Biographies of Great Mathematicians
Augusta Ada Byron, Countess of Lovelace (1815-1852)
Ada Byron, the only legitimate child of Lord Byron, was born in December of 1815, and one month later her mother in a bitter and celebrated separation, left the "mad and bad" Byron and took Ada with her.
Ada was educated at home by governesses and tutors hired by her mother. The Lady Byron strongly believed in mathematics as a discipline of the mind and saw to it that Ada was well grounded in this subject. She felt that it would be a way to provide a stable mental state and a good antidote to the "heedlessness, imprudence, vanity, prevarication and conceit" that Ada was bound to have inherited from her immoral father.
One of her tutors was William Frend, a mathematician who didn't believe in negative numbers; another was Augustus DeMorgan, the great English logician. In 1830, when she was 15, Ada met Mary Fairfax Somerville, a well known female mathematician from Scotland. Mary had two daughters the same age as Ada, and the four women, Ada, Mary and her daughters, attended geography lectures at the University of London. (It seems that the mathematician, Charles Babbage, had persuaded the university to allow women to attend lectures in 1830, a privilege which was rescinded within a year). Ada corresponded with Mary Somerville on mathematical topics for the next twenty years, until Ada's death.
During her teenage years, Ada was a member of the bluestockings, a group of ladies that visited together, holding conversations, and literary discussions. They often invited learned men to their gatherings, which were meant to replace frivolous social evenings with something more intellectual. They would sometimes visit museums or residences of well known scientists, and it was during one of these visits that Ada actually got to meet Charles Babbage.
Babbage had built a calculating machine, called the "Difference Engine". This machine could be used to determine the polynomial equation for a table of given data. He had a model of his difference engine, as well as some other mechanical devices on display in his home in London. In addition, he had displayed his preliminary plans for a much more sophisticated machine, which he called the "Analytic Engine". Ada was fascinated by these machines, but she was particularly interested in the plans for the Analytic Engine, what's more, she immediately understood how these machines would work. Babbage was very impressed with this young girl's quick grasp of the basic concept of the calculating machines and, thus, began a nine year long collaboration on the world's first computer.
While Babbage continued to tinker with his two machines, the difference engine, and the plans for the analytic engine (which he was never able to build), Ada grew up, got married (in 1835) and had three children (in 1836, 1837 and 1839). Ada's husband Lord William King, became the Earl of Lovelace in 1838. So now the person corresponding with Babbage about his computing machines was no longer Ada Byron, but rather Augusta Ada Lovelace (or A.A.L. as she was to become known).
Babbage had gotten government support for the difference engine, and he was supposed to use it to produce a table of trigonometric values for the British Navy to use for navigation, a task he never carried out. Instead, he spent all of the government grant trying to get materials and tools for building the analytic engine . Babbage had an abrasive personality and alienated everyone who could help him.
In scholarly circles, however, his ideas were in demand. In 1840, he was invited to lecture on his plans for the analytic engine to a group of scientists at the University of Turin in Italy. It was through this series of lectures, and by a circuitous route, that Ada made her contribution to mathematics. These lectures were written-up by a young Italian military engineer, Luigi Menabrea. He had them published, in French, in the Bibliotheque Universelle de Geneve in 1842; then Ada translated this article into English in 1843.
But she did much more than translate the article. She added her own notes, which became more significant, mathematically, than the original article itself. In these notes she outlined the fundamental concepts of computer programming, and she described the main elements that would be needed in any computer language.
Her "Notes", appearing under the pseudonym A.A.L. in the prestigious journal Taylor's Scientific Memoirs, were entitled NOTE A, NOTE B, etc. Here are some very brief descriptions of some partial content of the notes.
NOTE A told how the planned "analytic engine" (and any future general computing devices of this type) differed from the already existing difference engine. Her discussion predicted the general purpose computer and went beyond anything that Babbage had envisioned. She showed how the analytic engine could be built to accept various types of cards: "control cards", "data cards" and "operation cards" and how these would make the computer automatically perform the correct operation on the data as it was entered. In other words, the computer could "analyze the data". She also proposed that both numbers and other symbols, such as letters of the alphabet, could be "coded" as numerical data which the engine could handle and put out as written material. She even contended that the engine could produce music.
In NOTE B, Ada discusses the analytic engine's memory capability, called its "storehouse columns". She anticipated the idea of memory locations or addresses. She indicated the possibility of inserting comments or memoranda that would not be acted upon by the computer, but simply would let the human reader of the instructions see what was going on. (Computer science students will recognize this as the use of "documentation" statements.)
NOTE C. Here Ada, introduced the concept of "backing"--making an operation card move back into a position so that it could work on the next data card. She said the reason for doing this was, " to secure the possibility of bringing any particular card or set of cards into use any number of times successively in the solution of one problem." This idea, which we call "looping" was hinted at in Menabrea's article but not well developed. It also arose in earlier discussions between Ada and Babbage.
NOTE D. In this note Ada explained how to write down a sequence of instructions using the operations cards, the backing process, the storehouses and various control cards to accomplish a specific set of operations.
In NOTE E, she explained how the engine could be made to hold trigonometric and other functions. She was, essentialy, introducing the idea of built-in functions in a computer.
NOTE F. She showed that by using the backing process (a loop), she could solve a system of linear equations of any size by repeating just a few operations. She wrote out the details for solving a ten by ten system of linear equations. She also speculated about the possibility of generating tables of prime numbers by a simple looping procedure.
In NOTE G Ada warns the readers about the computer's inability to do anything about it if the user entered "untrue" information. Today we call this concept "Garbage in, Garbage out". Here is the way she said it: "The Analytical Engine has no pretensions whatever to originate anything. It can do whatever we know how to order it to perform. It can follow analysis; but it has no power of anticipating any analytical relations or truths." Joan Baum, The Calculating Passion of Ada Byron , Archon Books, Hamden, Connecticut, 1986
It was also in Note G that Ada wrote out a program by which the analytic engine could generate a table of the Bernoulli numbers.
Although she anticipated the field of computer science by 110 years, the work of Ada Byron Lovelace had little or no direct influence on this field. This was because everything that she had written about was gradually rediscovered in the 1940's and 1950's by computer scientists without any knowledge of her work. So, unfortunately, her work is mostly of historical interest. For whatever its worth, the U.S. Department of Defense has built a monument to Lady Lovelace in the form of a computer language called "Ada". The plan is to install, in all government computers, an "integrated programming support environment" for programs written in the Ada language.
1. Write the names of the following people in Ada's life:
(a) The famous English poet who was her father.
(b) Her mathematical tutor who didn't believe in negative numbers.
(c) The female mathematician from Scotland.
(d) The man who invented the calculating machines.
(e) The Italian engineer whose paper she translated.
2. Who were the bluestockings and how did they affect Ada's life?
3. What was the mathematical accomplishment of Lady Lovelace, mother of three children? What implication does this have for "re-entry" students?
4. Describe Ada's "Notes" in detail. What field of study are they related to? What impact do they have today?
5. What is the name of the computer language that the U. S. Department of Defense wants to install on all government computers? How do you feel about this honor being paid to Lady Lovelace?
Here is an interesting web page giving more details on Ada.