Yes, Islam is compatible with modernity because it is Muslims who spearheaded the much celebrated science we have today having taken a leaf from past modern civilizations and putting them into good use. Muslims of the past studied the sciences strenuosly; they translated original manuscripts from the Greeks and Romans thus creating broader instruments of greater significance some of which remain in use to this day. Muslims were pioneers in the fields of astronomy, astrology, oceanography and navigation, algebra, mathematics, and medicine which we reference exhaustively quite often in our pursuit of new scientific innovations.
Muslims plied the oceans in search of new lands and any existing novel societies ; they traded with far distant lands long before European civilization; they set up new posts and new administrations anywhere they set foot on; they introduced Islam to far places; in attempting to forge new relationships they intermarried with the local hosts finally leading to mutual understanding and social harmony among different breeds.
Islam penetrated the corners of the world with the speed of light with the Qur'an being the guiding light. Communities that were immersed in savagery and barbarism; those who lived in utter ignorance; and many who lived dormant lives saw themselves transfromed within a short period. Hostilities diminished in places where Islam was introduced and a new era of civilization had gotten off the ground with the introduction of law and order.
Muslim explorers introduced modern farming methods which drastically lowered levels of hunger prevalent those days and with their new discoveries, they were, in the long run, able to resuscitate many dwindling economies.
Today, due to selfish segmentation of Muslims into various denominations, the erronous misinterpretation of the Qur'an and the sheria by enemies of Islam and by semi-literate Muslims, the alarming manner in which Islam is being pushed into a corner and the negative perception of some non-muslims towards this divine religion, is, nothing but a distorted way of tarnishing the good name and reputaion of a divine religion whose absence from this world, would, without doubt, reverse entire humanity into a state of ignorance as witnessed in Islam's initial inception when the proud Qureish tribe of Arabia burried their daughters alive, gambled with their wealth, practised divination by arrows, drunk wine excessively, and above all worshipped idols as intermediaries.
In conclusion, whatever is contained in science is plainly content in the Qur'an i.e. from the smallest atom to the massive heavens we aspire to conquer and that without Islam, the modernity which we assume to be a western innovation, is, without doubt, compatible with Islam and is, in the real sense, an Islamic invention.