What is the age of the Gamburtsev Mountains?
The Lamont-Doherty Earth Observatory describes the Gamburtsev Subglacial Mountains (GSM) as being like:


  opening the door of an Egyptian pyramid and finding an astronaut inside.  There is no good reason for an astronaut to be inside an Egyptian pyramid just as there is no good reason for a major mountain range in the middle of East Antarctica.


Despite being buried under a considerable amount of ice and observed to have had slow erosion rates since at least the Permian (Cox et al. 2010), accessible detrital material has been determined to have been deposited as fluvio-deltaic deposits in Prydz Bay (Cox et al. 2010; Flierdt et al. 2008).

$\ce{U-Pb}$ dating of dertital zircons and $\ce{^40Ar/^39Ar}%edit$ dating of detrital hornblendes age them as ~530 Ma and ~519 Ma respectively, with no evidence of any yonger volcanic contributions (Flierdt et al. 2008).  These dates led Cox et al. (2010) to postulate that the GSM formed during the Pan-African Orogeny.

Veevers and Saeed (2013) suggest that detrital zircons found in the Ellsworth Land–Antarctic Peninsula–Weddell Sea–Dronning Maud Land sector of ages 1.4-1.7 Ga, 1.9-2.1 Ga and 3-3.35 Ga possibly have their provenance from the GSM.

In summary, in the absence of direct measurements of GSM petrology, detrital material from pre-glacial erosion has suggested that the youngest tectonothermal evidence is for a Cambrian age of the GSM.

References

Cox et al. 2010 Extremely low long-term erosion rates around the Gamburtsev
Mountains in interior East Antarctica, Geophysical Research Letters

Flierdt et al. 2008 Evidence against a young volcanic origin of the Gamburtsev Subglacial Mountains, Antarctica Geophysical Research Letters

Veevers and Saeed, 2013 Age and composition of Antarctic sub-glacial bedrock reflected by detrital zircons, erratics, and recycled microfossils in the Ellsworth Land–Antarctic Peninsula–Weddell Sea–Dronning Maud Land sector (240°E–0°–015°E) Gondwana Research