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Nitya Nigam | Sign petitions and donate to the cause through this link. In the wake of the deaths of George Floyd, Breonna Taylor, Tony McDade and countless more at the hands of police officers, protests have gripped the USA, and the Black Lives Matter movement has regained a lot of momentum. Police brutality is one of the many forms of racism that affect people of African origin. Racial injustices aren't just limited to violence, though. Black students are given fewer educational opportunities at a young age, which means they are less likely to end up doing well in higher academic studies, if they even get to university. Even after that, high-level academia in STEM fields, especially maths, is very white and Asian dominated. Only three African-Americans have received PhDs in mathematics from Stanford University in the US, in its entire 129-year history. But receiving a doctorate or a position as a tenured professor does not stop people of African origin from being taken less seriously in academic contexts, and they are often left wondering if they are being seen as a genuine expert in their field or just “the token African-American”. In today’s article, I’d like to take a look at three black individuals who have defied the odds to make a name for themselves in STEM fields, not just to celebrate their achievements, but to honour those who may have been just as bright, but were not given the opportunities to shine.
Joy Buolamwini is a computer scientist and researcher at the MIT Media Lab, where she focuses her work on identifying bias in algorithms and developing ways to hold algorithm designers accountable. Her work has been imperative in highlighting the many ways in which machine learning (the maths behind which we discussed in this article) amplifies the discrimination against women and minorities that already exists in our society. Google has cited her research as a reason for their decision to address gender and racial bias in their algorithms. What is perhaps most relevant right now is the work she has done that reveals the flaws of predictive policing, which makes use of algorithms to determine whether a felon is likely to reoffend. These algorithms are extremely unfair towards black people, and lead to increased violence against African-Americans as well as higher incarceration rates for them. Thanks in part to her work, the Los Angeles police department shut down their predictive policing program in April this year, and steps are being taken to do the same in other police departments around the USA. William Massey is a mathematician and professor at Princeton University. He is considered to be one of the most eminent researchers in the field of queuing theory, which studies (big surprise) properties of queues, such as lengths and waiting times. Classical queuing models rely on the assumption that “calling rates” (the rate of objects joining a queue) are constant, but in the real world, this is not the case. Dr Massey’s PhD thesis created an entirely novel method to deal with this. However, Dr Massey’s contributions to society are not just limited to his mathematical research. In 1995, he founded the Council for African-American Researchers in the Mathematical Sciences (CAARMS), which is an annual conference that provides a forum for minority researchers to showcase their work across a wide range of mathematical fields, and encourages minority graduate students to work towards doctorate degrees. In 2006, Dr Massey won the Blackwell-Tapia Prize for his contributions to maths as well as “his mentoring of minorities in the field of mathematics”. Kate Okikiolu is a mathematician and professor at Johns Hopkins University, having previously taught and researched at Princeton, MIT and UCSD. She is well known for her work with elliptic operators, which are used in solving partial differential equations (equations that deal with the rates of change of more than one variable at once), and appear frequently in the study of electrostatics and continuum mechanics. In 1997, she won a Sloan Research Fellowship, and was the first black person to receive the fellowship since its inauguration in 1955. She is also well known for her work in making maths more accessible to inner-city school children by developing curricula specific to their learning styles, and is active in improving mathematics education in underprivileged communities to this day. We hope this article served its purpose of increasing awareness about high-achieving black individuals in STEM fields, and will encourage more people to examine the ways in which they personally can help minority groups excel academically. On a more pressing note, though, this is a link to petitions you can sign and organisations you can donate to that will help further the fight against police brutality.
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Fresh Pisuttisarun In 2018, I participated in an unforgettable journey that took me from Bangkok, Thailand to Jakarta, Indonesia, and then to Melbourne, Australia. The World Mathematics Championships is a global series of maths competitions all leading to the final round hosted at the University of Melbourne. With various age divisions and qualifier rounds hosted in several locations across Asia and Europe, the competition attracts thousands of students each year from around the globe.
