# New Lincoln math pages suggest more education

Two math-notebook pages recently authenticated as belonging to Abraham Lincoln suggest the 16th president, who was known to downplay his formal education, may have spent more time in school than usually thought.

And the Illinois State University math professors behind the discovery say the work shows Lincoln was no slouch, either.

Math professors Nerida Ellerton and Ken Clements said Friday at the university in Normal that they'd recently confirmed that the two pages were part of a previously known math notebook from Lincoln's childhood. It was found in the archives of Houghton Library at Harvard University, where it remains.

The book, known as a cyphering book in Lincoln's day, is a sort math workbook in which Lincoln wrote math problems and their answers. It's the oldest known Lincoln manuscript.

Based on the difficulty of the problems involved and dates on some of the pages—1824 and, on the recently authenticated pages, 1826, when Lincoln was 17—Lincoln likely worked in the book intermittently over several calendar years while his family lived in Indiana, the married professors said. They think he could have started as early as the age of 10 and believe his work happened while he was in school.

"Most people say he went to school for anything between three months and nine months" over the course of his life, Clements said. "We think he went to school (up to) two years."

And very little of the work is wrong, he added.

"He made very few errors, and he always knew what he was trying to do," Clements added. "We've studied thousands of these cyphering books. You don't always get the feeling that 'this guy knew what he was doing.'"

The professors' find suggests Lincoln may have gone to school over as many as three to five winters, according to historian Daniel Stowell, director of the Papers of Abraham Lincoln project at the Abraham Lincoln Presidential Library in Springfield. The library owns one previously identified page of the book.

"They are arguing with some merit that a cyphering book would have been created in a school setting," Stowell said. "It does at least open the possibility that he may have had more formal schooling than originally thought. Not a whole lot more, but still more."

The pages—attached as a single leaf—include word problems that are the equivalent of roughly eighth-grade modern work, Clements said.

"If 100 dollars in one year gain 3½ dollars interest, what sum will gain $38.50 cents in one year and a quarter?" one reads.

Any student doing such work in the 1820s would have been more advanced than most on the frontier in Indiana, Clements said.

"If you got to that stage, you'd sort of done well," he said.

Lincoln is known to have later studied trigonometry and geometry on his own.

The newly authenticated pages have been in the Harvard library's archives since 1954. They were known as Lincoln documents, but their origin wasn't known, the professors said. The two looked at the documents as they researched a book they've written on math books from the period.

A letter from former Lincoln law partner William Herndon from 1875 that accompanied the papers, describing them, made the authentication relatively straightforward, Clements said.

Lincoln's stepmother, Sarah Bush Lincoln, gave the cyphering book to Herndon after Lincoln's death, and Herndon then gave them to other people, Stowell said.

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**Citation**: New Lincoln math pages suggest more education (2013, June 8) retrieved 15 September 2019 from https://phys.org/news/2013-06-lincoln-math-pages.html

It is a tricky question, because it doesn't specify whether you're talking about compound interest. I.e whether you calculate that 3.5% interest only for the original deposited sum, or for the compounding sum.

One way you could calculate that 100 dollars for 1.25 years earns you $4.375 so if you earn $38.50 you must have deposited a sum that was 8.8 times greater than $100. That's just multiplication and division, and that's trivial to do on paper.

But if you have to take into account compound interest, you actually have to calculate 1.035 to the power of 1.25 which gives you a profit of approximately $4.394 and subsequently the original sum was 8.76 times a hundred dollars. That's not trivial to do on paper due to the exponent.