by Andy Boyd

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Today, a different look. The University of Houston presents this series about the machines that make our civilization run, and the people whose ingenuity created them.

I first ran into the name Morris Kline while doing some Engines related research. His book, Mathematical Thought from Ancient to Modern Times, was quite a page turner. At over twelve-hundred pages I admit I have yet to finish it. In fact, I probably won't. But what makes the book so fascinating is that it focuses on how we've thought about mathematics over the centuries, not mathematics per se.

Kline was an avid student of mathematical history and wrote many historically oriented books. Mathematics in Western Culture. Mathematics: A Cultural Approach. But he's perhaps best known for his work related to the teaching of math.

Kline was born and reared in New York, receiving his bachelor's degree from New York University in 1930. During an interview late in his life, he admitted that though he held a graduate degree in math, throughout his training he "hadn't the least idea of what mathematics was all about." He added, "I could ... make good grades and so I preferred it, for example, to English." Kline attributed his lack of understanding of math to poor teaching.

His thoughts on teaching formed during the early part of his career. After a brief stay at Princeton, Kline returned to New York University where he taught math and was mentored by Richard Courant, a man known for his emphasis on applied mathematics. Here, Kline developed a keen sense of the power of math as a tool for understanding the physical world, and with that came a deeper appreciation of math as more than just rules for their own sake. It's no surprise, then, that Kline's philosophy on the teaching of math tended toward a focus on practical problem solving.

At times Kline pushed the limits. "Instead of presenting mathematics as rigorously as possible," he wrote, "present it as intuitively as possible ... Students will not lose sleep worrying about [it]." Kline advocated teaching math with the use of batting averages and puzzles. Among his more notable indictments of math as it was taught at the time was the 1973 book Why Johnny Can't Add: The Failure of the New Mathematics. Four years later, he challenged the role of faculty research in Why the Professor Can't Teach: Mathematics and the Dilemma of University Education.

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Kline's perspectives weren't uniformly embraced. Wrote one critic in a book review, "Morris Kline's books ... are well written, carefully thought out, and ask questions that are often ignored by more conventional books. I don't always agree with what he writes, but a provocative thesis is always worth having ..." The writer then added, "... I think three quarters of [what Kline's written] is superb, and the other quarter is outrageous nonsense."

And so it often goes when expressing strong beliefs. As for myself, I look forward to simply returning to the pages of Kline's Mathematical Thought from Ancient to Modern Times. Chapter 34, "The Theory of Numbers in the Nineteenth Century," promises to be riveting.

I'm Andy Boyd at the University of Houston, where we're interested in the way inventive minds work.

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M. Kline. Mathematical Thought from Ancient to Modern Times. Three volumes published as a single book. New York: Oxford University Press, 1972.

J.J. O'Connor and E.F. Robertson. Morris Kline. From the MacTutor History of Mathematics Archive at the University of Saint Andrews: Accessed April 25, 2017.

E. Pace. "Morris Kline, 84, Math Professor and Critic of Math Teaching, Dies," New York Times, June 11, 1992. See also: Accessed April 25, 2017.