Question

Dear Mitch,

For the past couple of weeks, beginning January 17th, which is the anniversary of Benjamin Franklin's birthday, a few of us in the math department have been arguing over what major contributions, if any, this founding father made in the area of mathematics. The way the whole thing began, I believe, is that until recently most biographies seemed to focus on other areas of his wide-spanning genius, and some have even suggested that although he certainly should be considered one of the greatest thinkers of all time, with contributions in almost every area of human achievement from science and politics to philosophy and literature, mathematics was about the only area in which his vibrant mind did not flourish. Yet, recently, there have been a number of biographies that seem to be more carefully researched and developed, and these books seem to say that Franklin was indeed a mathematician who was not only as gifted as can be but whose contributions to the world of mathematics are important and remain among the useful areas utilized today.

We were curious to hear your thoughts on this topic.

Sincerely,

Timothy P.

Cottage Grove, Wisconsin

Answer

Dear Timothy,

Thank you for your question. Benjamin Franklin has always been one of my favorite characters from American History and, I suspect, will always continue to be.

The man was indeed a mathematical thinker of major talent. You are correct that until recently most biographers seem to have either avoided this area of Franklin's many gifts or inaccurately managed to give the reader the impression that math was about the only observable hole in a solid mind of astounding capability.

I think at least part of the confusion comes from the fact that Benjamin Franklin had so many different interests and talents, and was so productive and prolific in most of the areas he pursued, that - relative to some of the famous contributions he made in politics, science, philosophy, etc. -- his work in mathematics could almost be viewed as a hobby that he used to pass time when not working on earth-shattering advances in other fields.

This is unfortunate, because had he not been a true 'renaissance man', mastering more areas of human intellect than the average group of ten geniuses could do together, and had he instead only left us his mathematics, he would today be known for that work, and would be named among the great thinkers of the field.

In a place like this, I cannot possibly enumerate, let alone go into any kind of depth, of Franklin's mathematical contributions, which is why one should refer to one or more of the recent books devoted to the topic. Still, a random sampling would include such things as: His invention of the still popular magic square, his contributions and discoveries in number theory, geometry, economics, and statistics. Several of these he combined to derive his population estimates in Poor Richard's Almanac.

One recent book, *Benjamin Franklin's Numbers: An Unsung Mathematical Odyssey*, written by Paul C. Pasles and published in 2008 by Princeton University Press, is devoted to this very topic.

"It seems to me, that if statesmen had a little more arithmetic, or were more accustomed to calculation, wars would be much less frequent," Franklin wisely stated 1787. I learned this from Pasles' book. I was also reminded of Franklin's important changes to Jefferson's first draft of our United States Constitution in which the line "We hold these truths to be 'sacred and undeniable'..." was replaced by "We hold these truths to be *self-evident*..." I am in agreement with Mr. Pasles, in his belief that this amendment is a product of Franklin's geometrical/analytical mind that held the aspects of logical proofs; in such proofs, the phrase 'self-evident' means that each truth is so obvious as to be unprovable and beyond the reach of logical argument. Again, more about this can be found in *Benjamin Franklin's Numbers*.

Also, it is always interesting to note that Benjamin Franklin was the inventor of Daylight Savings Time, which occurred to him while spending a night a Paris hotel and discovering the advantages of having daylight linger through the early evening, as it famously does in Paris. Finally, the book is written for a general audience, and requires no particular mathematical knowledge or skill to enjoy. It is available at Amazon.com.

Now, as some readers of these questions and answers have pointed out in their emails to Adler-n-subtract.com, we have recommended very few books for further reading on any given topic. That is accurate. Recommending books is a risky endeavor, as everyone has different tastes and can result in having people spend money on materials they may not enjoy; Still, the educational advantages of sharing books I believe to have some special quality makes the risk worth it.

And so now I am going to recommend a different book on Benjamin Franklin. This one, though, is about as different from the previous book described as can be.

The book is entitled *The Time Chest*. It is a novel written for the elementary school independent reader not yet a 'young adult', but soon-to-be, and was written - astoundingly - by a twelve-year-old boy. Like the book described above, *The Time Chest* is well-illustrated, but unlike Pasales' work, *The Time Chest* is not a book about Franklin's mathematics.

*The Time Chest* is a novel, written in the tradition of historical novels, and was researched and written accurately with respect to all plot points that could be true. In other words, as in the best historical novels, anything known to be true for historians is true in the book and woven into the plot that way. In this case, it is impressive because the novel fits within the category of 'fantasy' stories, and therefore there is magic connecting the relevant bits of history. Of course, I have no particular credentials to comment on the likelihood of the truth of the 'magic' parts of the story, as I was not around to witness the events. However, despite the true magic and seemingly impossible nature of time-travel, the book is written so compellingly that one's suspended disbelief quickly expands to allow more than one might expect. In short, it is a slender, delightful book, and it is written with such care and skill that one finds oneself wondering how a twelve-year-old could be more capable than most of us are at twice that age.

NOW: In the interest of full-disclosure, I cannot sign off without making it clear that the 12-year-old author of *The Time Chest* is my nephew, Ellis H. Adler.

The question arises: Would I be recommending this book had the author not been my nephew?

ANSWER: I don't know, because in a world that has thousands of new books published each year, I may not have been fortunate enough to have come across this particular one.

A second question arises: When reading the book, am I able to be objective in my assessment?

ANSWER: NO, I am not. **However**, I do not believe that one is *ever* able to be completely objective when taking in a new experience, because our minds are shaped by a lifetime of previous experiences; I am interested in Benjamin Franklin, and I enjoy books written for young readers; I like magic, and yes, I was already impressed by the author before I opened to page one. All I can say is this: From the first paragraph to the end I was unable to put the book down. And, though I love to read, I usually am able to exert more control over my reading schedule than I found myself this time. It is an intelligent and fun story that informs as much as it engages. Go for it!

Available at Amazon.com.

Hope this helps,

Mitch