When I participated in WMC, I was intrigued by the competition’s philosophy and approach to maths. We didn’t receive the traditionally insular experience of taking a multiple-choice theoretical maths exam. Instead, we engaged in diverse rounds that emphasized and fostered creativity, collaboration, presentation, analysis, evaluation and so on — often overlooked yet integral skills for a well-rounded mathematician. Whether engineering, cryptography, or data science, the competition ensured that our understanding of maths was carefully contextualized in a meaningful field of knowledge. As the competition came to an end, I couldn’t help but reflect on its unorthodox style of problem-solving and how this had shed a powerful new light on maths. So, when I was invited to apply as a question-writer for the competition, I knew I had some very large shoes to fill! I started off by writing theoretical maths questions, then began to apply these theoretical questions to real-life situations. Instead of asking students to solve an equation for x and y, I would ask them to find the number of apples and oranges. But even this approach quickly became dull, repetitive, and somewhat useless. After all, why should the students care about how many apples and oranges Alice and Ben have? Instead, I took this one step further. I didn’t apply maths to any old situation for the sake of it, but to situations that were realistic and valuable. Instead, I introduced students to a projectile falling in a gravitational field and asked them to use equations to solve for the speed of its descent. This was inherently more useful: if a student wanted to design a functional parachute, this maths would let them do that. All questions, when unraveled, had a mathematical core; however, the context surrounding this maths governed how valuable that learning experience would be. I even recently attended one of the WMC rounds that took place in Bangkok, Thailand. The competition was hosted at a school not far from my house and I was ecstatic to see the questions I had written being answered live in action! Beyond the immediate pride was the realization that the questions I contributed to this competition would shape the students’ confidence and passion for learning maths, much in the same way as it had shaped mine. When people think of maths, many will imagine baseless theories and foreign symbols on paper. But this outdated notion is now being replaced by more exciting innovations. Maths can also be used to program intelligent software, understand the physics of our existence, build revolutionary robots, and analyze patterns of economic development. Competitions like the WMC are truly paving the way towards an appreciation of maths for the thriving and colorful field that it is. I believe we must utilize these opportunities to instill this appreciation in student mathematicians, starting at a young age. Fresh Pisuttisarun Ever since the COVID-19 pandemic began, people have been skeptical about the numbers of cases being reported around the world. Many have claimed, although with little supporting evidence, that health officials are tampering with the numbers, in order to avert public fearmongering, economic decline, and international shame. As an ordinary person without access to global healthcare databases or CIA-level intelligence, it seems impossible to investigate this. However, an extraordinary law of mathematics gives us some fascinating insights into the situation! Benford’s Law states that real-world data follows a special pattern in which the leading digits of individual pieces of data appear in descending frequency from 1 to 9. Let’s take the population of countries as an example. The number of countries whose population starts with a 1 — China (1.4 billion), Mexico (130 million), Greece (10 million), Tonga (110,000), etc. — is higher than the number of countries with a population that starts with a 2. The pattern continues: 2 appears more frequently than 3, 3 appears more frequently than 4, and so on. This law can be extrapolated to all sorts of real-world data. Areas of countries, heights of skyscrapers, genome data, and macroeconomic spending are all known to obey Benford’s Law. In fact, the law is so powerful that it is even used to detect fraud in election results and credit card transactions! So how can this be applied to the COVID-19 numbers? Well, the number of national COVID-19 cases, being real-world data, is expected to obey Benford’s Law. If it doesn’t, that could suggest widespread fraudulent health reports. The blue bars in the graph shows how frequently each digit appears as the leading digit of COVID-19 cases in a country. The red bars show the frequency that would be expected if this data set perfectly obeyed Benford’s Law. Visibly, this seems like a good fit; the differences seem small enough to be accounted for by natural randomness. To mathematically confirm this impression, a chi-squared test can be used to test for goodness of fit. This statistical test takes into account the differences between the observed and expected values (the difference in height between the blue and red bars) to determine whether Benford’s Law is a good enough fit for our observed data set.
