Science claims that men originated through evolution. Christianity claims that men originated from Adam and Eves.
How Christianity respond the claims of modern science?
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Asking this question against all of "Christianity" turns this into an overview question of a very broad scope. In order to answer such a broad question, one must paint with broad strokes. There are two basic approaches taken.
Deny the validity or applicability of any scientific claims that directly conflict with the origin of man being God's direct creation. In general this position is held using one or more of the following ideas:
Science is based on presuppositions about reality, what kinds of things can be understood through observation/testing, etc. Asserting different presuppositions leads to a radically different outcome even using the same reference material. This relegates science to operate only inside a certain realm and refuses to allow it to draw conclusions about matters outside of that realm. Historically most of Christian theology has taken this approach. *
The actual nitty gritty of the science can be disputed. Facts, measurements, conclusions, methods of reasoning, the way unknowns are filled in, can and are often called into question. Many modern Creationists take this primary approach to the problem.
Explain away the creation account as metaphorical and not relevant to an actual historical understanding and adopt the current understanding of secular science. Those who take this approach usually fall along a scale, but we can still generalize two groups.
Some take the entire body of Scripture to be non-applicable to the physical world, only applying it in a "spiritual" sense. Very often, this position can be summarized as Non-Overlapping Magestaria, a principle which limits the ability of religion and science to make dogmatic pronouncements about each other.
Some take the content and try to reconcile it the content with modern scientific beliefs, producing things such as Theistic Evolution or Intelligent Design.
In between these two extremes lie several genres of belief depending on how much reign science is given, what premises it is allowed to operate under, and how the Scripture is to be understood.
If you would like more details on a particular view, ask a specific question rather than an overview one.
* My personal affiliation is here. By presupposing that the account we have in Scripture is true divine revelation, our understanding of the world as a spiritual reality with an aspect of physical manifestation makes all the pieces fall into place. Science has great value, but can only be trusted when it is based on these same presuppositions, often coming to faulty conclusions when those premises are altered or removed. It serves a very valuable purpose by informing our interaction with the created order, but steps out of bounds when it tries to define its own existence. See also my answer to How do Christians understand the omniscience of God in relation to the Uncertainty Principle
Genesis tells us how God created man in His own image. It gives us another specific details that they were created as male and female.
1:26 Then God said, “Let us make humankind in our image, after our likeness, so they may rule over the fish of the sea and the birds of the air, over the cattle, and over all the earth, and over all the creatures that move on the earth.” 1:27 God created humankind in his own image, in the image of God he created them, male and female he created them.
Bible says God created Man but does not give any step by step details of the process of creation of man. This leaves us with a broad space and scope for arguing that the process of creating man by God may not be an instantaneous one. On the contrary He may have devised a process (Evolution) for achieving this desired result.
Bible says that the “time span” or “time scale “for God, is not the same as that which we comprehend. The time of “millions of years” may be just a split of second for God. So evolution may have been the process adopted by God to create man, but evolution cannot execute by itself without a Creator and that is God Almighty.
I myself though has Masters in Mechanical Engineering,(Of course it is un related to theory of Evolution but with this scientifc background) find it difficult to accept evolution as a workable scientific process without God being architect and driving force behind it. This is my view also with all the laws of physics whihc are widely used in Mechanical Engineering. God is the architect of all these laws and He has left them to take care of the universe with the aid of their pre defined parameters, so that everything works in orderly manner.
At the most Christianity would accept the evolution as a tool that was in process with God at the helm of its affairs. There cannot be any "creation" without God being its "Creator".