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### Top 10 Greatest Moments in Math History: Isaac Barrow and Nonviolent Differentiation

Moment 7: Isaac Barrow and Nonviolent Differentiation
Sometimes, as Henry David Thoreau influenced Gandhi who influenced Martin Luther King Jr. to express nonviolent resistance, it’s what we don’t do that makes the difference.

In 1669, Isaac Barrow of Cambridge University stepped down from his Lucasian Chair, the most famous academic chair in the world [11], to let Sir Isaac Newton take over [12, page 16]. This should be considered a great moment in mathematics not for what it discovered, but rather for what it allowed to unfold in the history of math. If it wasn’t for Barrow’s ultimate selflessness, we may have never heard from Sir Isaac Newton.

It is argued by the English that Newton was the first to develop a method to find function derivatives. Although the Germans claim that mathematician Gottfried Wilhelm Liebniz was the first to differentiate, and we do in fact continue to use Liebniz’s notation style, most school children can tell you something about Isaac Newton and probably nothing of Gottfried Wilhelm Liebniz.

Newton and Liebniz briefly but amicably exchanged their ideas through letters, but unfortunately Barrow’s altruism didn’t rub off and the two went on to quarrel for years about who was first to develop differential calculus. It is believed that Newton developed his version “fluxational calculus” first but did not publish his work until 1684, after Liebniz published his “differential calculus” with no mention of his correspondence with Newton [12, page 21].

Three years later in 1687, Newton may have had a change of heart and cited his letters with Liebniz in his publication “Philosophiae naturalis principia mathematica”. Maybe in the end Newton did remember the good deed of Isaac Barrow that propelled him to the spotlight.

In defense of the old sayings “alls good that ends good” or “the end justifies the means”, if it wasn’t for the pressure Newton and Liebniz put on each other we may never have gotten to modern day differential calculus and math would still be flat and static. Calculus changed math from “find x” to “find how fast x is changing”. Calculus changed math from finite to infinite [12, page 24].

Eaves writes on page 38 of Great Moments in Mathematics After 1650 that “one can recognize the students on a college campus who have studied calculus- they are the students with no eyebrows.” Before reading the next line about “students of calculus being high-browed” I laughed at this statement in comfort that it wasn’t just me who pulled their eyebrows out trying to work through problem sets!

Works Cited:

[11] Bruen, Robert, http://www.lucasianchair.org, 1995-2007

[12] Eves, Howard, Great Moments in Mathematics Since 1650, The Mathematical Association of America, 1983