• Artificial intelligence is finding applications in everything from finance to healthcare.
• A group of mathematicians are now using machine learning techniques to classify and build a periodic table of shapes.
• This is a fundamental concept in mathematics, especially algebraic geometry.

While many shapes are familiar to us from our everyday experiences, in mathematics (algebraic geometry, in particular), the concept of shapes has a precise definition and purpose.

In algebraic geometry, shapes are mathematical entities defined as solutions to systems of polynomial equations. You might remember the polynomial equation ax²+bx+c=0 from school. 

The shape described by this equation is a parabola (as long as a ≠ 0). The parabola is a U-shaped curve that extends infinitely in both directions along the x-axis. The coefficients a, b, and c determine the specific characteristics of the parabola, such as its direction, width, and vertex.