Nature of Mathematics

After reviewing several definitions of mathematics from Webster's dictionary, peers, Wikipedia, universities, college professors,  and journals, the definition has boiled down to math being an abstract science or the study of numbers, space, quantity, change, structure, and patterns. Out of all the definitions that I read, math is referred to it as being "a science..." or "an abstract science." According to Google, science is the intellectual and practical activity encompassing the systematic study of the structure and behavior of the physical and natural world through observation and experiment. With this being said, why is there such a debate or opposing opinions on whether or not math is a science?  

Having a definite answer to whether or not math is a science is quite difficult for me to decide. However, I do believe that you cannot have one without the other. Science and math plays a vital role in our daily lives. Both topics are unique in their own way, but they have given us meaning to life. In other words, without science and math, we would not be able to have logical explanations of things or understand how the world around us works. I think the two subjects work hand in hand to supply us answers and supports to theories or questions we have about our world. 

Above is a video more so for humor as opposed to truth, but this is the battle I have with figuring out is math a science or is science a math. Understanding Science is website that was developed by the University of  California Museum of Paleontology to help with the understanding of science and how it works. According to Understanding Science, there is a science checklist of all the things science aims to do or accomplish and this list is compared to mathematics. The list consists of science focusing on the natural world, science aims to explain the natural world,  it uses testable ideas, relies on evidence, leads to ongoing research, and researcher behave scientifically. In the article, it is stated that mathematics does not necessarily focus on the natural world, but "mathematical abstractions arise directly from the natural world." In addition to the previous statement, mathematics helps us understand and explain the natural world. The example given is the fact that Isaac Newton''s laws of motion was made possible by the advances he made in calculus. Futhermore, science uses testable ideas; whereas math consists of testable ideas just not against evidence in the natural world, as in biology, chemistry, and physic. In math we can easily test a conjecture of whether or not an odd number plus an odd number equals an even number by computation. If we find one example where this is not the case, the conjecture would be invalid because we have that strong opposing evidence. In science, there are many factors to consider when posed with a new hypothesis. One counterexample is not enough to say a hypothesis is true because scientific ideas can never be absolutely proven. Moving forward, researchers in math and science behave scientifically. To put more simply, scientist and mathematician build upon each others work, share ideas/results, respond and act respectively on criticism, and are honest in their work (they give credit where  credit is due).

Above is a video that asks a panel of individuals, is math invented or discovered? Before actually watching the video, I automatically assumed that math was invented. I then asked myself, "is science invented or discovered?" Based off of my knowledge of science being the natural world around us, I assumed it was discovered. Yes, math is also a make up of the world around us, but it typically deals with some sort of computation or abstract idea. This new question gave me a different perspective when looking at the original question, is math a science? I still have not made an finalized decision, but I definitely have considered the question in a different point of view. Check out the video! Do you think math is discovered or invented? Do you think science is discovered or invented? Does this change your opinion at all about math being a science or vise versa?
Noted 12/12/15 -After several weeks of discussing is math a science, I've concluded that math is not a science. Math and science have distinct components, which separates the two. However, I still believe math  plays a role in science and there would be no way to complete science without math (Example: physics and chemistry).