Science itself never and can't contradict with hinduism. Only some partial (adhuri) knowledge scientist try to contradict. When knowledge of one topic is limited to someone (scientist) then they start to believe on behalf of that limited/incomplete knowledge and rejects all other (full) knowledge. Here is how...
The purpose of both science and our scriptures is just to tell truth about world. And truth is only one, it can't be different for differet field (science/hinduism). For example Earth is not alone in space, there are lot more in space is present like graha, nakshatra. Both science and our
scriptures told about them and they both also told their quantity also. And they both are right. Hence both science and scriptures only use to tell truth. And as already said Truth is one, so both of them has to show exact same views on one topic. For exaple they both shows list of planets and both are correct on their info.
So how there can be any contradict if they both tells the same truth?
If scientist and scriptures are telling something on one topic then they both must tell the same thing/answer towards that topic. And if they are telling different thing/answer about any topic then analysis of one surely gone wrong.
Means, one of them surely misscalculate that's why they came on different conclusion, If both of their analysis were correct then they must have came up with same conclusion or answer, isn't it?
So who went wrong in their analysis?
First of all let me clear one point, I said in beginning lines that they both can't and never contradict each other. And later I said, if one of them gone wrong in their calculation/analysis of finding truth about any topic (ex. no. of planets in space) then they seems to contradict with each other.
But that contradiction is only result of miscalculation of one field. That's why contradiction occurs. But that contradiction can't be from science but can be from partial knowledge scientist only. Because some scientists came up with wrong calculation that doesn't mean science gone wrong, but instead some scientists gone wrong.
Why I am saying that scientists gone wrong, why not our great Sages (who wrote scriptures) gone wrong?
Because they can't gone wrong but only today's scientists can gone wrong. Come up with wrong analysis has become trend among scientists. Here are one example in which we come to know that scientists came up with wrong calculations and ended up contradict with hinduism..
Earlier, Scientists used to believe that all planets including son use to move around Earth. But our scriptures (Rig Veda) says, all planets (Earth also) moves around son. Here contradict arrised...
This contradiction only arise because one was wrong in his calculation. To remove contradiction, we just need to remove the wrong calculation and then they both will say the same thing. The wrong calculation was done by scientist earlier.
Scientist used to believe everything moves around Earth until great scientist Galileo invented Telescope. When telescope invented by Galileo then all started to analyse space with telescope and they found everything is not moving around Earth but instead Earth itself moves around Son.
So because of Galileo, calculation from science gone right and they both(science and scriptures) came up with same answer.
But can our scriptures went wrong like scientists went wrong some times?
No, it's not possible. For example, our four vedas(which contains every possible information) are created by great sages but the information stored in them are provided by Lord himself. And Lord is the creator of world. So our scriptures can't tell wrong info because it was invented by creator of world himself. I mean who can tell better that whether everything
moves around Earth or around Son except creator of Son/Earth? No one...
The thing is scientists are also human, and they also can get wrong easily. And gets wrong mostly. For example: Earlier Scientists used to belive that universe is created cause of Big Bang.
They did present Big Bang theory to tell how universe is created. We all read about Big Bang theory in 10th class/standard. People are reading this since many dacades. But after long time Scientists
came up with new conclusion that rejected their own created theory. Now, even NASA has rejected Big Bang theory which we all used to read or belive since long.
There are lot more examples can be found where scientists gone wrong.
Note: Scientists don't only contradict with hinduism but they contradict with each other also coz of their partial/wrong knowledge. For example: some scientist says Donosour ends coz of poisons gass, some says coz of deseas, some says coz of volcano explosion starts their destruction and so on.
Getting wrong is habit of inpatient human of today's time, and scientists are no exception of this. So one should not bother if some scientists contradict with Hinduism because doing contradiction is habit of scientists to prove himself right and other wrong. That's why they do contradict with religions and with other scientists also.