Question
Does Science contradict Hinduism? How to deal with scientific discoveries that don’t line up with Vedas?
Answer
Hinduism is an intrinsically scientific religion.
The Vedas themselves accurately describe very complicated geometric concepts including six-dimensional spaces, distances between celestial bodies, and using changing skylines to measure time, just to name a few examples ("Vedic Geometry Course" Dr. S. K. Kapoor). If you follow the Dhashavataram carefully, you will see that it perfectly mirrors the evolution of life on Earth as well as the emergence of increased social structure (and eventual decline) among humans.
Furthermore, it has been written that the Vedas themselves are to be consulted only in matters which cannot be resolved by either Pratyaksha (direct observation) or Anumana (inferences and inductions based on said observations, or in other words science).
The third category of knowledge, Sabda, refers to the Vedas themselves. Smritis, Itihasas, and Puranas are also included here where they "do not contradict the Vedas". Sabda is to be relied on to resolve questions which either have not yet been answered by Pratyaksha and Anumana (e.g. how does physics behave in a six-dimensional space?) or cannot be answered (e.g. what happens to the Atma after death?).
Info above paraphrased from: "A Dialogue on Hinduism", Sri V. N. Gopala Desikan, pg. 24-25
In other words, Vedas and science do not contradict each other. They lie orthogonal to each other. Our gurus want us to use science to answer any worldly questions, and seek the Vedas for matters that science does not or cannot answer.
Ultimately, Hinduism is a very scientific religion. Many of our beliefs stem directly from scientific facts (ritual purity and not shaving during certain months just to name a few). The idea that one can either be a scientist or a Hindu but not both is simply untrue.
In summary, I'll leave you with this quote from "A Dialogue on Hinduism":
Student: I do not understand why logic should not be used to discuss Brahman.
Guru: Logic will be useful, when we discuss about known things, so that, with authority, we can make use of our logic and argument. But logic cannot be of use, in discussing about unknown things, unseen things like Brahman.
Student: Does this mean that logic cannot be used at all for studying or understanding Brahman?
Guru: No, it is not that. The primary authority is the Vedas and these can be supplemented by logic, without deviating from the authority of the Vedas.
Note: “The question: Does Science contradict Hinduism? How to deal with scientific discoveries that don’t line up with Vedas?” is licensed by Stack Exchange Inc (https://hinduism.stackexchange.com/); user contributions licensed under CC BY-SA.