Turns out... yes! Benford’s Law is a great fit for the data set at a 1% significance level, which seems to suggest that the number of COVID-19 cases retains real-world veracity. However, this does not mean that the numbers have not been tampered with at all. There could be dishonest numbers in the set, but these do not become noticeable. It only means that the health officials around the globe are generally being honest. We can rest assured that most countries are not reporting randomly made-up numbers! But why does Benford’s Law work? Given that the number of COVID-19 cases in a given country is totally random, shouldn’t that flatten the curve (pun intended) into a uniform distribution? This part of the law is harder to grasp, so hold tight. Imagine you are a country during the COVID-19 pandemic. The number of COVID-19 cases in your country is not randomly generated by a computer — it’s accumulated. You first start off with 0 cases, then as the disease spreads, the number goes up, one-by-one, from 0 to 1 to 2 to 3, etc. When you count, you always count 1 before 2, 2 before 3, 3 before 4, etc. You count the 10s before the 20s, the 20s before the 30s, etc. You count the 100s before the 200s, the 200s before the 300s, etc. Therefore, if I were to ask what number you’re on at any given moment, you are more likely to be on a number that starts with 1 than 2, 2 than 3, 3 than 4, etc. The number of COVID-19 cases is no different: the cases accumulate. Every country with 2 cases must have had 1 case at some point before; a country with 5,000 cases must have had 3,000 cases at some point before; a country with 900,000 cases must have had 600,000 cases at some point before, and so on. Therefore, if we stop the world and ask all the countries for their number of cases, as long as the health officials are honestly counting and not randomly generating numbers, the results should obey Benford’s Law. If you're interested in other applications of Benford's Law, check out this article which outlines how it can be used to help you do well on multiple choice tests! Nitya Nigam Mathematics is overwhelmingly perceived as the school subject which most accurately predicts intelligence. The general impression regarding maths is that people are either born good at it or they are not. This mentality regarding maths is harmful and counterproductive. When students feel that inherent talent is required to succeed at maths, it discourages them from pursuing the field if they don’t find themselves excelling immediately. This disillusions girls in particular, due to the false stereotype that girls and women cannot do well in STEM fields. If a girl is told at a young age that her gender means her mathematical capacity is limited, and is then told in school that an innate ability in the field is required for success, she will never be able to realise her full potential in areas that require mathematics. This effect can be observed throughout scientific and quantitative fields, and affects ethnic minorities as well as girls, leading to STEM areas being dominated by people representing only a small subset of perspectives.
Regardless of this being unfair to minorities (STEM degree holders tend to hold higher-paying jobs than non-STEM graduates, so a lack of diversity in STEM contributes to economic disparities), it is detrimental for scientific research. Having a wide range of perspectives on a research team increases productivity and sparks new ideas. For example, a 2010 study by MIT and CMU showed that teams with women tend to be more socially sensitive, which allows for a more fluid exchange of ideas. The results of increasing diversity of all kinds (racial, cultural and gender) in companies cannot be ignored: a 2018 study from the Boston Consulting Group showed that companies with more diverse management teams make 19% more revenue, due to increased innovation. Clearly, increasing diversity in STEM fields is more than worthwhile. Integral aims to make maths accessible and enjoyable - to show maths as the creative subject it is, rather than propagating the algorithmic way it is taught in many schools. We also want to disprove the belief that mathematical talent is entirely inherent. Positive reinforcement combined with curiosity and a work ethic can help push students to new mathematical heights, whereas discouragement and stereotyping hinders potential. Our team of writers is made up of high school students who are not only passionate about maths but also want to share that passion with others. Integral will be publishing articles about topics ranging from applications of maths in finance and medicine to recent developments in pure mathematics research, all aimed at students who are keen to learn more about maths but may not have had the opportunity to find resources that are both interesting and not too complex for their level of knowledge. We also encourage readers to contribute their own maths-related articles to the magazine. By providing insightful articles about various mathematical topics, and other engaging maths-related content, Integral hopes to make maths more accessible for those who may be intimidated by it, and spark curiosity in all STEM fields, which are heavily reliant on a foundational grasp of maths. We hope that our readers find Integral to not just be a valuable resource, but a way to connect with people internationally through a shared interest in mathematics. The online format of our magazine allows for discourse about its contents to traverse continents, and our problem of the week column provides a platform for students to discuss and share their solutions to challenging and intriguing maths problems. At its heart, Integral is about sharing a love for maths, and trying to spread that love as far as possible to make the world a better place. We hope we can achieve that. |
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