Pythagoras. Isaac Newton. Alan Turing. John Nash. Mathematicians rarely become famous but those who do receive celebrity treatment are invariably white men. Turing was played by Benedict Cumberbatch on the big screen; Nash by Russell Crowe.
That lens has been missing an infinitely richer, more nuanced, more multicultural story. A new book, The Secret Lives of Numbers, by Kate Kitagawa and Timothy Revell, shines a light on overlooked contributions to maths by women and men in China, India, the Arabian peninsula and other parts of the world.
âWhen we think of the history of mathematics, it is not just about ancient Greeks and bearded white men,â says Revell, 34, a British journalist, speaking via Zoom from London. âThis isnât about tearing anyone down. This is about explaining that the history of mathematics is way more complex, chaotic and amazing than you may have known. My hope is that our book goes some way to illuminating that.â
Kitagawa, 44, a maths historian from Japan, adds via Zoom from New York: âPeople already know about big figures and we do not want to challenge that idea: truth is truth. But we want to make it richer and so itâs about integration of knowledge as well.
âPersonally I enjoyed bringing in my background â raised in east Asia, reading in Chinese; I went to school in Canada and was in the US. It was precious for me recalling my time in the US and presenting those challenges that Black people and women faced in academia.â
Kitagawa and Revell came up with the idea of a history over a cup of tea at a bookshop in Charing Cross, London. They thought it would be straightforward but it was anything but. They found the origin of ideas to be as beautiful, varied and elusive as the most elegant of mathematical problems.
The authors write: âAs we worked our way through thousands of years of mathematics, almost everything we thought we knew was challenged in one way or another. Some well-known stories ended up being misrepresentations and others complete fabrications. Many mathematicians and mathematics have wrongly been excluded from history.â
For example, the invention of calculus â the theory for describing and determining how things change over time â is typically credited to Newton and Gottfried Leibniz, who each developed their own version in the 17th century. But Kitagawa and Revell contend that neither of them got their first, tracing the roots of calculus instead to 14th-century India and a a school in Kerala, where the mathematician Madhava of Sangamagrama used elements of calculus in his teaching.
Revell, who is executive editor of New Scientist, says: âThe origins of calculus are normally told as this battle between two titans of mathematics â Newton and Leibniz â and of course both of those people did an awful lot of work on calculus.
âThereâs a fun part of that story where Newton says, well, the person who will settle who got there first will be the Royal Society. The Royal Society decides itâs Newton. But of course Newton was head of the Royal Society â not the worldâs most independent report on that front.â
He continues: âBut hundreds of years before, in the 14th century, there was a mathematician called Madhava, and he was part of a school in Kerala, India, where they had loads of fantastic mathematicians. They worked on something that if you looked at it today, you would say, thatâs calculus.
âNow, it doesnât have all the polish of the modern calculus but it has the crucial parts of it. It has infinite series, which are absolutely crucial to calculus, and it also has some of the rules that they must have known, which you can infer from some of their writings also suggests they had a better understanding of the theory. For us that is part of the origin story of calculus.â
The book chronicles the life and work of extraordinary female mathematicians. Hypatia, who lived in the fourth to fifth century in Alexandria, was an astronomer, philosopher and mathematician whose talks about the geometry of the universe drew audiences from far and wide.
Revell says: âShe had this great school that she took over from her father and then she also reworked some of the classic texts of the time, which was how mathematicians then showed their acumen as mathematicians.
âThey improved on what had come before. Weâre not entirely sure because a lot of these books were then lost but we think some of the work that Hypatia did then went on and was basically rediscovered in the Renaissance period by European mathematicians later on.â
But Hypatia was accused of political meddling and met a grisly end. A Christian mob dragged her from her carriage and into a church, where she was stripped and beaten to death with broken pieces of pottery. Her body was then paraded through the streets and burned.
Kitagawa explains: âShe was accused of having a mythical sort of power. Itâs not like mathematics as we can see now. So she had this special ability even to attract people and it was like a witch-hunt and very sadly she had to meet this terrible death. Her story has been retold many times but not in a fair way until recently. There has been ages of misunderstanding and also miswriting about her character.
