Manoj Joshi, University of East Anglia; Andrew Rushby, Birkbeck, University of London, and Maria Di Paolo, University of East Anglia A team of researchers has recently claimed they have discovered a gas called dimethyl sulphide (DMS) in the atmosphere of K2-18b, a planet orbiting a distant star. The University of Cambridge team’s claims are potentially very exciting because, on Earth at least, the compound is produced by marine bacteria. The presence of this gas may be a sign of life on K2-18b too – but we can’t rush to conclusions just yet. K2-18b has a radius 2.6 times that of Earth, a mass nearly nine times greater and orbits a star that is 124 light years away. We can’t directly tell what kinds of large scale characteristics it has, although one possibility is a world with a global liquid water ocean under a hydrogen-rich atmosphere. Such a world might well be hospitable to life, but different ideas exist about the properties of this planet – and what that might mean for a DMS signature.

---

Get your news from actual experts, straight to your inbox. Sign up to our daily newsletter to receive all The Conversation UK’s latest coverage of news and research, from politics and business to the arts and sciences.

---

Claims for the detection of life on other planets go back decades. In the 1970s, one of the scientists working on the Viking mission to Mars claimed that his experiment had indicated there could be microorganisms in the Martian soil. However, these conclusions were widely refuted by other researchers. In 1996, a team said that microscopic features resembling bacteria had been found in the Martian meteorite ALH84001. However, subsequent studies cast significant doubt on the discovery. Since the early 2000s there have also been repeated claims for the detection of methane gas in the atmosphere of Mars, both by remote sensing by satellites and by in-situ observations by rovers. Methane can be produced by several mechanisms. One of these potential sources involves production by microorganisms. Such sources are described by scientists as being “biotic”. Other sources of methane, such as volcanoes and hydrothermal vents, don’t require life and are said to be “abiotic”.

Not all of the previous claims for evidence of extraterrestrial life involve the red planet. In 2020, Earth-based observations of Venus’s atmosphere implied the presence of low levels of phosphine gas. Because phosphine gas can be produced by microbes, there was speculation that life might exist in Venus’s clouds. However, the detection of phosphine was later disputed by other scientists. Proposed signs of life on other worlds are known as “biosignatures”. This is defined as “an object, substance, and/or pattern whose origin specifically requires a biological agent”. In other words, any detection requires all possible abiotic production pathways to be considered. In addition to this, scientists face many challenges in the collection, interpretation, and planetary environmental context of possible biosignature gases. Understanding the composition of a planetary atmosphere from limited data, collected from light years away, is very difficult. We also have to understand that these are often exotic environments, with conditions we do not experience on Earth. As such, exotic chemical processes may occur here too. In order to characterise the atmospheres of exoplanets, we obtain what are called spectra. These are the fingerprints of molecules in the atmosphere that absorb light at specific wavelengths. Once the data has been collected, it needs to be interpreted. Astronomers assess which chemicals, or combinations thereof, best fit the observations. It is an involved process and one that requires lots of computer based work. The process is especially challenging when dealing with exoplanets, where available data is at a premium. Once these stages have been carried out, astronomers can then assign a confidence to the likelihood of a particular chemical signature being “real”. In the case of the recent discovery from K2-18b, the authors claim the detection of a feature that can only be explained by DMS with a likelihood of greater than 99.9%. In other words, there’s about a 1 in 1,500 chance that this feature is not actually there. While the team behind the recent result favours a model of K2-18b as an ocean world, another team suggests it could actually have a magma (molten rock) ocean instead. It could also be a Neptune-like “gas dwarf” planet, with a small core shrouded in a thick layer of gas and ices. Both of these options would be much less favourable to the development of life – raising questions as to whether there are abiotic ways that DMS can form.

A higher bar?

