Advances in mathematical understanding can lead to sudden spurts of innovation and technological discontinuities. Mathematical insight can therefore lead to strategic surprise that can provide economic, scientific and technological breakthroughs which can have profound geopolitical significance. For example, the global economy, and with it the security of billions of people, is dependent on the security of "unbreakable" (mathematical) codes. But are they unbreakable?
This is why the major global players as well as some of the smaller ones place such emphasis on mathematics research and why the job title algorithm engineer has come into existence.
There are several possible developments that might lead to the Singularity - a mathematics breakthrough is one of them.
And then there is just the mystery, beauty and elegance of this lens on the universe and perhaps what lies beyond.
