GPT-5.4 Pro cracked a conjecture in number theory that had stumped generations of mathematicians, using a proof strategy that ...

Here is the new description without links: Learn how to graph a rational function. To graph a rational function, we first find the vertical and horizontal or slant asymptotes and the x and ...

Mathematicians just made a big leap forward on one of the field’s all-time favorite problems. Curves—squiggly lines through space, such as a comet’s trajectory or a stock market trend—are some of math ...

Abstract: In this paper we consider the problem of sparse signal modeling by means of rational functions. Our dictionary is composed by a finite collection of elementary rational functions. In order ...

I have had a fascinating few months. “Abundance,” the book I wrote with Derek Thompson, is either going to save the Democratic Party or destroy it. You think I’m kidding. Here’s The Wall Street ...

In the late 19th century, Karl Weierstrass invented a fractal-like function that was decried as nothing less than a “deplorable evil.” In time, it would transform the foundations of mathematics.

It’s surprisingly difficult to prove one of the most basic properties of a number: whether it can be written as a fraction. A broad new method can help settle this ancient question. In June 1978, the ...

Modification of natural enzymes to introduce new properties and enhance existing ones is a central challenge in bioengineering. This study is focused on the development of Taq polymerase mutants that ...

Hair loss can occur when the thyroid gland is not working properly. It can be a sign of either hypothyroidism or hyperthyroidism. The thyroid gland is a butterfly-shaped gland situated in the lower ...

The Greeks believed your thymus was home to your soul. In fact, thymus means “soul” in Greek. While no studies have proved that to be the case, your thymus does play an important role in your immune ...