But is the bar higher for claims of extraterrestrial life than for other areas of science? In a study claiming the detection of a biosignature, the usual level of scientific rigour expected for all research should apply to the collection and processing of the data, along with the interpretation of the results. However, even when these standards have been met, claims that indicate the presence of life have in the past still been meet with high levels of scepticism. The reasons for this are probably best summed up by the phrase “extraordinary claims require extraordinary evidence”. This is attributed to the American planetary scientist, author and science communicator Carl Sagan. While on Earth there are no known means of producing DMS without life, the chemical has been detected on a comet called 67/P, which was studied up close by the European Space Agency’s Rosetta spacecraft. DMS has even been detected in the interstellar medium, the space between stars, suggesting that it can be produced by non-biological, or abiotic, mechanisms. Given the uncertainties about the nature of K2-18b, we cannot be sure if the presence of this gas might simply be a sign of non-biological processes we don’t yet understand. The claimed discovery of DMS on K2-18b is interesting, exciting, and reflects huge advances in astronomy, planetary science and astrobiology. However, its possible implications mean that we have to consider the results very cautiously. We must also entertain alternative explanations before supporting such a profound conclusion as the presence of extraterrestrial life. Manoj Joshi, Professor of Climate Dynamics, University of East Anglia; Andrew Rushby, Lecturer, School of Natural Sciences, Birkbeck, University of London, and Maria Di Paolo, PhD Candidate, School of Engineering, Mathematics and Physics, University of East Anglia This article is republished from The Conversation under a Creative Commons license. Read the original article.

Richard E. Peltier, UMass Amherst The Trump administration is “reconsidering” more than 30 air pollution regulations, and it offered industries a brief window to apply for exemptions that would allow them to stop following many air quality regulations immediately if approved. All of the exemptions involve rules finalized in 2024 and include regulations for hazardous air pollutants that cause asthma, heart disease and cancer. The results – if regulations are ultimately rolled back and if those rollbacks and any exemptions stand up to court challenges – could impact air quality across the United States. “Reconsideration” is a term used to review or modify a government regulation. While Environmental Protection Agency Administrator Lee Zeldin provided few details, the breadth of the regulations being reconsidered affects all Americans. They include rules that set limits for pollutants that can harm human health, such as ozone, particulate matter and volatile organic carbon. Zeldin wrote on March 12, 2025, that his deregulation moves would “roll back trillions in regulatory costs and hidden “taxes” on U.S. families.“ What Zeldin didn’t say is that the economic and health benefits from decades of federal clean air regulations have far outweighed their costs. Some estimates suggest every $1 spent meeting clean air rules has returned $10 in health and economic benefits.

How far America has come, because of regulations

In the early 1970s, thick smog blanketed American cities and acid rain stripped forests bare from the Northeast to the Midwest. Air pollution wasn’t just a nuisance – it was a public health emergency. But in the decades since, the United States has engineered one of the most successful environmental turnarounds in history. Thanks to stronger air quality regulations, pollution levels have plummeted, preventing hundreds of thousands of deaths annually. And despite early predictions that these regulations would cripple the economy, the opposite has proven true: The U.S. economy more than doubled in size while pollution fell, showing that clean air and economic growth can – and do – go hand in hand. The numbers are eye-popping. An Environmental Protection Agency analysis of the first 20 years of the Clean Air Act, from 1970 to 1990, found the economic benefits of the regulations were about 42 times greater than the costs. The EPA later estimated that the cost of air quality regulations in the U.S. would be about US$65 billion in 2020, and the benefits, primarily in improved health and increased worker productivity, would be around $2 trillion. Other studies have found similar benefits. That’s a return of more than 30 to 1, making clean air one of the best investments the country has ever made.

Science-based regulations even the playing field

The turning point came with the passage of the Clean Air Act of 1970, which put in place strict rules on pollutants from industry, vehicles and power plants. These rules targeted key culprits: lead, ozone, sulfur dioxide, nitrogen oxides and particulate matter – substances that contribute to asthma, heart disease and premature deaths. An example was the removal of lead, which can harm the brain and other organs, from gasoline. That single change resulted in far lower levels of lead in people’s blood, including a 70% drop in U.S. children’s blood-lead levels.

The results have been extraordinary. Since 1980, emissions of six major air pollutants have dropped by 78%, even as the U.S. economy has more than doubled in size. Cities that were once notorious for their thick, choking smog – such as Los Angeles, Houston and Pittsburgh – now see far cleaner air, while lakes and forests devastated by acid rain in the Northeast have rebounded.

