According to the Merriam Webster Dictionary, science is “a knowledge about or study of the natural world based on facts learned through experiments and observation”. Last Wednesday my history of mathematics class carried out a neat experiment called barbie bungee. The activity involves rubber bands, and a barbie or action figure. Similar to a bungee jumper, we tied a string of rubber bands to the figures legs with the goal of seeing how we could drop our figure from a ledge so it ended up very close to the ground! To carry out this experiment with accuracy we had to conduct a series of smaller trials before we dropped our figure off the bridge!
The activity was a blast and we nearly won the competition between 6 groups of math students, but our hulk like figure barely nicked the ground because our calculations were just off! He may not have died, but he would have been severely injured which was not our intent! Following the activity my professor proposed a unique question, “Is math a science?”
At first my reaction was that yes mathematics is a science. Mathematicians carry out trials in which they test conjectures and see if the conjectures hold. Mathematicians look at patterns in the natural world, and seek explanations for their being. Mathematics can be utilized to make sound hypothesis and we can test our predictions. Lastly, I thought about the scientific method. First we ask questions, then research and gather background information, construct a hypothesis, test our hypothesis by doing an experiment, analyze your data and draw a conclusion, communicate our results. In mathematics it seems to me there are very similar processes, first we ask a big question, then we think about it and construct a conjecture. Once mathematicians have a conjecture they form a proof and test their conjecture trying to think of counterexamples, then mathematicians build a proof or share their counterexample, and draw a conclusion about the validity of a conjecture. Then they share out their idea by having a formal proof published on their conjecture.
On that last point I immediately detected a difference between math and the natural sciences. I could be wrong about this, but it seems to me that mathematicians only communicate their results when they have constructed a formal proof. I mean they do not publish their counterexamples, or if they find a conjecture to be false. They may discuss their results with others, but they will not end up in a paper. In science a hypothesis could be wrong, and a conclusion can still be developed. Another distinction between science and mathematics is that science deals with that which we can feel, smell, see, hear, and touch most times whereas mathematics is more abstract. Mathematics deals with the concepts behind the manipulation and exploration of patterns. Mathematics builds on previous axioms and provides explanations for patterns rather than drawing from experiments we can see.
A great example of math not being a science involves number theory. Number theory was not created through experimentation and observation, but rather by abstract thinking and critiquing counting objects in the world. Mathematics can be used to form great predictions in the sciences, but it is not a science itself because it does not rely on physical experiments for its growth and development as a field. Mathematics and science are closely related, but I would say that math is not a science because it does not involve experimentation on the physical world, but rather abstract quantities and figures.
The reality behind this whole discussion is that math needs science, and science needs math in order to effectively grow and expand. Without science, math is just a made up and distant group of ideas. Without math, science will progress extremely slowly because data cannot be organized clearly, and predictions made by scientists will be weak and faulty. In our barbie bungee activity we saw the importance of utilizing mathematics in a scientific experiment. Science and math are connected like peanut butter and jelly, they are separate entities, but they combine to make something wonderful!