Today we’re talking about the unseen contributions of women mathematicians.

Einstein declared of his first wife, Mileva Maric, “I need my wife. She solves for me all my mathematical problems”. Helping him was one of her few options after she gave up a promising career before it really got started when he got her pregnant out of wedlock. That didn’t stop him from divorcing her so he could marry his cousin, but he later met Emmy Noether, who took up the position of overlooked collaborator in the 1930s, after the Jewish Noether was forced to flee Nazi Germany. She laid the mathematical groundwork for Einstein’s general theory of relativity and made major advances in algebra. Yet despite her brilliance, Noether herself wrote of Princeton University, where she collaborated with Einstein and others, that she was unwelcome at "the men's university, where nothing female is admitted." She also spent years working in academic positions without pay, even after earning her PhD.

The women of Harvard Observatory and others like it helped map the skies, but were derided for working outside the home and crudely referred to as Pickering’s Harem, after director Edward Pickering. He explicitly said he hired women because he could pay them less - only 25 cents an hour - getting significantly more labour on a limited budget. When one of the computers, Henrietta Swan Leavitt discovered the period-luminosity relationship, meaning the brighter a star is, the more slowly it seems to pulses, her work enabled astronomers to calculate the distance of stars from Earth, getting a better sense of the scale of galaxies, causing a radical shift in how astronomers looked at the universe. Years after her death, her discovery made it possible for Edwin Hubble to establish his observations that the universe is continuously expanding, known as Hubble’s law. He often said Leavitt should have won a Nobel Prize.

Her colleague Annie Jump Cannon devised the Harvard classification system, the first real attempt to organise and classify stars based on their temperatures and spectral types. It is still in use today.

In the 1940s, Kathleen Antonelli, Betty Jean Jennings Bartik, Betty Holberton, Marlyn Meltzer, Frances Spence and Ruth Teitelbaum collaborated to program ENIAC, the world’s first programmable, electronic, general-purpose digital computer. They had to learn to program without a programming language or tools, because they simply did not exist yet. But from the first demonstration on 15 February 1946 — which Betty and Betty Jean wrote the program for — they received no recognition. The programmers were not even invited to the gala dinner afterward for "government and scientific men," as reported by The New York Times. Herman Goldstine, who oversaw the project for the U.S. Army, claimed that he and his wife Adele — who was a programmer and did write the original technical manual for the ENIAC — had programmed that first successful demonstration for the VIPs, which Betty Jean later declared a "boldface lie." Some historical images caption the women as models, rather than actual staff. When the Army used a War Department publicity photo for a recruitment ad, they cropped out the three women in the photo, and the department’s press releases credited a vague "group of experts" for the work, naming only Goldstine and ENIAC designers John Mauchly and J. Presper Eckert. This fundamentally ignored that the machine Mauchly and Eckert designed would never have functioned without the work of the programmers.

In the 1980s, Harvard University student Kathy Kleiman came across a photo of the women with ENIAC while researching her thesis, on early programmers and software developers. When she enquired about the images, she was told the women were models, hired to make the image more appealing. Fortunately, Kleiman kept digging, discovered the women’s story and launched the ENIAC Programmers Project to get them the recognition they should have received decades earlier.

Jess Harper and the incomparable Nellie Melba