Science, humanism, and artistic production during 15th century Italy do indeed have quite a relationship. During the 14th and 15th century, Italian humanists began to demand and search for more answers instead of believing the church's claims. They steered away from the church, and found answers themselves. After studying more about the mechanics of nature and humans, science was founded. People were focusing less on the church, and more on science and education. The movable type-writer and printing-press was founded through all the studies of science; this meant that not only the pope and clergy could read and interpret the Bible. Almost all could be educated now, and interpret what the Bible meant to them. Scientists raised questions to everything, and sought all the answers They could also become educated on numerous other subjects, such as math. Mathematics helped them study the perspective, scale, and depth of items. Artists began to not only be artists, but also mathematicians. One example of these artists is da Vinci. He educated himself on perspectives and methods to creating a better image, and become not only an artist, but a wonderful scientist and inventor. So now the paintings were becoming much more accurate in turns or depth, scale, and perspective after studying the scale, and developing techniques to achieve a great depth and perspective point. The paintings had a new conception of space, and three-dimensional scenes. The images were no longer emotional less and somewhat dull religious scenes. They had a more emotional, political, social, and spiritual connection with the viewer. Therefore, because humanists were wondering more about their biological bodies, and the world around them, science was developed, and because science was developed, a more wide spread education was released also causing more political power instead of piety, and artists started to develop art that was much more accurate and beautiful than previous art.
Such a relation I believe does exist today. Producing a beautiful, incredibly accurate painting is simply not enough today. One can easily go out and shoot a scene with a camera. So artists are striving to find and create something interesting and well liked. They may perhaps even use science to come up with a different and exciting method of creating something artistic, such as what Martin Schonogauer achieved by mastering metal engraving. So artists raise the questions why and how to make the viewers content with their art and try to produce a better method, just as 15th century Italians did by creating better methods of making their images more accurate in perspective, and exciting and full of emotion in terms of the scenes.