Researcher: Konstantin Batygin, Caltech
Description: Konstantin Batygin talks about using math to investigate the existence of Planet Nine.

Researcher: Michel C. Molinkovitch, University of Geneva Description: Michel C. Milinkovitch used math, physics, and biology for an amazing discovery about the patterns on a lizard's skin.

Researcher: Andy Andres, Boston University Moment: http://www.ams.org/samplings/mathmoments/mm136-baseball.pdf Andy Andres on baseball analytics.

Researcher: Stefan Siegmund, TU-Dresden Moment: http://www.ams.org/samplings/mathmoments/mm137-hurricane.pdf Description: Stefan Siegmund talks about his an invention to protect homes during hurricanes.

Researcher: Derek Moulton, University of Oxford Moment: http://www.ams.org/samplings/mathmoments/mm138-shells.pdf Description: Derek Moulton explains the math behind the shapes of seashells.

Researchers: Christopher Brinton, Zoomi, Inc. and Princeton University, and Mung Chiang, Purdue University Moment: http://www.ams.org/samplings/mathmoments/mm139-netflix.pdf Description: Christopher Brinton and Mung Chiang talk about the Netflix Prize competition.

Researcher: Christine Darden, NASA (retired) Description: Christine Darden on working at NASA.

Researchers: Vikash V. Gayah and S. Ilgin Guler, Pennsylvania State University Description: Gayah and Guler talk about mitigating the clustering of buses on a route.

Researcher: Jordan Hashemi, Duke University Description: Jordan Hashemi talks about an easy-to-use app to screen for autism.

Tom Patterson and Bojan Savric discuss the Equal Earth projection map that they created with Bernhard Jenny.

Steven Strogatz and Mary Bushman talk about math's role in controlling HIV and understanding malaria, respectively. Mary Bushman says, "It's really cool to try and use math to nail down some questions that have gone unanswered for a really long time."

Rob Schneiderman talks about the metaphorical connections between math and music

Hany Farid talks about fighting fake videos: "Mathematically, there's a lot of linear algebra, multivariate calculus, probability and statistics, and then a lot of techniques from pattern recognition, signal processing, and image processing."

Fumie Tazaki talks about creating the first image of a black hole and its shadow, which relied on Fourier transforms. About the work to make the image, she says, "Our collaboration has 200 members and we did it with all of our efforts."

Located in a global hotspot for biodiversity, Los Angeles County is home to more than 4,000 distinct species of plants and animals, including 52 endangered species - more than any county outside of Hawaii. And with 1 million animal and plant species facing extinction due to human activity, according to the United Nations, efforts to better understand the factors that shape biodiversity in Los Angeles could help shape global conservation efforts.

Water scarcity, a socio-environmental threat to anthropogenic activities and ecosystems alike, affects large regions of the globe. However, it is often the most vulnerable and disadvantaged populations that suffer the severest consequences, highlighting the role of economic and institutional factors in water scarcity. In this way, researchers generally consider not only the physical constraints but socio-economic determinants as well.

A new study from University of Michigan climate researchers concludes that some of the latest-generation climate models may be overly sensitive to carbon dioxide increases and therefore project future warming that is unrealistically high.

Fishery collapses can be difficult to forecast and prevent due to hyperstability, a phenomenon where catch rates remain high even as fish abundance declines. In a recent Canadian Journal of Fisheries and Aquatic Sciences study, researchers conducted a whole-lake experiment to reveal the causes of hyperstability in recreational fisheries. Fish habitat preferences were found to leave them vulnerable to overexploitation.

Researchers at Western and Suncor are teaming up to use algae as a way to produce serological test kits for COVID-19 - a new process that overcomes shortfalls of existing processes while saving money.

In a ground breaking study, an international team of 21 scientists led by Sean Hoban, Ph.D., Conservation Biologist at The Morton Arboretum in Lisle, Illinois, evaluated five genera spanning the plant tree of life (Hibiscus, Magnolia, Pseudophoenix, Quercus and Zamia) to understand how much genetic diversity currently exists in collections in botanical gardens and arboreta worldwide.

In these unprecedented times, we are all spending much more time at home and in our gardens. And, now that spring has well and truly arrived, it's the perfect time to get reacquainted with one of our country's busiest workers - the bee.

A new way of looking at marine evolution over the past 540 million years has shown that levels of biodiversity in our oceans have remained fairly constant, rather than increasing continuously over the last 200 million years, as scientists previously thought.

