Science and Buddhism have both been often quoted as being compatible, especially in areas regarding evolution, quantum theory, and cosmology.
There are many cases where the world of science will discover something, only for us to realize that it matches inline with the Buddhist thought/philosophy. Or in many cases, the finding has already been discovered by Buddhist philosophers at a much earlier time.
E.g. The previous study of an atom was "confirmed" to be matter. However, scientists altered that finding to state that it's nothing but mere energy, and even the concept of energy is disappearing gradually and scientist don't even know what to call it. The concept of energy is nothing but a concept, and in extension, so too is everything around us.
Sounds really familiar lol.
E.g. Previously, it was thought that Earth was the center of the universe. Now it is of general understanding (unless you've been living under a hole), that we are but a speck in the vast universe. As to the nature of the universe, the Buddha said that the beginning and ending of the universe is inconceivable. The universe is vast, and there are indefinite world systems and living beings.
For science, this doesn't even touch the topic of there being different planes of existence - although, paranormal events does help to entice the curiosity of scientists!
There are also many cases where science will turn to the Buddhist world. During the 1970s, several experimental studies suggested that Buddhist meditation could produce insights into a wide range of psychological states.
I found this article a while ago on how the brains of Buddhist monks were scanned in a study on meditation.
http://www.bbc.co.uk/news/world-us-canada-12661646. The neuroscientist speaks about how there seemed to be an intrinsic and extrinsic way the brain functions. Sounds a little like the gross and subtle mind...
It's rejoicing to see the 12th Gyalwang Drukpa, as well as Buddhist nuns, on Reuters news. It shows how compassionate they are... any way to get the Dharma to others.
Pretty awesome how the title of the article is "Kung fu nuns teach cosmic energy to CERN scientists". The world of science should open their minds up to Buddhism. It may speed up their findings much faster!