Kirkman's schoolgirls to quantum spin pairs : a 150-year thread of mathematics that runs through Bombay

“In 1850, a clergyman and amateur mathematician, Thomas Kirkman, solved a combinatorial problem involving 15 schoolgirls. Later, this became an example of what are called "designs" in a branch of mathematics called Design Theory, born out of the work of the population geneticist R.A. Fisher from his "design of experiments" in agricultural statistics. The subject connects to coding theory, finite projective geometries, Latin squares (and the game SuDoKu) and other mathematical structures. Fisher's visit to the 1938 Bombay Science Congress and his collaboration with Indian mathematicians that he met on that trip played a central role in these developments. Surprisingly, the (Lie and Clifford) algebra of the quantum operators involved in systems of qubits in the currently active area of quantum information is closely connected to Kirkman's problem. Links between all these topics will be discussed along with some interesting human interest stories of some of the physicists and mathematicians involved in these subjects.”