What lies beneath a structure with an unimaginable 196,883 dimensions?
In 1981, Freeman Dyson addressed a typically distinguished group of scholars gathered at the Institute for a colloquium, but speaking on a decidedly atypical subject: “Unfashionable Pursuits.”
The problems which we face as guardians of scientific progress are how to recognize the fruitful unfashionable idea, and how to support it.
To begin with, we may look around at the world of mathematics and see whether we can identify unfashionable ideas which might later emerge as essential building blocks for the physics of the twenty-first century.*
He surveyed the history of science, alighting eventually upon the monster group—an exquisitely symmetrical entity within the realm of group theory, the mathematical study of symmetry. For much of the twentieth century, mathematicians worked to classify “finite simple groups”—the equivalent of elementary particles, the building blocks of all groups. The classification project ultimately collected all of the finite simple groups into eighteen families and twenty-six exceptional outliers. The monster was the last and largest of these exceptional or “sporadic” groups.READ MORE>