Do biodiversity losses aggravate transmission of infectious diseases spread by animals to humans? The jury is still out but several scientists say there is a "biodiversity dilution effect" in which declining biodiversity results in increased infectious-disease transmission.

Rampant deforestation, uncontrolled expansion of agriculture, infrastructure development and exploitation of wild species have created a 'perfect storm' for the spillover of diseases from wildlife to people.

THE Oxford Dictionary describes the environment as "the surroundings or conditions in which a person, animal, or plant lives or operates". Humankind has been reliant on the environment for its existence for as long as humans have been living on earth. In numerous ways, the future survival of humankind will depend on how we take care of our air, soil, rivers, oceans, animals and plants.

"The coronavirus pandemic has made abundantly clear that if life is to thrive on this Earth, human and nonhuman, we need cooperation at all scales-global, regional, binational, within a nation, interstate, and in our local communities. And we need to learn how to coexist with and have compassion for our nonhuman relatives-and acknowledge in the midst of this pandemic that bats are not our enemies."

Jiuzhaigou National Nature Reserve is one of China's most popular tourist attractions, drawing more than five million visitors per year to the sparsely populated mountains of north-western Sichuan. The reserve has been home to farmer-herders for thousands of years, but to conserve the biodiversity and scenic quality of the reserve, park policies prohibit residents from farming, herding and wood cutting.

Sovereign nations typically measure economic success in terms of GDP (income) but this approach is risky as it fails to track and measure the impact of this on nature. Inclusive wealth, on the other hand captures financial and produced capital, but also the skills in our workforce (human capital), the cohesion in our society (social capital) and the value of our environment (natural capital).

The good thing about BirdLife is that, as a truly global organisation, we're already great at staying connected, even when we're thousands of miles apart. Here are just a few of the ways our work will carry on over the coming months, even if it's from our living rooms.

The earth we abuse and the living things we kill will, in the end, take their revenge; for in exploiting their presence we are diminishing our future. ~ Marya Mannes Each species represents a thread in the closely woven fabric of Nature. For centuries, we humans have prided ourselves on being the most 'evolved' species. Superior intelligence and technological capability have bred this arrogance.

In these unusual and tragic times, I am indeed grateful that we are able to connect virtually to continue the business of environmental governance. While the efforts of all your capitals are correctly focused on preventing human suffering, as parts of the world move slowly towards recovery, the environmental agenda remains one of our most powerful insurance policies in preventing future global pandemics like COVID-19.

Tropical rainforests are the world's richest land habitats for biodiversity, harbouring stunning numbers of plant and animal species. The Amazon and the Congo basins, together with Asian rainforests, represent only 6 per cent of earth's land surface, and yet more than 50 per cent of global biodiversity can be found under their shade.

When did you last see a glow worm? Most likely, quite some time ago. Depending on how young you are, you may have never seen one at all. Those light-emitting insects, Wordsworth's "earthborn stars", have been declining in the UK for decades. That means that scientists now see them in fewer places, and even in those pockets where conditions are right for them, there are fewer of them to be found.

To imagine earth without greenhouse gases in its atmosphere is to turn the familiar blue marble into a barren lump of rock and ice on which the average surface temperature hovers around -18ºC. Such a planet would not receive less of the sunlight which is the ultimate source of all Earth's warmth. But when the energy it absorbed from the sunlight was re-emitted as infrared radiation, as the laws of physics require, it would head unimpeded back out into space.

And against the backdrop of threatened lives, crippled businesses and damaged economies, the UN chief warned the Petersberg Climate Dialogue in Berlin that the Sustainable Development Goals (SDGs) are also under threat.

As the coronavirus pandemic continues to wreak havoc, the world's energies are rightly focused on efforts to contain the virus and manage the economic fallout. Yet, in the background, the climate emergency remains as urgent as ever.

"Pollinators were the key," says Edgar Mora, reflecting on the decision to recognise every bee, bat, hummingbird and butterfly as a citizen of Curridabat during his 12-year spell as mayor.

We asked Guardian readers living in cities and towns across the world to share their images of the wildlife they can see from their homes. You answered in your droves, from Canada to Cardiff, and here are some of the best.

In the wake of the COVID-19 crisis, any economic stimulus measures must safeguard nature or governments risk exposing humanity to further pandemics.