“It is a capital mistake to theorize before one has data.” ~ Sherlock Holmes in A Study in Scarlet by Sir Arthur Conan Doyle
In “Convergence”, Numb3rs S2E7, Meghan Reeves and Charlie Epps have the following conversation.
MEGAN: Wouldn’t that much data make it harder to find what you’re looking for?
CHARLIE: The opposite.
More data means more chances to find something.
It’s like when you’re trying to put together a jigsaw puzzle. You start with a few pieces, and the rest are in the box. All the pieces you have should eventually fit your puzzle. All the pieces and nothing more come in the box. But with a real-world problem, that’s just like trying to solve a jigsaw puzzle when all the pieces you need are mixed in with pieces from many other puzzles. Now, when you grab a few pieces from the box, most won’t fit. You got to go through the entire box and pull out the pieces that fit your puzzle.
The algorithm goes through it all, pulls out what fits together.
I am somewhat biased toward applied mathematics rather than pure mathematics. I have been able to use mathematics to solve a number of problems I encountered in the many different jobs I have had over the years. Applied mathematics provides insight into the world around us. As the Top Rankers website puts it: “Pure mathematics involves the use of pure numbers while applied mathematics involves quantities such as numerical values and units of measurement. Applied mathematics is used in practical applications in day-to-day life while pure mathematics is the study of principles without much practical application. Pure mathematics is abstract and theoretical. It is used to solve problems, find facts and answer questions that do not depend on the world around us, but on the rules of mathematics itself.” In essence, you cannot have one without the other. Consider Leonhard Euler (pure mathematician) and the seven bridges of Königsberg. In a letter written in 1736 to an Italian mathematician, Euler wrote: “This question is so banal, but seemed to me worthy of attention in that [neither] geometry, nor algebra, nor even the art of counting was sufficient to solve it.” Based on this banal problem Euler created graph theory (applied mathematics).
“Data is like garbage. You’d better know what
Mark Twain
you are going to do with it before you collect it.”
Because applied mathematics involves quantities such as numerical values and units of measurement that means gathering data. Not only gathering meaningful data but understanding what story that data might tell you. Over the years and many different jobs, collecting the right data is crucial to any investigation, and that data can come from technical drawings, databases (e.g., e-commerce websites), streaming data (e.g., stock market prices), existing graphs, Excel files or even paper.
The purpose of collecting data is to answer questions when the answers are not immediately obvious. Data collection and analysis might be the most effective way to answer a difficult question. To answer that question may include:
- creating and interpreting graphs of the data,
- curve fitting,
- performing integration to get the area under curve
- performing differentiation to see how the data changes, or
- using probability, statistics or both to find the answer.
Both pure and applied mathematics are essential to solve problems, and when dealing with real-world problems data is the means to the answer.
References
“Bad Data”. 2021. Dilbert. https://dilbert.com/strip/2018-04-03.
“Convergence – Numb3rs S2E7 Script”. 2005. TranscriptDB. https://transcripts.thedealr.net/script.php/numb3rs-2005-1oir/s2/e7.
“Difference Between Applied Mathematics And Mathematics”. 2021. toprankers.com. https://www.toprankers.com/applied-mathematics-vs-mathematics.
“The Purpose Of Collecting Data. Why Do Math, How To Get Better At Math”. 2021. Erikson Institute Early Math Collaborative. https://earlymath.erikson.edu/big-ideas/the-purpose-of-collecting-data-is-to-answer-questions-when-the-answers-are-not-immediately-obvious-how-to-get-better-at-math/.
Mathematical Mysteries 