Remember the graph paper you used at school, the kind that’s covered with tiny squares? It’s the perfect illustration of what mathematicians call a “periodic tiling of space”, with shapes covering an entire area with no overlap or gap. If we moved the whole pattern by the length of a tile (translated it) or rotated it by 90 degrees, we will get the same pattern. That’s because in this case, the whole tiling has the same symmetry as a single tile. But imagine tiling a bathroom with pentagons instead of squares – it’s impossible, because the pentagons won’t fit together without leaving gaps or overlapping one another.

Barclays, the UK bank, is to replace the password system on its phone banking service with personal voice recognition. “Unlike a password, each person’s voice is as unique as a fingerprint,” said Steven Cooper, Barclays' head of personal banking. Yet the reality is we have no idea whether either fingerprints or voices are unique at all.

You may have heard of graphene, a sheet of pure carbon, one atom thick, that’s all the rage in materials-science circles, and getting plenty of media hype as well. Reports have trumpeted graphene as an ultra-thin, super-strong, super-conductive, super-flexible material. You could be excused for thinking it might even save all of humanity from certain doom.

If you have ever travelled on an aeroplane the chances are you have experienced some form of turbulence. For those of us who fly infrequently, it can be alarming and unnerving, but rest assured that for the pilots and crew who experience turbulence every day, it is business as usual.

We have built a world of largely straight lines – the houses we live in, the skyscrapers we work in and the streets we drive on our daily commutes. Yet outside our boxes, nature teams with frilly, crenellated forms, from the fluted surfaces of lettuces and fungi to the frilled skirts of sea slugs and the gorgeous undulations of corals.

Antimatter was one of the most exciting physics discoveries of the 20th century. Picked up by fiction writers such as Dan Brown, many people think of it as an “out there” theoretical idea – unaware that it is actually being produced every day. What’s more, research on antimatter is actually helping us to understand how the universe works.

People who have seen Earth from space report a “cognitive shift in awareness”. Space philosopher, Frank White, calls this “the overview effect”. It is often experienced as a profound feeling of awe and interconnection, and a renewed sense of responsibility for taking care of the environment.

What is mass, in the sense of its physical meaning? Why do some particles have mass and others don’t? And you may not think this would be important, but the biggest question is: why do particles have mass at all?

According to recent estimates, the Earth’s solid inner core started forming between half a billion and one billion years ago. However, our new measurements of ancient rocks as they cool from magma have indicated that it may actually have started forming more than half a billion years earlier.

It is often claimed that the Ancient Greeks were the first to identify objects that have no size, yet are able to build up the world around us through their interactions. And as we are able to observe the world in tinier and tinier detail through microscopes of increasing power, it is natural to wonder what these objects are made of.

Before Pilkingtons invented plate glass in the mid-19th century, flat panes could not be made. Old windows are uneven.

Ofcom, the UK’s independent telephony regulator, has just released a Wi-Fi checker app for your smart phone. At the same time, it warned in its press release that your Christmas tree fairy lights could affect the quality of your Wi-Fi connection.

A little over 100 years ago Albert Einstein submitted the first paper fully describing the general theory of relativity. It was both breathtaking and revolutionary.