When we think of Kelvin temperature, we think only in positives, since zero Kelvin is also absolute zero, the point at which a particle has absolutely no energy, and thus no movement or vibration. Scientists in Germany, however, managed to create the hottest temperatures ever recorded by creating a substance with a negative Kelvin temperature.
How is this possible? Well, in order to understand this bizarre concept, we have to go back to our definition of temperature. In thermodynamics, we typically refer to temperature as the average temperature of the particles in a substance. However, because quantum physics deals with energies as the smallest of small scales, and because quantum physics is, from a mathematical perspective, about probabilities, it makes more sense to define temperature as the distribution of the energies of the particles in a substance. So, for example, a boiling pot of water would obviously have plenty of high energy particles buzzing around, but it would have a few low-energy particles too. We simply would pay them no mind because the average energy of the particles is consistent. To a quantum physicist, however, those few low-energy particles matter, because they form part of the energy distribution of the substance.
By definition, when a substance has a positive Kelvin temperature, the particles start from a minimum temperature (absolute zero) and spread out toward higher energies. The German scientists, however, wanted to create a substance that started at a maximum temperature and spread toward lower energies. By definition, such a substance would have a negative temperature.
Paradoxically, having a negative temperature makes the gas that the scientists created extremely hot. Since the particles start from a maximum temperature and spread to lower temperatures, and since energy flows from hot to cold, heat will always flow away from the negative temperature gas, making it the hottest thing we've ever observed.
One of the other interesting properties of negative temperature gases is that they not only have the hottest temperatures, but negative pressures. Normally, a gas concealed in a container would spread out and apply pressure to all sides of the container. A negative temperature gas, on the other hand, causes the atoms in the container to cave inward, as if everything converges to a single point. Because dark matter is believed to have negative pressure as well, this characteristic of negative temperature gases leads scientists to think that studying them may reveal more to us about the elusive dark matter that is believed to account for a lot of "missing mass" in the universe.
You can read more about the negative temperature gas and the study conducted by the German scientists here: