals that co-existed with mammoths, i.e., horses, camels, lions, tigers and bears.

http://packrat.aml.arizona.edu/Journal/v37n1/vartanyan.html
Last upper molar from the bed of the lower Mamontovaya River (N-MAM-6) BC 2574-2464
Tusk (8 cm diameter (d)) from the bed of the lower Neozhydannaya River BC 2192-2038

http://findarticles.com/p/articles/mi_qn4176/is_/ai_n24977637
Fossils of mammoths, bison, cave bears and horses all seem to disappear from parts of Alaska and Siberia around

35,000 years ago.

“And then they show up again around 10,000 years later,” he said. “So they came in from elsewhere.”

http://www.blm.gov/education/feature/2000/ut/

Gillette believes that present-day vegetation in the area is similar to what was here 11,500 years ago. Mammoth remains are most often found in areas that were covered by grasslands during the last Ice Age; in this area, there were likely both conifers and grasses, probably fed by a good water source. The mammoths co-existed with other now-extinct species, such as saber tooth tigers, giant ground sloths, musk oxen, camels, horses, tapirs, and lions.