Word Problem of the Week: From the Notebook of Benjamin Banneker

This morning I had the pleasure of attending a talk by John Mahoney concerning his experience teaching at Benjamin Banneker Academic High School in the District of Columbia. Part of the talk concerned Banneker himself, who is a fascinating personality about whom I'm going to have to write more later.

Banneker kept a notebook in which he recorded interesting problems. This one is interesting because there is an elegant solution that is unintuitive to someone educated in the modern way. At least to me, it was unintuitive. Problems such as this seem to have been popular in the 18th century, though.

Question by Elliot Geographer General
Divide 60 into four Such parts, that the first being increased by 4, the Second decreased by 4, the third multiplyed by 4, the fourth part divided by 4, that the Sum, the difference, the product, and the Quotient shall be one and the Same number.

You start by making a guess as to the number mentioned at the end, then adjust things based on the error you get.

James Joseph Sylvester: Mathematitian and "poet".

There is a rather interesting transcribed speech here which discusses the poetical efforts of J. J. Sylvester, who was the first Jew to hold a professorship at Oxford. In particular, as mentioned by Bell, he wrote a poem called, "To a missing member of a family of terms in an algebraical formula" which starts as such:

Lone and discarded one! divorced by fate,
From thy wished-for fellows--whither art flown?
Where lingerest thou in thy bereaved estate,
Like some lost star or buried meteor stone?

So yeah, his math was better than his poetry.

What I'm Reading: Men of Mathematics

Men of Mathematics by Eric Temple Bell is a collection of personal and professional biographies of thirty great mathematicians. The first three are from ancient Greece: Zeno, Eudoxus, and Archimedes. The others are from the seventeenth to nineteenth centuries, from Descartes to Cantor.

It was written in 1937, which shows. Not just when the author refers to Bertrand Russell in the present tense, but also, for example, when he mentions in the introduction that certain "writers and artists (some from Hollywood)" have been interested in "how many of the great mathematicians have been perverts." ("None.")

The great thing about this book is the richness of detail Bell gives in the details of the subjects' personal lives. One gets the sense that Bell cares for the mathematicians personally, and also that there is a distinct lack of objectivity here. Gauss in particular is the recipient of torrents of praise. Anyone who opposed or insulted him, or who he disliked, is savaged, usually hilariously.

For example, Napoleon apparently once told Laplace that he would read his book "the first free month he could find." Bell, after relating this, proceeds to write that "Newton and Gauss might have been equal to the task; Napoleon no doubt could have turned the pages in his month without greatly tiring himself."

Later in the chapter, Bell mentions that Gauss didn't like Lord Byron, then goes on to describe the poet in terms of "posturing", "reiterated world-weariness", "affected misanthropy", and "histrionics". He then points out that "no man who guzzled good brandy and pretty women as assiduously as Byron did could be so very weary of the world as the naughty young poet with the flashing eye and the shaking hand pretended to be."

Right now, I'm on the chapter about William Hamilton. It starts with relating that when Hamilton was thirteen he knew a language for every year of his life. Bell does not approve. ("Good God! What was the sense of it all?") At fourteen he wrote a letter of welcome to the Persian Ambassador, in Persian, which Bell imagines may have been responsible for the Ambassador giving an excuse to avoid meeting him. According to an article of Nature (from 1883!) I found on Google Books, it read like this:

As the heart of the worshiper is turned towards the altar of his sacred vision, and as the sunflower to the rays of the sun, so to thy polished radiance turns expanding itself the yet unblossomed rosebud of my mind, desiring warmer climates whose fragrancy and glorious splendor appear to warm and embalm the orbit about thee, the Star of the State, of brilliant lustre.

The article says it was received warmly.

So all in all, this book is amusing and a good read for those interested in the personalities behind the major mathematical discoveries of the seventeenth to nineteenth centuries. But while Bell was an accomplished mathematician in his own right, Men of Mathematics is in large part a work of opinion, and does not in all cases possess the rigor that history is capable of having.

10 Remarkable Female Mathematicians

I wrote a post much like this one, a while back.
The post is here.

A 29th twofer.

First, an interesting little article on a very strange research project that, strangely, seems to have produced some results. Strange ones. Basically, they are trying to map personality traits according to geography in the US.

Second, an article about the mistakes made by Einstein. This, in my opinion, is an important thing to write and read about, because it defuses the idea that science is ideology. If a physicist whose name and countenance are symbols of intelligence itself can be shown to have been wrong - well, that's only to be expected really.

All the other great scientists of the past were wrong about things, because advancing the state of the art in knowledge is like that - better theories, better data, better models - but never The Truth. Just a useful approximation. This is the power and glory of science: to recognize and correct its errors.

This is why I dislike terms such as "Darwinism" and "evolutionism" so intensely. They attempt to crystallize the ever changing ideas of how species originate into an ideology that, if somehow shown to be false, can then be defeated. It surely must be comforting for opponents of science and knowledge to think that this could possibly work. However, they are just as wrong about this as they are about so many other things.

Mathematical Personalities: Gerolamo Cardano

Sorry about the lack of updates, but the life has been busy.

Down to business.

The Italian Renaissance was one of those interesting times in world history in which the great increase in knowledge and trade led to an explosion of wealth, which led to more knowledge and trade, and so on...but we have to remember that these are not modern people. This was a time that was altogether more violent and chaotic than anything we see today (in the Western world, anyway) because for some reason the people of that time and place really knew how to work the chaos into something rather creative. I mentioned Cardano before, but in the context of the solution to the cubic equation, which is a great story. Now I want to mention some other things about the man. The events of his life illustrate the differences between that era and this.

Remember that the modern world comes largely from the Enlightenment with heavy doses of Modernism and Postmodernism thrown into the mix. This all happened after the Renaissance, and the 16th century was more like the medieval world than like ours. His mother fled the plague. He had trouble starting a career in medicine because his parents were not married. He was a gambler and wrote a book on the subject that was the first to make probability into a science. While he contributed to the sciences and mathematics, he was an astrologer as well and was arrested for heresy after casting the horoscope of Jesus.

People who are brilliant enough to make lasting contributions to mathematics have a tendency to be eccentric. Add to this the fact that many discoveries were made before what we would call the modern era, and we find that the people of the history of mathematics are incredible to study.

A new blog.

I created this to blog about the history of math and science, which is a subject I really enjoy. I teach math in a high school, and it is not always possible to talk much about this sort of thing, because it is not actually in the curriculum. Science has historical developments which are covered in science class, but the development of math is not.

One of my favorite parts of the subject is the personalities of the people who made historical developments. I like to tell my classes that anyone smart enough to make a lasting contribution to mathematics is likely to also be a bit colorful. One of my favorites is John Napier, hence the name of the blog.

If you have noticed that the description mentions comics, let's just say that public domain images from old artwork are very handy.