There are three ways that the concept of intelligent design in nature comes across in science. The first is the general design of the universe, the second is design within living things, and the final one is design as a requirement for the origin of life. All three of these are a critical part of the issue when it comes to whether or not science can prove intelligent design in nature.
One of the ways of suggesting intelligent design in nature in terms of the general design of the universe is the fine-tuned nature of the universe itself. Now, while some of the factors originally placed under fine-tuning may have broader ranges than originally suspected, many aspects of the universe still require some degree of fine-tuning in order to have a universe capable of supporting life. However, the primary way in which the universe as a whole gives evidence of being intelligently designed is on the subatomic scale, where the properties of particles do not have definite values but exist as waves of probability until observed; only then do these properties obtain actual specific values. Furthermore, the behavior of particles can change based on what we know about them, for example the quantum erasure double slit experiment has shown that whether or not particles behave as particles or waves depends upon whether or not we know if they went through a particular slit or not.
In general biology, individual kinds of animals show traits that give definite evidence of design for that particular type of animal. This is because the organized complexity of these traits goes beyond the possibility of natural selection producing them. In fact, the basic structure most organisms are filled with traits there could not be the result of something as broad as natural selection from any previous form there is evidence for.
The question of the origin of life is where intelligent design shines its brightest. This is in part because there is no actual naturalistic model for the origin of life that can even come close to solving the problems. For example, just getting the proteins that are necessary for the simplest possible living cell let alone getting them assembled in the right way to produce an actual cell, exceeds the number of possible events in the history universe by thousands of orders of magnitude.
So the question before us is can science prove intelligent design? Well, the first requirement is that it would have to be allowed to even consider it. The biggest problem in this discussion is that the mainstream scientific community has rejected intelligent design to the point of getting this US supreme court to force it out of public educational institutes. It is literally disallowed by the scientific establishment before any data is considered. This is because they have already decided that there has to be a 100% naturalistic atheistic materialistic explanation and that the evidence doesn't matter, the lack of any ability to overcome the problems doesn't matter, and in fact, science itself doesn't even matter. In other words, intelligent design is excluded from mainstream science by a priori insistence on absolute atheistic naturalism rather than actual science.
The problem is that, ultimately, the entire Big Bang to man story is nothing but an atheist mythology that tries to explain our origins apart from an intelligent desire. What's on my claim that such a designer could be aliens, rather than God. Anybody who actually thinks about it will easily see that just got back this does not solve the problem but only moves to problem of the origin of life a long time ago in a Galaxy far, far away. One way that science can prove an intelligent designer is by demonstrating the fact that life or other biological systems could not have come into existence by any naturalistic mechanism. Ultimately, the indications from quantum mechanics that our reality is fundamentally information require an intelligent designer at the most basic levels of reality because, at the very least, such a system would need an intelligent programmer.
So, can science prove intelligent designers? Calling what we have proof is probably a little stronger than is justified. After all, there is always the possibility that some new discovery could provide another solution. However, based on what we do know in the direction the research is pointing out, this is highly unlikely. Furthermore, no evidence can ever prove the existence of something or someone who has already made up their mind that the individual or object does not exist. The best way of answering the question is that science strongly indicates the existence of an intelligent designer. Furthermore, it indicates that this is the most reasonable conclusion that we have based on the knowledge that we currently have.
