Alan Veliz-Cuba, University of Dayton

You can probably think of a time when you’ve used math to solve an everyday problem, such as calculating a tip at a restaurant or determining the square footage of a room. But what role does math play in solving complex problems such as curing a disease?

In my job as an applied mathematician, I use mathematical tools to study and solve complex problems in biology. I have worked on problems involving gene and neural networks such as interactions between cells and decision-making. To do this, I create descriptions of a real-world situation in mathematical language. The act of turning a situation into a mathematical representation is called modeling.

Translating real situations into mathematical terms

If you ever solved an arithmetic problem about the speed of trains or cost of groceries, that’s an example of mathematical modeling. But for more difficult questions, even just writing the real-world scenario as a math problem can be complicated. This process requires a lot of creativity and understanding of the problem at hand and is often the result of applied mathematicians working with scientists in other disciplines.

As an example, we could represent a game of Sudoku as a mathematical model. In Sudoku, the player fills empty boxes in a puzzle with numbers between 1 and 9 subject to some rules, such as no repeated numbers in any row or column.

The puzzle begins with some prefilled boxes, and the goal is to figure out which numbers go in the rest of the boxes.

Imagine that a variable, say x, represents the number that goes in one of those empty boxes. We can guarantee that x is between 1 and 9 by saying that x solves the equation (x-1)(x-2) … (x-9)=0. This equation is true only when one of the factors on the left side is zero. Each of the factors on the left side is zero only when x is a number between 1 and 9; for example, (x-1)=0 when x=1. This equation encodes a fact about our game of Sudoku, and we can encode the other features of the game similarly. The resulting model of Sudoku will be a set of equations with 81 variables, one for each box in the puzzle.

Another situation we might model is the concentration of a drug, say aspirin, in a person’s bloodstream. In this case, we would be interested in how the concentration changes as we ingest aspirin and the body metabolizes it. Just like with Sudoku, one can create a set of equations that describe how the concentration of aspirin evolves over time and how additional ingestion affects the dynamics of this medication. In contrast to Sudoku, however, the variables that represent concentrations are not static but rather change over time.

But the act of modeling is not always so straightforward. How would we model diseases such as cancer? Is it enough to model the size and shape of a tumor, or do we need to model every single blood vessel inside the tumor? Every single cell? Every single chemical in each cell? There is much that is unknown about cancer, so how can we model such unknown features? Is it even possible?

Applied mathematicians have to find a balance between models that are realistic enough to be useful and simple enough to be implemented. Building these models may take several years, but in collaboration with experimental scientists, the act of trying to find a model often provides novel insight into the real-world problem.

Mathematical models help find real solutions

After writing a mathematical problem to represent a situation, the second step in the modeling process is to solve the problem.

For Sudoku, we need to solve a collection of equations with 81 variables. For the aspirin example, we need to solve an equation that describes the rate of change of concentrations. This is where all the math that has been and is still being invented comes into play. Areas of pure math such as algebra, analysis, combinatorics and many others can be used – in some cases combined – to solve the complex math problems arising from applications of math to the real world.

The third step of the modeling process consists of translating the mathematical solution into the solution to the applied problem. In the case of Sudoku, the solution to the equations tells us which number should go in each box to solve the puzzle. In the case of aspirin, the solution would be a set of curves that tell us the aspirin concentration in the digestive system and bloodstream. This is how applied mathematics works.

When creating a model isn’t enough

Or is it? While this three-step process is the ideal process of applied math, reality is more complicated. Once I reach the second step where I want the solution of the math problem, very often, if not most of the time, it turns out that no one knows how to solve the math problem in the model. In some cases, the math to study the problem doesn’t even exist.

For example, it is difficult to analyze models of cancer because the interactions between genes, proteins and chemicals are not as straightforward as the relationships between boxes in a game of Sudoku. The main difficulty is that these interactions are “nonlinear,” meaning that the effect of two inputs is not simply the sum of the individual effects. To address this, I have been working on novel ways to study nonlinear systems, such as Boolean network theory and polynomial algebra. With this and traditional approaches, my colleagues and I have studied questions in areas such as
decision-making,
gene networks,
cellular differentiation and
limb regeneration.

When approaching unsolved applied math problems, the distinction between applied and pure mathematics often vanishes. Areas that were considered at one time too abstract have been exactly what is needed for modern problems. This highlights the importance of math for all of us; current areas of pure mathematics can become the applied mathematics of tomorrow and be the tools needed for complex, real-world problems.

Alan Veliz-Cuba, Associate Professor of Mathematics, University of Dayton

This article is republished from The Conversation under a Creative Commons license. Read the original article.

Filomena Nunes, Michigan State University

Out of 225 people awarded the Nobel Prize in physics, only five have been women. This is a very small number, and certainly smaller than 50% – the percent of women in the human population.

