Ethics in Mathematics: Resources
Federico Ardila

What does it mean to do mathematics ethically?

(Last updated: Dec. 2020)

Dear students,

In 2013, my SFSU student Brian Cruz asked me whether mathematicians have an ethical code, similar to the Hippocratic Oaths adopted by physicians. More than two decades into my mathematical career, I had never thought of this question, or heard anyone discuss it. Thanks to him, I now devote one day of each semester to discuss this question with my students.
Asking you the question is surely more important than proposing an answer to you. It would be disingenuous and disrespectful to you to pretend that I do not have political opinions on this matter. Even trying to "remain apolitical" is itself a political choice. But the point of this exercise is not for you to have the same opinions that I have, but to form your own critical opinions. This is an invitation for you to turn in a:

Writing Assignment:

What does 'doing mathematics ethically' mean to you? This question is an invitation to recognize the power you carry as a mathematician, and the privilege and responsibility that comes with it. When you enter a scientific career, you do not leave yourself at the door. You can choose how to use that power. My hope is that you will always continue to think about this in your work.


This is a small selection of resources to help each other think about this. Your writeup does not have to be based on this, I want to read *your* thoughts on this question. These are just some possible starting points, but there are many others, depending on your interests ("pure" math, teaching, data science, biotechnology, environmental science, finance, etc.) If there are other resources that you find interesting or useful, please send them along!

Make sure to think critically about what you read or hear below, discuss it with each other, and form your own opinions. Ask yourself:
-- Who is benefitting from this work? Who is not?
-- Who is funding this work?
-- Whose voices are we hearing? Whose voices are we not hearing?
-- How might I be able to contribute?


I wrote the short paper CAT(0), Geometry, Robots, and Society where I collect some of my own thoughts on this question, in the context of a research project that started in "pure" mathematics and found potential applications.


Many mathematicians do work with police departments to provide modeling and data work. For example, the ICERM math institute sponsored a workshop on Predictive Policing which included ride-alongs with the Providence Police Department. This workshop was organized by a founder and an investor of PredPol, a for-profit company which has lucrative contracts with police departments across the country, providing software that claims, among other things, to predict where crimes occur, and when they are gang related.

Here is a short video overview on this topic by Wired magazine. A summary of the feedback loops created by PredPol, and the racist consequences, can be found in this report. There are also deep concerns about the use of machine learning, AI, and facial recognition technologies to justify and perpetuate oppression. See, for example, this article and this article.

(This section is taken from a letter written by 10 mathematicians (in full disclosure, I am one of them) and signed by thousands of mathematicians, calling for a boycott to collaboration with the police on June 15, 2020. In the above link you can also read the responses of some mathematicians to this letter. Here you can read a response to those responses by the Just Mathematics Collective.)


A famous recent case of mathematics and ethics in the US concerns the National Security Agency's domestic spying program. Mathematician William Binney, a former intelligence official with the NSA and whistleblower, discusses his role as a codebreaker for the NSA and his eventual disagreement with the agency's work.

The NSA is the largest employer of mathematicians in the US. In 2014, mathematicians urged colleagues to refuse working for the NSA.

This is a preview to a 1.5 hour documentary on the work of a group of scientists, including mathematician William Tutte (one of my favorite mathematicians!), mathematician/computer scientist Alan Turing, engineer Tommy Flowers, breaking the Nazi codes for top-secret communication. This mathematical action is said to have shortened World War II significantly, saving millions of peoples' lives.
It is worth mentioning that, after his work in World War II, the United Kingdom prosecuted Turing for homosexuality (which was a crime in the UK at the time), and accepted chemical castration so he would not have to go to jail. He committed suicide soon afterwards.


Mathematician and data scientist Cathy O'Neil summarizes her book Weapons of Math Destruction in this TED talk. Algorithms decide who gets a loan, who gets a job interview, who gets insurance and much more -- but they don't automatically make things fair. O'Neil coined a term for algorithms that are secret, important and harmful: "weapons of math destruction." She talks about the hidden agendas behind the formulas.
Computer scientist Latanya Sweeney discusses a specific example in her personal experience.


Benetech is a Silicon Valley nonprofit using technology towards human rights issues. Here is an overview of their work. This video (watch 0:00-2:53 and 5:00-8:30 especially) and this article describe the role of Benetech statisticians in the clarification of human rights violations in Guatemala in the 70s and 80s.

Maria De-Arteaga and Artur Dubrawski's report on Gender Equality and Big Data from 2018.


In 2016, US President Barack Obama invited Joi Ito, who was then the Director of the MIT Media Lab, to discuss the role of artificial intelligence in society, including self-driving cars, national security, and the economy. Their conversation, available on video or text is an enlightening, accessible introduction to this topic, the numerous ethical issues that arise, and the role of researchers, industry, and the government in addressing them.
Ito later shared: ``I told President Obama that we had iterated on the Media Lab's famous motto `Demo or Die' and had changed it to `Deploy or Die.' He thought about it and told me, `maybe you should work on that messaging.'"

This is a longer discussion on Big Data, Inequality, and the Law between Computer Science Professor Latanya Sweeney and Law Professor Alvaro Bedoya.


Perhaps the most famous case of science and ethics meeting in the 20th century is the creation of the atomic bomb around World War II.
-- Many years later, Feynman discusses his early years as a student and his role in the development of the atomic bomb.
-- Neil deGrasse Tyson and Stephen Colbert discuss ethical issues in science. Watch 12:17-17:35.


Most medical doctors swear the Hippocratic Oath: a >2000 year old oath (which has been rewritten over time) of moral behavior. Here is a short article on it.

Cathy O'Neill has argued that a similar oath for data scientists is necessary (and not sufficient). She highlights a predecessor, a modeler's hippocractic oath by Emanuel Derman and Paul Wilmott.

More recently, mathematician Hannah Fry has argued that mathematicians and technologists also need a similar oath. (To tell the full story, one of her areas of research is modeling for policing, as discussed above.)

Other sources of resources

-- The Just Mathematics Collective works to shift the global mathematics community towards justice, via genuine anit-racism, anti-miliarism, and solidarity with the Global South.

-- Data for Black Lives hosts a truly interdisciplinary conference seeking to use data science to create concrete and measurable change in the lives of Black people. You may watch the conference videos, full of valuable perspectives. Their Twitter feed is an excelent source of information.

-- Black in AI is an initiative to increase the presence of Black people in the field of AI. Many of their researchers have done excellent scholarly and organizing work on the ethical aspects of algorithms. Their Twitter feed is an excelent source of information.

-- In 2018, Jamylle Carter, Kim Seashore, Matt Beck, and I organized an AMS Special Session on Social Change in and Through Mathematics and Education. The titles and abstracts of the talks in this session will lead you to lots of interesting work. In 2021, Ashia Wilson, Robin Wilson, Shandy Hauk, and I are organizing an AMS Session on Social Change in and Through Mathematics and Education.

-- The Cambridge University Ethics in Mathematics Project is a group of mathematicians who have developed a course and a conference on this topic. Videos are available in these links.