And most importantly, lives have been saved. The Clean Air Act requires the EPA to periodically estimate the costs and benefits of air quality regulations. In the most recent estimate, released in 2011, the EPA projected that air quality improvements would prevent over 230,000 premature deaths in 2020. That means fewer heart attacks, fewer emergency room visits for asthma, and more years of healthy life for millions of Americans.

The economic payoff

Critics of air quality regulations have long argued that the regulations are too expensive for businesses and consumers. But the data tells a very different story. EPA studies have confirmed that clean air regulations improve air quality over time. Other studies have shown that the health benefits greatly outweigh the costs. That pays off for the economy. Fewer illnesses mean lower health care costs, and healthier workers mean higher productivity and fewer missed workdays. The EPA estimated that for every $1 spent on meeting air quality regulations, the United States received $9 in benefits. A separate study by the non-partisan National Bureau of Economic Research in 2024 estimated that each $1 spent on air pollution regulation brought the U.S. economy at least $10 in benefits. And when considering the long-term impact on human health and climate stability, the return is even greater.

The next chapter in clean air

The air Americans breathe today is cleaner, much healthier and safer than it was just a few decades ago. Yet, despite this remarkable progress, air pollution remains a challenge in some parts of the country. Some urban neighborhoods remain stubbornly polluted because of vehicle emissions and industrial pollution. While urban pollution has declined, wildfire smoke has become a larger influence on poor air quality across the nation. That means the EPA still has work to do. If the agency works with environmental scientists, public health experts and industry, and fosters honest scientific consensus, it can continue to protect public health while supporting economic growth. At the same time, it can ensure that future generations enjoy the same clean air and prosperity that regulations have made possible. By instead considering retracting clean air rules, the EPA is calling into question the expertise of countless scientists who have provided their objective advice over decades to set standards designed to protect human lives. In many cases, industries won’t want to go back to past polluting ways, but lifting clean air rules means future investment might not be as protective. And it increases future regulatory uncertainty for industries. The past offers a clear lesson: Investing in clean air is not just good for public health – it’s good for the economy. With a track record of saving lives and delivering trillion-dollar benefits, air quality regulations remain one of the greatest policy success stories in American history. This article, originally published March 12, 2025, has been updated with the administration’s offer of exemptions for industries. Richard E. Peltier, Professor of Environmental Health Sciences, UMass Amherst This article is republished from The Conversation under a Creative Commons license. Read the original article.

Courtney Gibbons, Hamilton College You scrambled up a Rubik’s cube, and now you want to put it back in order. What sequence of moves should you make? Surprise: You can answer this question with modern algebra. Most folks who have been through high school mathematics courses will have taken a class called algebra – maybe even a sequence of classes called algebra I and algebra II that asked you to solve for x. The word “algebra” may evoke memories of complicated-looking polynomial equations like ax² + bx + c = 0 or plots of polynomial functions like y = ax² + bx + c. You might remember learning about the quadratic formula to figure out the solutions to these equations and find where the plot crosses the x-axis, too.

Equations and plots like these are part of algebra, but they’re not the whole story. What unifies algebra is the practice of studying things – like the moves you can make on a Rubik’s cube or the numbers on a clock face you use to tell time – and the way they behave when you put them together in different ways. What happens when you string together the Rubik’s cube moves or add up numbers on a clock? In my work as a mathematician, I’ve learned that many algebra questions come down to classifying objects by their similarities.

Sets and groups

How did equations like ax² + bx + c = 0 and their solutions lead to abstract algebra? The short version of the story is that mathematicians found formulas that looked a lot like the quadratic formula for polynomial equations where the highest power of x was three or four. But they couldn’t do it for five. It took mathematician Évariste Galois and techniques he developed – now called group theory – to make a convincing argument that no such formula could exist for polynomials with a highest power of five or more. So what is a group, anyway? It starts with a set, which is a collection of things. The fruit bowl in my kitchen is a set, and the collection of things in it are pieces of fruit. The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12 also form a set. Sets on their own don’t have too many properties – that is, characteristics – but if we start doing things to the numbers 1 through 12, or the fruit in the fruit bowl, it gets more interesting.

