That mountain is mount Evans (3,950 m), located in the Sentinel Range in inner Antarctica (S 78.30698°, W 85.91698°), the highest mountain range in the continent.
(Map courtesy of @KeithMcClary see comments)
In general, geologic features become smoother by erosion (by water, glaciers or wind). These peaks are so high that there were never covered by glaciers and the area is so cold that liquid water almost doesn't exist. Therefore, there is no erosion by water (or freeze thaw cicles), neither the wind, because of the lack of dust/sand particles (the wind doesn't erode by itself, what do erode are the particle it carries). Consequently, those mountains are so sharp due to the lack of erosion.
Take for example any rock: If you break it into pieces, those pieces will have sharp edges, with no erosion those sharp edges will persist. Similarly, at a larger scale, sharp ridges and edges on mountains can persist and withstand the pass of time.
This is me on mount Tyree camp one, during The Omega Foundation mapping expedition of 2005, mount Evans is in the background