Does modern science (e.g., “big bang” theory, evolution, the age of the world) contradict traditional readings of the Torah?
Probably, but science is getting better all the time and one can expect agreement eventually… Seriously, there are numerous neo-traditional readings that put new interpretations on various commentaries and are allegedly compatible with Orthodoxy. Judaism has a long tradition of not interpreting the creation narative of Genesis 1 literally. Rambam [Maimonides], for example, warns at the beginning of his Mishneh Torah that the literal reading of the opening of Bereshis [Genesis] is for the masses. [The non-literal reading he had in mind was metaphysical, not scientific. See The Guide for the Perplexed.] Both literalism and non-literalism have a long history, yielding a variety of resolutions of the problem of creation and science. Here are some solutions: • Rejection of scientific data. Since, as one opinion in the Talmud has it, Adam was created as a fully mature man of 20, and trees were created fully grown, it is clear that this opinion would hold that the universe as a whole was fo