There is a chapter on Sophie Kowalevski, born in Moscow in 1850, the daughter of a patriarch who thought that women needed education only to participate in fine society. But her uncle Pyotr often talked with her about maths. She later wrote in her memoir: âThe meaning of these concepts I naturally could not yet grasp, but they acted on my imagination, instilling in me a reverence for mathematics as an exalted and mysterious science, which opens up to its initiates a new world of wonders.â
When Kowalevski was 18, she entered into a âwhite marriageâ (a marriage of convenience) so she could escape her fatherâs control to move abroad and study maths.
Al principio, él no quería aceptar la unión, pero “inspirada por las novelas de Dostoyevski, armó un escándalo”, encerrándose en el apartamento de su futuro esposo hasta que su padre aceptara.
En la Universidad de Berlín, Kowalevski fue prácticamente impedida de obtener un doctorado porque a las mujeres no se les permitía participar en la defensa oral estándar de su trabajo frente a un panel de expertos. Finalmente, logró obtener un doctorado de la Universidad de Göttingen.
Dedicó gran parte de su tiempo como profesora de matemáticas en el University College de Estocolmo a un problema que ella llamaba “la sirena matemática”. Como los autores lo expresan, las bailarinas de ballet ajustan intuitivamente sus rotaciones a la perfección al modificar las variables de forma, aceleración o velocidad. Pero los matemáticos no podían descifrar cómo expresarlo en una ecuación. Incluso un trompo que no era completamente redondo les resultaba esquivo.
Revell dice: “Lo que no podían resolver era cuando era ligeramente de forma extraña, cuando no era simétrico. Lo que hizo Sophie Kowalevski fue lograr avances en eso y eso finalmente le valió el Prix Bordin [un prestigioso premio anual otorgado por la Academia de Ciencias de Francia]. Hay este momento sorprendente en el que resulta ser la ganadora, aunque casi todos los matemáticos que hubieran estado ganando ese tipo de premios eran hombres.”
El libro también cuenta las historias de Ban Zhao de China, una de las primeras matemáticas conocidas que enseñó matemáticas y astronomía a la Emperatriz Deng Sui, y Euphemia Lofton Haynes, quien se convirtió en la primera mujer negra en obtener un doctorado en matemáticas y luchó contra el racismo sistémico en la educación.
Luego estaban los eruditos de la “Casa de la Sabiduría”, una biblioteca y templo del conocimiento fundado en Bagdad en el siglo VIII, asociado con Muhammad ibn Musa al-Jwarizmi, quien introdujo los números decimales y los primeros indicios de algoritmos y álgebra. La destrucción de la Casa de la Sabiduría en el asedio de Bagdad del siglo XIII fue una pérdida comparable a la de la Biblioteca de Alejandría.
Kitagawa reflexiona: “Tenían traductores y eruditos haciendo cola y recopilaban tanta información y libros, tratando de examinar en qué tipo de cosas podían creer. Estaban tratando de examinar sin prejuicios. No solo eligieron una cultura, sino muchas culturas de todas direcciones. Quizás por eso este lugar fue destruido, porque tenía tanto poder, tanta sabiduría. Era un lugar muy importante que sintetizaba todo el trabajo hasta entonces.”
“Las Vidas Secretas de los Números” hace que los lectores reconsideren las historias de origen de conceptos como pi o cero. Es un recordatorio de que las matemáticas, como cualquier rama de la ciencia, es una actividad humana emprendida en un contexto social. Es una colaboración entre los vivos y los muertos, a menudo abarcando continentes y milenios. Los autores del libro no afirmarían que el suyo es la última palabra sobre el tema.
“Mi esperanza es que sea uno de muchos”, comenta Revell. “Este es un punto de partida. Como decimos en el libro, no hay tal cosa como una historia completa. Nunca puede haberlo.
“Pero ahora estamos en una nueva era donde podemos ver estas cosas ligeramente diferentes y eso significa que cuando miras la historia de las matemáticas a través de este prisma puedes verla por lo que realmente es: hermosamente caótica, intrincada. A veces las ideas surgen y luego desaparecen, a veces alguien más asume el manto y las continúa pero desde diferentes partes del mundo, de diferentes personas.
“No habíamos anticipado hasta qué punto sería eso cuando comenzamos a hablar de esto. Pero mirando hacia atrás ahora, ese es el viaje en el que nos embarcamos y el que intentamos contar.”