Mathematics can get pretty complicated. Fortunately, not all math problems need to be inscrutable. Here are five current problems in the field of mathematics that anyone can understand, but nobody has been able to solve.

Computer scientists have come up with a bounded algorithm that can fairly divide a cake among any number of people. By Erica Klarreich.

We hold this mathematics to be self evident. By Adam Kucharski.

Using yarn and two pointy needles (knitting) or one narrow hook (crochet), pretty much anyone can stitch up a piece of fabric. Or, you can take the whole yarncraft thing light-years further to illustrate a slew of mathematical principles.

When looking at a case of pastries in a bakery it's usually possible to intuit what something might taste like because of its familiar shape or color. Such is not the case with these radically unusual cake designs by Ukrainian pastry chef Dinara Kasko whose experimental techniques result in edible objects unlike anything we’ve ever seen.

Good students should have been able to do it - but needed more time, professor says.

I was a wayward kid who grew up on the literary side of life, treating math and science as if they were pustules from the plague. So it’s a little strange how I’ve ended up now—someone who dances daily with triple integrals, Fourier transforms, and that crown jewel of mathematics, Euler’s equation. It’s hard to believe I’ve flipped from a virtually congenital math-phobe to a professor of engineering. One day, one of my students asked me how I did it—how I changed my brain.

By Victor Powell and Lewis Lehe

Most of the world’s mathematicians fall into just 24 scientific 'families', one of which dates back to the fifteenth century. The insight comes from an analysis of the Mathematics Genealogy Project (MGP), which aims to connect all mathematicians, living and dead, into family trees on the basis of teacher–pupil lineages, in particular who an individual's doctoral adviser was.

They got the same results when they asked,"How reliable are bar graphs?"

Are some scientific results so unexpected that we should just reject them?

Physicists want equations that connect behaviors directly to the foundations of reality. With the continuity equation, they actually pull it off. By Brendan Cole.

Mathematical toys by Nico Disseldorp. Play with contstruction, tesselations, fractals and automata.

Deciphering mathematical card tricks is a wonderful pastime, but it can get you into some bizarre predicaments. By Jesse Dunietz.

3Blue1Brown

Researchers have uncovered deep connections among different types of random objects, illuminating hidden geometric structures. By Kevin Hartnett.

Douglas Hofstadter

Conference on Shinichi Mochizuki’s work inspires cautious optimism. By Davide Castelvecchi.

The sounds of languages that died thousands of years ago have been brought to life again through technology that uses statistics in a revolutionary new way.