Despite several studies exposing the barriers for women in science and the many efforts to increase their representation, physics continues to be a male-dominated field. Only 1 in 5 physicists are women, a number that has not moved since 2010.

Three of the five Nobel Prizes in physics awarded to women have been in the past decade. As a woman physicist, seeing three women join the cadre of Nobel laureates in Physics in just a handful of years is beyond exciting.

Nobel Prize-winning work

The three woman physicists receiving Nobel Prize honors in the 21st century are Donna Strickland, who won in 2018, Andrea Ghez, who won in 2020, and Anne L’Huillier, who won in 2023. All three made important contributions to science.

Strickland, a physicist from the University of Waterloo, won the award for her work on lasers, implementing a method called chirped pulse amplification.

Ghez, an astrophysicist from UCLA, got the Nobel for her work observing stars, especially those near the center of the Milky Way.

L’Huillier, a physicist from the University of Lund, received the 2023 Nobel, also for her work with lasers.

What are some common threads in their lives?

Being a minority in a research field isn’t easy. Sticking with it long enough to have a storied career, as the three winners have, is a huge accomplishment. Since winning the prize, the three winners have recounted their research journeys and offered advice to the next generation of physicists in a variety of interviews. I’ve noticed a few common threads.

A career in academia is a long haul. All three women emphasize the timescale involved in going from first steps in their research to being recognized by the Nobel committee. L’Huillier refers to it as a long journey.

While winning a Nobel may come with some glamour and notoriety, if you are after a quick reward, this career may not be the right line of work. It now takes an average of 28 years between publishing a discovery and receiving a Nobel in physics.

You cannot predict which basic science topic is going to lead to a Nobel – nor, for that matter, which will end up having any kind of impact. The best an early-career physicist can do is to explore different topics, try new things, lean into discomfort and find something they’re passionate about.

All three women talk about how many times they ran into difficulties. Before she got the chirped pulse amplification method to work, Strickland had started to wonder whether she would ever get a Ph.D., having hit so many dead ends. The first time Ghez proposed the project that would lead to her celebrated work, she was turned down.

All three of them thought of quitting at some point. So don’t be discouraged if you are turned down or if others say you cannot do it.

“Keep going,” says L’Huillier. “You need to be obstinate.”

Ghez recommends seeing experiments that don’t work not as failures but as opportunities.

Movies and TV shows paint a picture of the scientist as a social misfit, an individual working alone in the laboratory. But that’s not how it works. All these women work in teams.

“Science is a team sport. You need to know what you don’t know and seek help for what is missing,” says Strickland.

Seeking help often leads to collaborations with other research groups. As Ghez puts it, “Science is a very social enterprise.”

And above all else, the three medalists referred to luck as an essential ingredient for success. The world is full of physicists just as dedicated and just as smart who don’t get the Nobel.

Themes specific to women

Strickland, Ghez and L’Huillier are always asked about their experiences being a woman in science and their views on diversity and equity in physics. All of them emphasize the importance of diversity.

The three laureates have recognized how critical female role models have been in their lives. To believe a physics career is even possible, you need to see people in the field who look like you.

They also mention the importance of a support network, especially for women. Having a group of people you trust to cheer you on can help when you feel discouraged.

The three women also talk about their experiences balancing work and life. It’s not always easy.

Strickland left the standard academic path after a postdoctoral fellowship to become a technician so she could be close to her husband and start her family. L’Huillier walked away from her job and moved from France to Sweden, where she was unemployed for a while. Ghez waited years to have kids. There is no single trajectory. But time away from research can give you fresh perspectives and inspiration to take the next steps.

They also talk about how diversity enriches the research itself. A team that is open to different points of view is more creative. It is also more fun to work in.

These women have pointed out that the culture for women in science has improved over their careers and they are optimistic about the future. If you calculate the percent of Nobel Prizes in physics awarded to women in the past decade alone, then about 1 in 10 Nobel recipients have been women. To me, this indicates that, indeed, things may be getting better.

And perhaps the Nobel committee is addressing, at least in part, possible gender inequities in their processes. For example, the lack of nominations of women and the influence that stereotypes could play in their evaluations. So it is with great expectation that I await this year’s announcement.

Filomena Nunes, Professor of Physics, Michigan State University

This article is republished from The Conversation under a Creative Commons license. Read the original article.

Jonathan D. Quick, Duke University and Eszter Rimanyi, Duke University

In 2023, 42 state attorneys general sued Meta to remove Instagram features that Meta’s own studies had shown – and independent research had confirmed – are harmful to teenage girls.

The same year, a report from the nonprofit Sandy Hook Promise found gun manufacturers were targeting the youth market with eye-catching ads and product placements in video games.

And in the run-up to the Paris Olympics, a leading international health journal urged the International Olympic Committee to end its relationship with Coca-Cola because of the increased obesity, diabetes, heart disease and high blood pressure associated with sugary drinks.

