The following is an extract from our Lost in Space-Time newsletter. Each month, we hand over the keyboard to a physicist or mathematician to tell you about fascinating ideas from their corner of the universe. You can sign up for Lost in Space-Time here. The Navier-Stokes equations have been used to model the flow of fluids for almost 200 years – but we still don't really understand them. This can often feel a little odd, especially as we rely on these equations every day to help build rockets, design drugs and understand climate change. But here is where you have to think like a mathematician.

Japan's Slim (Smart Lander for Investigating Moon) mission has now touched on the Moon. If this proves to have been a safe landing, Japan will become only the fifth country to land on the moon. Slim has completed its descent to the lunar surface and we are awaiting confirmation of whether the landing was a success. JAXA, Japan's space agency, expects the landing to take around 20 minutes, with touchdown expected by 15:20 GMT. MailOnline will also be bringing you all the latest updates as the landing progresses, so make sure you check back in!

Japan's Slim (Smart Lander for Investigating Moon) mission is now only hours away from attempting its perilous landing on the lunar surface. If successful, Japan will become only the fifth country to land on the moon. But after America's first landing attempt in 50 years failed before even reaching the Moon, the risk of failure is clear. Japan's space agency, JAXA, is hoping to stack the odds in its favour by using precision navigation equipment, earning the mission the nickname'Moon Sniper'. Unlike previous missions, which have aimed for areas more than a mile across, Japan's lander will attempt to land no more than 330ft (100m) from its target.

Source: OpenAI's DALL·E 2 with prompt "a hyperrealistic picture of a robot reading the news on a laptop at a coffee shop" Welcome to the inaugural edition of Robo-Insight, a biweekly robotics news update! In this post, we are thrilled to present a range of remarkable advancements in the field, highlighting robotics progress in terrain traversability, shape morphing, object avoidance, mechanical memory, physics-based AI techniques, and new home robotics kits. Recently, researchers from the University of California San Diego have given four-legged robots forward-facing depth cameras to enable them to clearly analyze the environment around and below them. This data can also be compared with past images to estimate possible 3D transformation. Furthermore, their system is also self-checking, as it fuses information to give it a sort of short-term memory. Although the model does not guide the robot to a specific location, it enables the robot to traverse challenging terrain.

Robots are all around us, from drones filming videos in the sky to serving food in restaurants and diffusing bombs in emergencies. Slowly but surely, robots are improving the quality of human life by augmenting our abilities, freeing up time, and enhancing our personal safety and well-being. While existing robots are becoming more proficient with simple tasks, handling more complex requests will require more development in both mobility and intelligence. Columbia Engineering and Toyota Research Institute computer scientists are delving into psychology, physics, and geometry to create algorithms so that robots can adapt to their surroundings and learn how to do things independently. This work is vital to enabling robots to address new challenges stemming from an aging society and provide better support, especially for seniors and people with disabilities.

This connection of springs is a new type of material that can change shape and learn new properties. A new type of material can learn and improve its ability to deal with unexpected forces thanks to a unique lattice structure with connections of variable stiffness, as described in a new paper by my colleagues and me. Architected materials – like this 3D lattice – get their properties not from what they are made out of, but from their structure. The new material is a type of architected material, which gets its properties mainly from the geometry and specific traits of its design rather than what it is made out of. Take hook-and-loop fabric closures like Velcro, for example.

What would it take to transform a flat sheet into a human face? How would the sheet need to grow and shrink to form eyes that are concave into the face and a convex nose and chin that protrude? How to encode and release complex curves in shape-shifting structures is at the center of research led by the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) and Harvard's Wyss Institute of Biologically Inspired Engineering. Over the past decade, theorists and experimentalists have found inspiration in nature as they have sought to unravel the physics, build mathematical frameworks, and develop materials and 3D and 4D-printing techniques for structures that can change shape in response to external stimuli. However, complex multi-scale curvature has remained out of reach.

If you've had a window seat next to the wing of an airplane, you've probably watched as flaps on the wing engage and disengage as a plane takes off and lands. That's because in each phase of flight -- take off, landing, cruising and maneuvering -- the ideal wing parameters vary. Until now, we've made do by modifying rigid wings with hinged surfaces. But imagine if the entire wing could change shape -- that's what researchers led by NASA and MIT are working towards. In a paper in the journal Smart Materials and Structures, the research team explains how it has radically redesigned the airplane wing.

Drugs could be delivered by microscopic, shape-shifting robots you swallow in the future, scientists believe. Researchers have created the tiny gadgets, which are around 5mm in length and can navigate the narrow channels of the human body. The tiny robots, developed by Swiss researchers, even change shape and speed as they travel through bendy blood vessels and thick bodily fluids. Drugs may one day be delivered by microscopic robots (pictured) we swallow. When tested in the lab, the robot adapted to squeeze through narrow tubes.

Liquid metal robots that can change their form and repair from damage just like the androids of the Terminator films could soon become a reality. Researchers in China have developed a palm-sized prototype inspired by T-1000 from the science fiction franchise, albeit a lot less sinister. The small, shape-shifting robot could be used to access environments that would be difficult for a human or fixed-shape bot to navigate, such as disaster zones. Liquid metal robots that can change their form and repair from damage just like the androids of the Terminator films could soon become a reality. The prototype, created by a team from the University of Science and Technology of China and the University of Wollongong in Australia is made up of a small plastic wheel, a lithium battery, and drops of gallium, a soft silvery metal, according to the South China Morning Post.