By: Claudia, Meghan, Elizabeth, Yunjing

Born on October 6, 1958, Alice Silverberg is a 1979 Harvard University graduate who then received her master’s degree and Ph.D from Princeton University under the supervision of Goro Shimura. Her academic career began at Ohio State University where she worked as an Assistant and Associate Professor of Mathematics from 1984 to 1996. In 2004, she moved to the University of California, Irvine as a Professor of Mathematics and Computer Science. For the next twenty years, Silverberg gave lectures at universities around the world and served as an active member of the nominating committee of the American Mathematical Society. Since 2008, Silverberg has worked as an editor for the Association for Women in Mathematics. She is also the writer of her own blog, *Alice’s Adventures in Numberland*, where she addresses prominent social issues of sexism and discrimination in her field.

Alice Silverberg’s research is focused on number theory and cryptography. Number theory is a branch of pure mathematics dealing with integers and integer functions, and cryptography is the study/practice of writing and solving codes. While both studies might seem completely unrelated, cryptography actually uses concepts from number theory during the encryption and decryption processes. Some of the concepts include prime numbers, Euler’s function, modular arithmetic, and greatest common divisors. Since integers and prime numbers have unique qualities, they work well in creating complex codes, especially when they’re large, which increases the run-time for encrypted messages to be decrypted. Silverberg’s research in cryptography led to the development of the CEILIDH system in 2003 alongside Karl Rubin, a mathematician at the University of California, Irvine. The system is a public key algorithm (a type of encryption that everyone can use but a private key is needed to decrypt the codes) that uses algebraic tori and discrete logarithm in its ciphers (the way codes are “scrambled” and “unscrambled”). As of now, Silverberg holds over ten patents related to cryptography.

In 1990, Alice Silverberg was awarded the Sloan Fellowship, an award used to “provide support and recognition to early-career scientists and scholars”. In 2012, she became a fellow at the American Mathematical Society. In general, this job works with other mathematical teams worldwide and invites new members to their community. Then in 2018, she was named as a Distinguished Professor at the University of California. A year later, Alice became a fellow of the Association for Women in Mathematics (AWM) for her “outstanding research in number theory and deep commitment to the promotion of fairness and equal opportunity evidenced by her service and outreach efforts”. AWM is an association that was founded in 1971, and it encourages equal opportunities in education and mathematical careers for women. Alice became an editor in that association, writing about her experience of being a female mathematician. These are a few of the awards and positions she has been given, although Alice has also received many others: Sloan, IBM, MSRI, Bunting, NSF, and Humboldt fellowships.

One challenge throughout Alice Silverberg’s career was facing gender discrimination. In the colleges she attended, including Princeton and Harvard, sexism was common and fewer opportunities were given to women. Alice says, “People have told me that affirmative action must have helped me get into Harvard. They do not realize that Harvard’s affirmative action favored men and not women; discrimination against women was institutionalized.” During her time at Harvard University, male students would call female students sexist and hateful names. Even some professors at the school would make comments undermining what kind of careers women were capable of.

Harvard has a history of gender discrimination and not providing enough opportunities for women. In the 1800’s, when women applied to Harvard University, they were constantly denied. “The first women to knock at Harvard’s doors came from the middle class, typically school teachers looking for extra instruction in the sciences. But they were merely ‘thrown crumbs,’ such as access to lectures or labs,” said Horowitz. It wasn’t until 1920 that the university started accepting applications from women in their Graduate School of Education. In the 1970’s and 1980’s, women protested against Harvard’s lack of fairness for women’s sports, consideration of applications from women, and the constant sexual harassment and mistreatment from male teachers and students. 40 years later, there are many more opportunities for women at Harvard, but there is still more work to be done. Women in male dominated careers and classes (especially STEM fields) are still undermined by their classmates and professors; 50% today experience gender discrimination, and 22% endure harassment.

In 1887, Princeton made a separate school for women to attend called Evelyn College for Women. It wasn’t until 1969, after both schools merged, that women were allowed to attend Princeton. From Alice Silverberg’s experience at the school, she found that not many students were aware of the past prohibition of women, making male classmates believe that women were not intelligent enough to get accepted into the college. Princeton has been working to fight against gender discrimination and provide more opportunities for women. After discovering the pay gap between both the male and female professors at the college, Princeton has decided to give $1 million pay back to the women teaching at their school. They’ve also included other inclusive courses and activities for women, including a women’s varsity sports program in 1971 and a Women and Gender studies course for students since 1982. However, it is still challenging for female students to work in many classes due to sexism from classmates and teachers.

Although learning in a sexist environment was a challenge for Alice Silverburg, she has acquired tips from experience of working in a STEM field. She said “decisions that should be based on merit and fairness are often (subconsciously) instead of based on empathy”. Alice also mentioned that learning to listen to others, not to stress about what your classmates say, and being optimistic has helped her grow as a mathematician.

Alice Silverberg has had a distinguished career that has impacted people worldwide. Silverberg has given over 300 lectures to students at universities around the world and organized more than ten conferences in mathematics and cryptography. Professor Silverberg continues to impact the field of mathematics and computer science as she teaches at the University of California, Irvine. Alice Silverberg is a role model for young women wanting to pursue a career in mathematics. Her career impacts how women are viewed in STEM; she has excelled in her career and recognized the sexism that she and other women face. In her blog Silverberg discusses sexism in academia; Alice is open about this topic which is the first step to change. A successful mathematician like Silverberg being truthful about her experiences with sexism will inspire other women to share their stories and have an immense impact on future mathematicians. Throughout the numerous lectures and conferences Silverberg has held to share her work, she has, and will continue to, inspired her students and colleagues.

**Bibliography**

*Alice Silverberg — Curriculum Vitae*, http://www.math.uci.edu/~asilverb/cv/index.html.

2. “Alice Silverberg.” *Wikipedia*, Wikimedia Foundation, 4 May 2021, en.wikipedia.org/wiki/Alice_Silverberg.

3. “Association for Women in Mathematics.” *Wikipedia*, Wikimedia Foundation, 28 Apr. 2021, en.wikipedia.org/wiki/Association_for_Women_in_Mathematics.

4. Walsh, Colleen. “Hard-Earned Gains for Women at Harvard.” *Harvard Gazette*, Harvard Gazette, 22 July 2019, news.harvard.edu/gazette/story/2012/04/hard-earned-gains-for-women-at-harvard/.

5. “Living Proof: Stories of Resilience along the Mathematical Journey.” *PDF Download.*, The American Mathematical Society and The Mathematical Association of America, http://www.maa.org/sites/default/files/pdf/ebooks/pdf/LivingProof_WEB.pdf.

6. “Sloan Research Fellowship.” *Wikipedia*, Wikimedia Foundation, 5 June 2021, en.wikipedia.org/wiki/Sloan_Research_Fellowship.

7. “Simons Institute for the Theory of Computing.” *Alice Silverberg | Simons Institute for the Theory of Computing*, simons.berkeley.edu/people/alice-silverberg.