Blanche Descartes was a collaborative pseudonym

Pseudonym

A pseudonym is a name that a person assumes for a particular purpose and that differs from his or her original orthonym...

 used by the English

English people

The English are a nation and ethnic group native to England, who speak English. The English identity is of early mediaeval origin, when they were known in Old English as the Anglecynn. England is now a country of the United Kingdom, and the majority of English people in England are British Citizens...

 mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

s R. Leonard Brooks

R. Leonard Brooks

Rowland Leonard Brooks was an English mathematician, known for proving Brooks' theorem on the relation between the chromatic number and the degree of graphs. He studied at Trinity College, Cambridge University, and also worked with fellow Trinity students W. T...

, Arthur Harold Stone

Arthur Harold Stone

Arthur Harold Stone was a British mathematician born in London, who worked mostly in topology. His wife was American mathematician Dorothy Maharam...

, Cedric Smith, and W. T. Tutte

W. T. Tutte

William Thomas Tutte, OC, FRS, known as Bill Tutte, was a British, later Canadian, codebreaker and mathematician. During World War II he made a brilliant and fundamental advance in Cryptanalysis of the Lorenz cipher, a major German code system, which had a significant impact on the Allied...

. The four mathematicians met in 1935 as undergraduate students at Trinity College, Cambridge

Trinity College, Cambridge

Trinity College is a constituent college of the University of Cambridge. Trinity has more members than any other college in Cambridge or Oxford, with around 700 undergraduates, 430 graduates, and over 170 Fellows...

, where they joined the Trinity Mathematical Society and began meeting together to work on mathematical problems. The pseudonym originated by combining the initials of the mathematicians' given names (Bill, Leonard, Arthur, and Cedric) to form BLAC. This was extended to BLAnChe. The surname Descartes was chosen as a play on the common phrase carte blanche.

Over 30 works were published under the name, including whimsical poetry and mathematical humour, but some serious mathematical results as well. Notably, the foursome proved

Mathematical proof

In mathematics, a proof is a convincing demonstration that some mathematical statement is necessarily true. Proofs are obtained from deductive reasoning, rather than from inductive or empirical arguments. That is, a proof must demonstrate that a statement is true in all cases, without a single...

 several theorem

Theorem

In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms...

s in mathematical tessellation

Tessellation

A tessellation or tiling of the plane is a pattern of plane figures that fills the plane with no overlaps and no gaps. One may also speak of tessellations of parts of the plane or of other surfaces. Generalizations to higher dimensions are also possible. Tessellations frequently appeared in the art...

. In particular, they solved the problem of squaring the square

Squaring the square

Squaring the square is the problem of tiling an integral square using only other integral squares. The name was coined in a humorous analogy with squaring the circle. Squaring the square is an easy task unless additional conditions are set...

, showing that a square can be divided into smaller squares, no two of which are the same. They also discovered "Blanche's Dissection", a method of dividing a square into rectangles of equal area but different dimensions. They modelled these using abstract electrical network

Electrical network

An electrical network is an interconnection of electrical elements such as resistors, inductors, capacitors, transmission lines, voltage sources, current sources and switches. An electrical circuit is a special type of network, one that has a closed loop giving a return path for the current...

s, an approach that yielded not only solutions to the original problem,
but techniques with wider applications to the field of electrical networks. They published their results—under their own names—in 1940. Tutte, who is believed to have contributed the most work under Descartes's name, kept up the pretense for years, refusing to acknowledge even in private that she was fictitious.

"Descartes" also published on graph colouring, and Tutte published the fourth known snark

Snark (graph theory)

In the mathematical field of graph theory, a snark is a connected, bridgeless cubic graph with chromatic index equal to 4. In other words, it is a graph in which every vertex has three neighbors, and the edges cannot be colored by only three colors without two edges of the same color meeting at a...

 under the pseudonym. She also published the poem "Hymne to Hymen" as a gift to Hector Pétard (another fictitious mathematical personage) on the day of his wedding to Betti Bourbaki (daughter of Nicolas Bourbaki

Nicolas Bourbaki

Nicolas Bourbaki is the collective pseudonym under which a group of 20th-century mathematicians wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935. With the goal of founding all of mathematics on set theory, the group strove for rigour and generality...

, yet another fictitious mathematical personage).

External links

• Brooks, Smith, Stone and Tutte (Part 1) at squaring.net
• Brooks, Smith, Stone and Tutte (Part 2) at squaring.net
• When was the Bourbaki Wedding? by Lieven Le Bruyn