A Twitter thread by John Carlos Baez.

The famous mathematician James Sylvester, born in 1814, got in lots of trouble. He entered University College London at age 14. But after just five months, he was accused of threatening a fellow student with a knife in the dining hall!


His parents took him out of college and waited for him to grow up a bit more. He began studies in Cambridge at 17. Despite being ill for 2 years, he came in second in the big math exam called the tripos. But he couldn't get a degree... because he was Jewish.


At age 24 he became a professor at University College London. At 27 he got his BA and MA in mathematics. In the same year he moved to the United States, to become a professor of mathematics at the University of Virginia. But his troubles weren't over.


When he called out a student for reading a newspaper in class, the student insulted him. Sylvester struck him with a sword stick. The student collapsed in shock. Sylvester thought he'd killed the guy! He fled to New York, where one of his brothers was living.


Later Sylvester came back to the University of Virginia, but "the abuse suffered by Sylvester from this student got worse after this".

He quit his job and moved to New York. He was denied an appointment at Columbia University, again because he was Jewish.


He returned to England and took up a job at a life insurance company. He needed a law degree for this job, and in his studies he met another mathematician, five years younger, studying law: Cayley!

They worked together on matrices and invariant theory.


Sylvester only got another math job in 1855, at the Royal Military Academy of Woolwich. He was 41.

At age 55 he had to retire - those were the rules - but for some reason the school refused to pay his pension!


The Royal Military Academy only relented and paid Sylvester his pension after a prolonged public controversy, during which he took his case to the letters page of The Times.

When he was 58, Cambridge University finally gave him his BA and MA.


At age 62, Sylvester went back to the United States to become the first professor of mathematics at the newly founded Johns Hopkins University in Baltimore, Maryland. His salary was $5,000 - quite generous for the time.

He demanded to be paid in gold.


They wouldn't pay him in gold, but he took the job anyway.

At age 64, he founded the American Journal of Mathematics. At 69, he was invited back to England to become a professor at Oxford. He worked there until his death at age 83.


One thing I like about Sylvester is that he invented lots of terms for mathematical concepts. Some of them have caught on: graph, matrix, discriminant, invariant, totient, and Jacobian!

Others have not: cyclotheme, meicatecticizant, tamisage and dozens more.


One of the many things Sylvester studied was the amazing special features of 6-element sets.

Sylvester defined a 'duad' to be a way of choosing 2 things from a set. A set of 6 things has 15 duads. A hypercube has 16 corners. This has surprising consequences.


This picture by Greg Egan shows a hypercube with 15 of its 16 corners labelled by duads in a clever way. This can help you see a wonderful fact: the group of permutations of 6 things is isomorphic to the symmetry group of a 4d symplectic vector space over F2.


For details, read my Visual Insight post:

https://blogs.ams.org/visualinsight/2015/09/01/hypercube-of-duads/ …

And if you've come this far, please do me a favor and tell me: do the links in this post work, or is the page "frozen" in a weird way? I complained to the AMS about this, and they say it's fine.


While I've told you some of the tawdry details of Sylvester's life, like any great mathematician he spent *most* of his life in worlds of abstract beauty.

He also loved poetry, and translated poems into English from French, German, Italian, Latin and Greek.

(15/n, n = 15)