Social media, guns, sugar: These are all examples of what we call “market-driven epidemics.”

When people think of epidemics, they might think they’re caused only by viruses or other germs. But as public health experts, we know that’s just part of the story. Commerce can cause epidemics, too. That’s why our team coined the phrase in a recent study because you can’t solve a problem without naming it.

Market-driven epidemics follow a familiar script. First, companies start selling an appealing, often addictive product. As more and more people start using it, the health harms become clearer. Yet even as evidence of damage grows and deaths pile up, sales continue to rise as companies resist efforts by health authorities, consumer groups and others to control them.

We see this pattern with many products today, including social media platforms, firearms, sugar-sweetened beverages, ultra-processed foods, opioids, nicotine products, infant formula and alcohol. Collectively, their harm contributes to more than 1 million deaths in the U.S. each year.

How to fight a commercial epidemic

In our study, we asked two critical questions: Is it possible to combat such epidemics by changing the consumption patterns of millions of people? And if so, what does it take?

We found the answers by looking at decades of efforts to reduce unhealthy consumption of three products: cigarettes, sugar and prescription opioids.

In each case, Americans kept consuming more and more of these products, even in the face of growing health concerns, until a tipping point was reached. That was followed by steady declines in consumption.

The immediate cause for each tipping point varied considerably. For cigarettes, it was the trusted, authoritative voice of the U.S. Surgeon General unequivocally declaring in 1964 that smoking causes cancer.

In the case of sugar, one of the key moments was a high-profile 1999 petition titled “America: Drowning In Sugar” submitted by the Center for Science in the Public Interest and supported by 72 leading public health organizations and experts. The petition urged the Food and Drug Administration to require food labels to disclose the number of added sugars and their percentage of the daily recommended intake.

Once enacted, this policy helped consumers make healthier food choices, while also highlighting just how full of sugar many items on the market were.

And for prescription opioids, in 2011, the U.S. Centers for Disease Control and Prevention declared an opioid epidemic, signaling to doctors that they were overprescribing, and to the drug industry that it was acting irresponsibly.

In each case, success came after years of persistent efforts by scientists, public health officials and advocates to sway public opinion, often against the deliberate efforts of corporations to undermine them.

The 1964 report on smoking came after a decade of confusion that the industry had sown to distract the public from the scientific consensus about the harms of tobacco. The report offered conclusive authority that changed the narrative. Smoking went from being viewed as a widely accepted social custom to a deadly habit almost overnight. Today, just 1 in 9 American adults smoke, down from nearly half of all adults in 1954.

The push in 1999 by public health leaders connected the dots between rising obesity rates and sugar-laden foods and drinks. People began scrutinizing their diets, especially their sugar intake. As result, annual sugar consumption has since dropped by more than 15 pounds per person, erasing half of the amount of sugar Americans added to their diets between 1950 and 2000.

And the CDC report on opioids effectively communicated to doctors that they couldn’t just rely on patients to avoid misuse of the highly addictive drugs, underscoring their responsibility to help control the epidemic by reducing prescriptions of opioids such as OxyContin. Since the report, opioid prescription has been reduced by 60% – more in line with actual medical need.

Learning from the past

While there are no easy solutions for today’s market-based epidemics, we can learn from history about steps that can be effective in reducing the consumption of harmful products.

Changing attitudes on smoking show that an authoritative governmental voice can still be immensely useful to combat corporate resistance and the spread of corporate mis- and disinformation.

It can be effective to provide clear guidance about products and alternatives, as public health leaders did in telling consumers to cut consumption of sugar-sweetened beverages.

And from opioids, we can learn that applying pressure to those who make decisions about consumption, who are not always the consumers themselves, can be immensely powerful in bending patterns of use.

Despite the progress made in these three cases, the U.S. continues to face ongoing and emerging epidemics of unhealthy products. For example, while smoking has dramatically declined, the shift to vaping and other nicotine delivery products is creating new challenges, especially among teenagers.

Meanwhile, gun deaths keep rising, and firearms are now the leading killer of children under 18, and the gun industry remains committed to opposing public health measures to reduce gun violence.

And ultra-processed foods now account for nearly 60% of the average American’s diet, yet as new evidence confirms their harms, the food industry defends them.

But our research shows that these problems can be solved – that it is in fact possible to change millions of Americans’ behavior. This is very good news. It means sound evidence and public health action can turn the tide on some of the world’s biggest health challenges, potentially saving millions of lives and billions of dollars in health-care costs.

Jonathan D. Quick, Adjunct Professor of Global Health, Duke Global Health Institute, Duke University and Eszter Rimanyi, Chronic disease and addiction epidemiologist, Duke University

This article is republished from The Conversation under a Creative Commons license. Read the original article.