Specifically, it is the person who achieves the highest overall mark among the Wranglers – the students at Cambridge who gain first-class degrees in mathematics. The Cambridge undergraduate mathematics course, or Mathematical Tripos, is famously difficult.
Many Senior Wranglers have become world-leading figures in mathematics, physics, and other fields. They include George Airy, Jacob Bronowski, Christopher Budd, Kevin Buzzard, Arthur Cayley, Donald Coxeter, Arthur Eddington, Ben Green, John Herschel, James Inman, J. E. Littlewood, Lee Hsien Loong, Jayant Narlikar, Morris Pell, John Polkinghorne, Frank Ramsey, Lord Rayleigh (John Strutt), George Stokes, Isaac Todhunter, and Sir Gilbert Walker.
Senior Wranglers were once fêted with torchlit processions and took pride of place in the University's graduation ceremony. Years in Cambridge were often remembered by who had been Senior Wrangler that year.
The annual ceremony in which the Senior Wrangler becomes known was first held in the 18th century. Standing on the balcony of the University's Senate House, the examiner reads out the class results for mathematics, and printed copies of the results are then thrown to the audience below. The examiner no longer announces the students' exact rankings, but they still identify the Senior Wrangler, nowadays by tipping their academic hat when reading out the person's name.