Let’s call this set of numbers 1 through 12 “clock numbers.” Then, we can define an addition function for the clock numbers using the way we tell time. That is, to say “3 + 11 = 2” is the way we would add 3 and 11. It feels weird, but if you think about it, 11 hours past 3 o’clock is 2 o’clock. Clock addition has some nice properties. It satisfies:

• closure, where adding things in the set gives you something else in the set,
• identity, where there’s an element that doesn’t change the value of other elements in the set when added – adding 12 to any number will equal that same number,
• associativity, where you can add wherever you want in the set,
• inverses, where you can undo whatever an element does, and
• commutativity, where you can change the order of which clock numbers you add up without changing the outcome: a + b = b + a.

By satisfying all these properties, mathematicians can consider clock numbers with clock addition a group. In short, a group is a set with some way of combining the elements layered on top. The set of fruit in my fruit bowl probably can’t be made into a group easily – what’s a banana plus an apple? But we can make a set of clock numbers into a group by showing that clock addition is a way of taking two clock numbers and getting to a new one that satisfies the rules outlined above.

Rings and fields

Along with groups, the two other fundamental types of algebraic objects you would study in an introduction to modern algebra are rings and fields. We could introduce a second operation for the clock numbers: clock multiplication, where 2 times 7 is 2, because 14 o’clock is the same as 2 o’clock. With clock addition and clock multiplication, the clock numbers meet the criteria for what mathematicians call a ring. This is primarily because clock multiplication and clock addition together satisfy a key component that defines a ring: the distributive property, where a(b + c) = ab + ac. Lastly, fields are rings that satisfy even more conditions. At the turn of the 20th century, mathematicians David Hilbert and Emmy Noether – who were interested in understanding how the principles in Einstein’s relativity worked mathematically – unified algebra and showed the utility of studying groups, rings and fields.

It’s all fun and games until you do the math

Groups, rings and fields are abstract, but they have many useful applications. For example, the symmetries of molecular structures are categorized by different point groups. A point group describes ways to move a molecule in space so that even if you move the individual atoms, the end result is indistinguishable from the molecule you started with.

But let’s take a different example that uses rings instead of groups. You can set up a pretty complicated set of equations to describe a Sudoku puzzle: You need 81 variables to represent each place you can put a number in the grid, polynomial expressions to encode the rules of the game, and polynomial expressions that take into account the clues already on the board. To get the spaces on the game board and the 81 variables to correspond nicely, you can use two subscripts to associate the variable with a specific place on the board, like using x₃₅ to represent the cell in the third row and fifth column. The first entry must be one of the numbers 1 through 9, and we represent that relationship with (x₁₁ – 1)(x₁₁ – 2)(x₁₁ – 3) ⋅⋅⋅ (x₁₁ – 9). This expression is equal to zero if and only if you followed the rules of the game. Since every space on the board follows this rule, that’s already 81 equations just to say, “Don’t plug in anything other than 1 through 9.” The rule “1 through 9 each appear exactly once in the top row” can be captured with some sneaky pieces of algebraic thinking. The sum of the top row is going to add up to 45, which is to say x₁₁ + x₁₂ + ⋅⋅⋅ + x₁₉ – 45 will be zero, and the product of the top row is going to be the product of 1 through 9, which is to say x₁₁ x₁₂ ⋅⋅⋅ x₁₉ – 9⋅8⋅7⋅6⋅5⋅4⋅3⋅2⋅1 will be zero. If you’re thinking that it takes more time to set up all these rules than it does to solve the puzzle, you’re not wrong.

What do we get by doing this complicated translation into algebra? Well, we get to use late-20th century algorithms to figure out what numbers you can plug into the board that satisfy all the rules and all the clues. These algorithms are based on describing the structure of the special ring – called an ideal – these game board clues make within the larger ring. The algorithms will tell you if there’s no solution to the puzzle. If there are multiple solutions, the algorithms will find them all. This is a small example where setting up the algebra is harder than just doing the puzzle. But the techniques generalize widely. You can use algebra to tackle problems in artificial intelligence, robotics, cryptography, quantum computing and so much more – all with the same bag of tricks you’d use to solve the Sudoku puzzle or Rubik’s cube. Courtney Gibbons, Associate Professor of Mathematics, Hamilton College This article is republished from The Conversation under a Creative Commons license. Read the original article.