Math Teacher Discovers Flaw in Calculus While Trying to Explain it to His Students
One of the core concepts of calculus is known as the "derivative"
However, the notation for the second derivative has always been strange and usually baffles students. In most mathematics textbooks, the notation is presented without explanation for the reasons for why it looks the way it looks. In an effort to provide more background for his students, Jonathan Bartlett decided to pursue the matter further, and figure out why the notation is the way that it is.
During his investigation, he discovered that this strange notation for second derivatives itself is problematic—
However, Bartlett continued to search deeper to find a way to establish the notation from first principles. After some initial mis-steps, he discovered a new notation for the second derivative which can be used literally and does not require special formulas to manipulate. Additionally, when using the new notation, Bartlett was able to infer a new formula for relating different derivatives.
In order to validate his findings, Bartlett enlisted the help of Asatur Khurshudyan, a mathematician specializing in calculus-related problems. Khurshudyan validated his findings, and showed how the new formula can be used to solve several classes of calculus-related problems that were previously very difficult.
Together they coordinated on a paper describing the new notation, titled "Extending the Algebraic Manipulability of Differentials,"
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