Blanche Descartes was a collaborative

pseudonym A pseudonym (; ) or alias () is a fictitious name that a person assumes for a particular purpose, which differs from their original or true meaning ( orthonym). This also differs from a new name that entirely or legally replaces an individual's o ...

used by the English

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

s R. Leonard Brooks, Arthur Harold Stone, Cedric Smith, and W. T. Tutte. The four mathematicians met in 1935 as undergraduate students at

Trinity College, Cambridge Trinity College is a Colleges of the University of Cambridge, constituent college of the University of Cambridge. Founded in 1546 by King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any ...

, where they joined the Trinity Mathematical Society and began meeting together to work on mathematical problems.

Pseudonym

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 A blank cheque or blank check in the literal sense is a cheque that has no monetary value written in, but is already signed. In the figurative sense, it is used to describe a situation in which an agreement has been made that is open-ended or va ...

''.

Publication

Over 30 works were published under the name, including whimsical poetry and mathematical humour, but some serious mathematical results as well. Many of these publications appeared in '' Eureka'', a mathematical student magazine in Cambridge. Notably, the foursome proved several

theorem In mathematics and formal logic, a theorem is a statement (logic), statement that has been Mathematical proof, proven, or can be proven. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to esta ...

s in mathematical

tessellation A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety ...

. In particular, they solved the problem of

squaring the square Squaring the square is the problem of tessellation, tiling an integral square using only other integral squares. (An integral square is a square (geometry), square whose sides have integer length.) The name was coined in a humorous analogy with sq ...

, 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 An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sou ...

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 pretence for years, refusing to acknowledge even in private that she was fictitious. "Descartes" also published on graph colouring, and Tutte used the pseudonym to publish the fourth known

snark Snark may refer to: Fictional creatures * Snark (Lewis Carroll), a fictional animal species in Lewis Carroll's ''The Hunting of the Snark'' (1876) * Zn'rx, a race of fictional aliens in Marvel Comics publications, commonly referred to as "Snarks ...

, now called the

Descartes snark In the mathematical field of graph theory, a Descartes snark is an undirected graph with 210 vertices and 315 edges. It is a snark, a graph with three edges at each vertex that cannot be partitioned into three perfect matchings. It was first disco ...

. 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 () is the collective pseudonym of a group of mathematicians, predominantly French alumni of the École normale supérieure (Paris), École normale supérieure (ENS). Founded in 1934–1935, the Bourbaki group originally intende ...

, yet another fictitious mathematical personage).

Selected publications

* * * Ungar, Peter; Descartes, Blanche; Advanced Problems and Solutions: Solutions: 4526. Amer. Math. Monthly 61 (1954), no. 5, 352–353.

References

External links

Brooks, Smith, Stone and Tutte (Part 1)
at squaring.net

at squaring.net

by Lieven Le Bruyn
On Blanche Descartes
Richard K. Guy, Gathering 4 Gardner 2017 {{DEFAULTSORT:Descartes, Blanche Academic shared pseudonyms Pseudonymous mathematicians 20th-century English mathematicians Cambridge mathematicians

Pseudonym

Publication

Selected publications

See also

References

External links