What does the Bible say about Science?

There are many references to now what has been proven by science. As has been already said, science is not explicitly mentioned in the Bible.

Isaiah 40:22 (ESV)

²²It is he who sits above the circle of the earth...

Refers to the fact that the Earth is round.

Job 26:7 (ESV)

⁷He stretches out the north over the void
  and hangs the earth on nothing.

Refers to the fact that the Earth floats freely in space.

Ecclesiastes 1:6 (ESV)

⁶ The wind blows to the south
   and goes around to the north;
around and around goes the wind,
   and on its circuits the wind returns.

Wind currents.

Job 28:25 (ESV)

²⁵When he gave to the wind its weight
  and apportioned the waters by measure,

Air has weight.

Hebrews 11: (ESV)

³By faith we understand that the universe was created by the word of God, so that what is seen was not made out of things that are visible.

Depending on your interpretation, it could be referring to molecules/atoms.

Psalm 8:8 (ESV)

⁸the birds of the heavens, and the fish of the sea,
  whatever passes along the paths of the seas.

Isaiah 43:16 (ESV)

¹⁶Thus says the LORD,
who makes a way in the sea,
a path in the mighty waters,

Both verses attest to the fact that there are currents on the sea.

Job 38:16 (ESV)

¹⁶"Have you entered into the springs of the sea,
or walked in the recesses of the deep?

Jonah 2:5-6

⁵The waters closed in over me to take my life;
the deep surrounded me;
weeds were wrapped about my head
⁶at the roots of the mountains.

Both address the fact that there are mountain and valleys in the sea.

There are repeated references in Daniel to knowledge of the world being a blessing from God. Likewise, Colossians 2:3 speaks of Christ "in whom are hid all the treasures of wisdom and knowledge". However, 1 Timothy 6: 2 contains a warning about the opposition of "science so called," or in other words, incorrect knowledge that claims authority but contradicts revealed truth.

Scientific investigation has shown that the world around us works according to consistent laws, which is very much in keeping with what we know of God as a God of order, and there is much benefit to be found in learning about the rules that He set up. But it's important to keep in mind that science is only based on observation and investigation, and trying to reverse-engineer the nature of the rules from the results we can observe, and thus the actual "scientific truth" about certain things tends to change as they become more fully understood. (For some interesting reading on the subject, do a bit of research on the history of the Cosmological Constant.) When current scientific understanding conflicts with revealed truth, it's likely that someone didn't quite get their experiment right.

It's also important to keep in mind that not all things that are believed or taught by religious leaders are actually based in revealed truth. One of the obvious examples would be the medieval Catholic Church's persecution of Copernicus for his scientific notions about the nature of the Solar System. This knowledge contradicted dogmatic notions held by the Church that have no actual basis in the Bible, but instead derive from Greek philosophy and got incorporated into the dogma back when the Church was the state religion of the Roman Empire.

And finally, it's important to remember that scientists are human too. They occasionally have an agenda beyond simply furthering the spread of knowledge of how the world works. Experiments don't lie, but experimenters sometimes do.

I believe that God is a God of order, and that there is no conflict between true science and true religion, but that for various reasons sometimes non-true versions of both science and religion do spring up and gain widespread popularity and acceptance. If you run into something claiming scientific authority that contradicts your religious beliefs, then one or the other (or possibly both) is in error. Reason about it, try to find an explanation that makes sense, then pray about it and ask God if you've reached the right conclusions. He won't steer you wrong, even if other authorities do.

To expect the Bible to mention "science" directly is anachronistic.

But here are some passages that embrace the idea that we humans were created to be systematically curious.

Genesis 1:26 The word "dominion." (NRSV and other translations)

Genesis 2:19ff The Holy One gave the man the task of giving a name to every creature.

Job 38-40: The fact that we cannot know everything about creation.