Tridymite is a silicon dioxide (silica) mineral that crystallizes at low pressure and high temperatures in excess of 800 degrees Celsius (1,472 degrees F). As far as we know, it is only associated with the high temperatures and conditions seen in silicic volcanism — volcanoes with magma containing a large proportion of silica. These geological processes are the result of plate tectonics and flowing water on Earth, but Mars doesn’t have either of those.
The tridymite on Mars was found in Gale Crater after Curiosity drilled down in search of interesting minerals, which were identified via x-ray examination. After confirming a high concentration of tridymite in the samples, NASA began looking at terrestrial processes that might provide an alternative way of producing the mineral — something that Mars does have. According to the paper, they’ve come up with no alternative.
Other researchers are sure to begin looking for a lower temperature processes that can produce tridymite now, but maybe we’re just wrong about Mars’ past. It’s possible the planet was once much more geologically active than we thought. These levels of tridymite would also mean that Mars had more water available on the surface as well. There’s only so much we can learn here on Earth, though. Mars is a very different environment, and it’s possible there are processes active there that we don’t yet understand. We might not have an answer to this mystery until we get another rover to the planet with new instruments.