One of the universal laws of nature is the law of the least rate of energy expenditure. …

There’s a mathematical order inherent in our universe. Let’s start with rivers. If we measure the length of a river and divide it by the direct route from the start to the end, we’ll get its sinuosity or bendiness.

Mathematicians found that the average sinuosity of every single river in…

The moving sofa problem is inspired by the real-life issue of moving furniture around. A mathematician was probably carrying his sofa down a corridor. He had to navigate some obstacles and asked himself that question; what is the sofa of the largest area to move around the corner?

Consider these two examples:

** “This statement is false,”** &

- If the statement is true, then it’s wrong because a statement is false.
- If the statement is false, then that the…

How do you explain the deep interaction between philosophers and mathematicians throughout history?

In the history of human thought development, there has been constant interaction between philosophical and mathematical aspects. Many intellectual movements have sought their support, inspiration, and even their model in the style and way of mathematics. …

One of the best-known features of Jupiter is the great red spot. It’s been there for hundreds of years, and it’s a big storm, a vast hurricane on Jupiter. And when the Voyager spacecraft got a look at that, it noticed you get complicated, turbulent vortices spinning off. What we…

Mathematics is something extraordinarily precise. Moreover, it is more accurate in different areas than in some areas we know less about it. People often find mathematics very abstract. But mathematics can describe reality as we understand it.

When we think about solid stuff like an umbrella scientifically, we picture molecules…

What is reality? Does reality exist? Is reality independent of the mind? How does a person find reality? What is “truth”? What does it mean to understand something truly? How does the brain come to understand something? How do we know if we understand something? What do we mean by…

We know that Kurt Gödel (1906–1978) worked intensively with Leibniz (1646–1716) towards the end of his life. Gödel was obsessed with Leibniz. When some people had destroyed some of Leibniz’s writings, Menger asked Gödel, “*Who could have an interest in destroying Leibniz’s writings?”* Gödel would say, *“Naturally, those people who…*

Mathematics is a vast and diverse field, and so many good mathematicians can share their knowledge with humans in a beautiful way.

Although this year, 2020, has ruined our lives, it helped me read many math books this year. …