I used to think that Buddhism was compatible with modern science, but not anymore.
That Buddhism is scientific is not a new idea. As Donald Lopez explains -
Statements about the compatibility of Buddhism and science were being made in the 1860s—in Europe and America during the Victorian period, as Buddhism became fashionable in intellectual circles, and at the same time in Asia, as Buddhist thinkers were defending themselves against the attacks of Christian missionaries… Some even went so far as to declare that Buddhism was not a religion at all, but was itself a science, a science of the mind. 
This idea that Buddhism and science are compatible was popularised in the 1960s by authors like Fritjoff Capra, who in his best selling The Tao of Physics had argued that Western science and Eastern religions were now converging. In the 1990′s, former monk Stephen Bachelor argued the case for a socially engaged, secular Western Buddhism free from its cultural and religious accretions in Buddhism Without Beliefs – a book that subsequently prompted me to investigate for myself what Buddhism had to offer.
However, given that the Pali Cannon is generally accepted as the wellspring from which all main variants of ‘Buddhism’ flow, we cannot in all honesty just ignore the fact that the suttas are peppered with references to devas inhabiting other realms of existence, or that the Enlightened Noble One is referred to thus –
Itipi so bhagavā arahaṃ sammā-sambuddho,
(He is a Blessed One, a Worthy One, a Rightly Self-awakened One),
Vijjā-caraṇa-sampanno sugato lokavidū,
(Consummate in knowledge and conduct, one who has gone the good way, knower of the cosmos),
Anuttaro purisa-damma-sārathi satthā deva-manussānaṃ buddho bhagavāti.
(Unexcelled trainer of those who can be taught, teacher of human and divine beings; awakened; blessed).
As Stephen Ruppenthal notes in his commentary on the Dhammapada, the Buddha urges us time and again to attain nibbana by suspending our creative thinking – the very process that all humanists value so highly. 
Moreover, the Kalama Sutta – so often wrongly interpreted as meaning that we are free to basically pick and choose what bits of the Dhamma accords with our own (deluded) experience – is actually a call for faith in the Buddha, though not the blind faith one often sees in those who follow a theistic path. The faith that’s being talked of here is more akin to trust or confidence that Buddha’s advice will yield good results (i.e. enlightened liberation from stress) if practiced sincerely and intelligently, neither accepting it on hearsay nor rejecting it according to one’s personal prejudices.
When I first came to Buddhism I was only interested in making my life more peaceful and satisfying. The following paragraph describes exactly the attitude I had –
Newcomers to Buddhism are usually impressed by the clarity, directness, and earthy practicality of the Dhamma as embodied in such basic teachings as the Four Noble Truths, the Noble Eightfold Path, and the threefold training. These teachings, as clear as day-light, are accessible to any serious seeker looking for a way beyond suffering. When, however, these seekers encounter the doctrine of rebirth, they often balk, convinced it just doesn’t make sense. At this point, they suspect that the teaching has swerved off course, tumbling from the grand highway of reason into wistfulness and speculation… A few critics even question the authenticity of the texts on rebirth, arguing that they must be interpolations. 
For years I operated under the humanistic assumption that the teachings on kamma and rebirth and cosmology were either cultural accretion, or else the Buddha may actually have given them in deference to the rigid social hierarchy of his time. But as Ven Bhikkhu Bodhi says, a quick glance through the Pali scriptures soon reveals that these claims just don’t bear up to scrutiny.
 Donald S. Lopez, ‘The Scientific Buddha: Why do we ask that Buddhism be compatible with science?‘, on Tricycle website (accessed 20 February 2013)
 Stephen Ruppenthal in Eknath Easwaran Tr), The Dhammapada (2nd Ed), Niligiri Press, 2007, p. 114.