The Rebbe's letters on faith and reason, and on Torah and science:
Science and faith do not conflict. Science does not contradict faith: it rests on human assumptions and hypotheses, while Torah is absolute truth (IK 1704). Science deals only with what can be measured and cannot deny what lies beyond it (IK 4209). Scientific theories keep changing, while the Torah tradition remains constant (IK 4414), and science itself admits that its conclusions are probable rather than certain (IK 9114). Modern achievements such as landing on the moon pose no challenge to Torah or faith (IK 10213). Both Torah study and scientific inquiry uncover hidden powers within creation (IK 8831).
Specific questions. Scientific claims about the age of the world are based on speculative assumptions, not real evidence (IK 3868). Reading each day of Creation as an era contradicts Torah tradition (IK 1803). Torah sources and rational analysis both challenge evolution as commonly presented (IK 1996). By relativity, science cannot say definitively whether the sun or the earth moves (IK 6877, 8677). Differences between the Rambam's figures and modern science arise because they measure different things (IK 8454). The Torah's "four elements" are foundational qualities, not physical substances (IK 7242_star). On Tanya and anatomy, see IK 8505; on Chazal's views of astronomy, see IK 001.
Faith beyond understanding. What we accept today with faith may become clear to the intellect as we grow (IK 2649). Asking questions is encouraged, but one must not delay action until every question is answered (IK 10137). True faith transcends intellectual understanding, especially in hard times, and means trusting G-d even when we cannot comprehend His ways (IK 7671, 9124). Concern over one's faith is itself evidence of faith (IK 6475), and every Jew has an innate simple faith (IK 7513, 8333).
See also: Faith and Chassidus – Free will, Providence and miracles; Bitachon – Everything happens for a reason; Education – Secular studies and college.