# James Mercer (mathematician)

**James Mercer** FRS^{[1]} (15 January 1883 – 21 February 1932) was a mathematician, born in Bootle, close to Liverpool, England.^{[2]}

He was educated at University of Manchester, and then University of Cambridge. He became a Fellow, saw active service at the Battle of Jutland in World War I and, after decades of ill health, died in London.

He proved Mercer's theorem, which states that positive-definite kernels can be expressed as a dot product in a high-dimensional space. This theorem is the basis of the kernel trick (applied by Aizerman), which allows linear algorithms to be easily converted into non-linear algorithms.

## References[edit]

**^**Hobson, E. W. (1933). "James Mercer. 1883-1932".*Obituary Notices of Fellows of the Royal Society*.**1**(2): 164–165. doi:10.1098/rsbm.1933.0016.**^**O'Connor, John J.; Robertson, Edmund F., "James Mercer",*MacTutor History of Mathematics Archive*, University of St Andrews

Categories:

- 1883 births
- 1932 deaths
- 19th-century British mathematicians
- 20th-century British mathematicians
- Mathematical analysts
- People from Bootle
- Alumni of the University of Manchester
- Senior Wranglers
- Scientists from Liverpool
- Fellows of the Royal Society
- Alumni of the University of Cambridge
- British mathematician stubs