Show Your Work

Hadi Shanaa, Guest Writer

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Why do we show our work? Is it to retrace our steps? Rarely. Is it to get partial credit? Yes. Forget about the partial credit, forget about the grade, and instead focus on the real life applications. Why does showing our work really matter?

As it turns out, showing your work in an understandable way is a valuable skill that is critical for research. Unlike tests, in research and proofs, you are not showing your work to receive partial credit; rather, you show your work so that other can review and replicate your work to confirm its viability. By showing your work, you allow for collaboration with others that are interested in your study. Collaboration and verification of studies are how mathematicians and their proofs gather recognition. Because of this scientific model of peer collaboration to verify work, if you do not properly collaborate or show your work, you can receive backlash from your academic peers.

Shinichi Mochizuki made the critical error of not showing his work when he spent 10 years working on the proof of the ABC conjecture. The ABC conjecture states that when two coprime (do not share prime factors) numbers A and B are added to get C, the number of prime factors that A and B have is less than the number of prime factors of C. This seemingly simple conjecture is very complicated and, if proved, would open up any doors to solving other problems. Word of Mochizuki’s proof stirred up a great deal of excitement in the math world until they read it. It was inscrutable. Mochizuki had written a 500 page proof using vocabulary he had developed to simplify the functions he used. Even the brightest minds were unable to understand his work and the process he used. Additionally, Mochizuki would not explain his proof to the public or colleges that offered to pay him to do so.

What does his unwillingness mean for the math world? It means tat his proof will not be proved for a while. He will have to work with someone to try and explain his proof and hopefully it will be legible after editing.

In conclusion, the applications of showing your work go beyond getting partial credit in your math class. Much like defining your terms in an English paper, showing step-by-step details make difficult proofs legible, thereby making your work open to being proved or disproved. Without showing your work, all of the work is for naught.

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