Maybe This Was A Dumb Idea…

Write, write, write...

Missing the maths part :'(

sorry what

Littlewood polynomials are polynomials all of whose coefficients are either +1 or −1 (so even 0 is not allowed). If you take all Littlewood polynomials up to a certain degree, calculate all their (complex) roots, and plot those roots in the complex plane, then you get a beautiful fractal-like structure above.

The image is slightly misleading, because the “holes” on the unit circle tend to completely fill in if the degree goes up. Intuitively, the holes mean that complex numbers on the unit circle that are close to low-degree roots of unity are hard to approximate by low-degree Littlewood polynomials (unless they already are roots of unity).

In particular the structure at the edge of the ring is deeply interesting. Notice the familiarity with the dragon curve?

https://twitter.com/dreugeniacheng/status/1097969617014804480?s=21

No. 448

A new geometric design every day

Well my week has been exciting so far.

ESO’s La Silla Observatory over the night sky

Image credit: ESO

Could you imagine?

You’re Charlotte Scott. You’re determined to get your math degree as a woman in the late 1800s. You fight sexism and condescension every day and somehow wrangle your way into a special and prestigious exam. And then this happens:

“In 1880, Scott obtained special permission to take the Cambridge Mathematical TriposExam, as women were not normally allowed to sit for the exam. She came eighth on the Tripos of all students taking them, but due to her sex, the title of “eighth wrangler,” a high honour, went officially to a male student.[1]

At the ceremony, however, after the seventh wrangler had been announced, all the students in the audience shouted her name.

***

The man read out the names and when he came to ‘eighth,’ before he could say the name, all the undergraduates called out ‘Scott of Girton,’ and cheered tremendously, shouting her name over and over again with tremendous cheers and waving of hats.

— contemporary report, “Charlotte Angas Scott (1858–1931)” in Women of Mathematics: A Biobibliographic Sourcebook[1]

***

Because she could not attend the award ceremony, Scott celebrated her accomplishment at Girton College where there were cheers and clapping at dinner, a special evening ceremony where the students sang “See the Conquering Hero Comes”, received an ode written by a staff member, and was crowned with laurels.[1]

After this incident women were allowed to formally take the exam and their exam scores listed, although separately from the men’s and thus not included in the rankings. Women obtaining the necessary score also received a special certificate instead of the BA degree with honours. In 1922, James Harkness remarked that Scott’s achievement marked “the turning point in England from the theoretical feminism of Mill and others to the practical education and political advances of the present time”.[1]“ — wikipedia

😭♥️

Later on, Charlotte became one of the core mathematics faculty of Bryn Mawr College, and also is seen as one of the key figures in the transition to abstract mathematical proofs, as well as the first female member of the New York Mathematical society, later known as the AMS. What a cool lady.