Maybe it's a bit like asking whether the chicken came before the egg?
My first reaction was just like Zeashan's. But then I thought, when primitive humans first discovered clubs, the wheel, how to make fires, bows and arrows, did they use physics and chemistry? Or was it the other way around?
It seems more likely that trial and error created those early technologies, and that inquisitive people then figured out the science behind them? And then with that science, they could make innovations that would have been unlikely with just trial and error alone.
Although science and technology have an increasingly interactive relationship and at times are used interchangeably, they do not share the same conceptual mapping. In other words, science and technology represent specific categories of activities that are distinct but interdependent. Notably, science can serve as the basis of generating technologies simply because science and technology have a symbiotic relationship in that they are interlinked in the process of seeking solutions to the problems demanding scientific understanding and material design. As an illustration, scientific facts are a prerequisite for solving technological problems, whereas modern technologies pave the way for discovering new scientific knowledge. Therefore, it can be stated that in asking questions and making inquiries , scientists may need to enlist the services of related technologies while sometimes their attempt in solving problems leads to the production of new technologies. I hope the following link provides you further details concerning the question.
We should distinguish between technical tools and technology (tech-know-logic); B. Franklin opined that humans are tool-making animals. Technology is the modern multiplication of skills and knowledge, technology is science at the assembly production line, now becoming exponential. Scientific methodology is the foundation of technology,
I think science is the mother of technology. Science is a process on the other hand technology might be perceived as a product of this process. If the process is methodical then many products such as many technology would be generated. So at best I believe technology is a child of science.
Science and technology both are the complimentary to each other and they should go hand in hand together.
No technology can be assumed without scientific principles, explanations, and logic.
So in my view "Science is the mother of all technology" Although it is well said that "Need is the mother of all inventions", where inventions are the technology while the Scientific principles are the base for these inventions.
If I understand it well, your questions have to do with the relation between science and technology, namely what is it first: Science or technology? To some extent, as Albert suggests, such a question reminds us of the egg-chicken problem. In other words, the relation between science and technology is bilateral and dialectical rather than unidirectional and static. As I see it, science lies at the heart of technological inventions, such as planes, computers, microwaves, TV, and the like. In this sense, technology is, say, applied science and, hence, we can say that science is the mother of technology. However, it is often the case that when science and basic research is used to generate technological devices, some technological problems arise. In its turn, these problems are, as it were, a source of inspiration for further and better science. Here, we may think of technology as the mother of science. Therefore, one might say that the relation between science and technology is a spiral that never ends. Scientific progress leads to technology progress, and the other way around. This reminds me of a bootstrapping or a go back and forth procedure.
As Albert says, early technologies (e.g., how to make fires, bows and arrows) may have been due to a trial and error procedure. Note, however, that when this is the case, unknown scientific laws were at issue. History has shown us that there seems to be no limits for scientific progress because there will be always an unknown to be known, and for technological progress because there will be always, say, technological domains waiting for scientific solutions. As I see it, both science and technology should be guided by the pursuit of true, the good, and the beautiful. Note that the true, the good, and the beautiful are universal categories regardless of how they are seen at different places and times.