We love numbers. We love to celebrate Pi Day on March 14, or 3/14, the day that the first 10 digits of pi are.

As the ratio of a circle's diameter to its circumference is irrational, pi cannot be written as a simple fraction. It is not the root, or solution to the equation, such as x + 2 + 3.

For people who are paid to think about numbers all day long, the circle constant can be a bit of a bore. Several mathematicians were asked to tell us their favorite numbers. Here are some of their responses.


Two gooseberry pies. Tau.

(Image credit: Shutterstock)

One pie is cooler than two pies. Two times pi, or the numbertau, which is roughly 6.28.


John Baez, a mathematician at the University of California, Riverside, said that using the name tau makes every formula clearer and more logical than using pi.

He said that tau is what shows up in the most important formulas.

Many mathematicians argue that the relationship between a circle's circumference and its radius is more important than pi. The equation for a circle's area and the equation for elastic energy are both symmetrical.

On Pi Day, tau will be remembered. The Massachusetts Institute of Technology will make a decision at 6:28 pm today. On June 28, it will be called Tau Day.

Natural log base

Natural log

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The base of natural logarithms, written as "e" for its namesake, the 18th-century Swiss mathematician Leonhard Euler, has its own holiday. On March 14, natural log base is celebrated, but on February 7, irrational number is celebrated.

The base of natural logarithms is used in a lot of equations.

The director of the mathematics outreach project at the graduate school of education said that it has a wonderful definition of being the one number for which the exponential function y x has a slope equal to its value. If the value of a function is 7.5 at a certain point, then its slope is also 7.5. It comes up all the time in mathematics, physics and engineering.

Imaginary number i

Imaginary number i.

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What do you get when you take the pi out? The number i is correct. I is a pretty cool number, but that is not how it works. The square root of a negative number is not supposed to be taken as the square root of a positive number.

If we break that rule, we get to invent the imaginary numbers and the complex numbers, which are both beautiful and useful. The sum of both real and imaginary parts can be expressed in complex numbers.

Cheng said that the number i is an odd number because it has two square roots.

Cheng said it was weird and wonderful.

i to the power of i

i to the power of i

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There are ways to make me weirder. You can raise the power of i to the power of the square root of the power.

David Richeson, a professor of mathematics at Dickinson College in Pennsylvania and author of the book Tales of Impossibility, said that at a glance, this looks like the most imaginary number possible.

A formula relating the irrational number e, the imaginary number i, and the sine and cosine of a given angle is needed to find the value of i to the i power. The formula for a 90-degree angle can be expressed as pi over 2 and you can simplify it to show that I equals e raised to the power of negative pi over 2.

If you dare to read the full calculation, you will see that the result is a very real number. In the case of a 90-degree angle.

Richeson said that I to the i power does not have a single value, but rather takes on many values depending on the angle you're solving for. It is unlikely that we will ever celebrate an i to the power of i day.

Belphegor's prime number

Depiction of the demon Belphégor, a demon of discovery and of ingenious inventions who often takes the form of a young woman, from J.A.S. Collin de Plancy.

(Image credit: Louis Le Breton/Dictionnaire Infernal)

Belphegor has a palindromic prime number with a 666 hiding between 13 zeros and a 1 on each side. The ominous number can be abbreviated as 1 0(13) 666 0(13) 1, where the number of zeros between the 1 and 666 is represented by the number.

The number was named after Belphegor, one of the seven demon princes of hell in the Bible.

The number has a symbol that looks like an upside-down symbol for pi. Pickover says that the symbol is derived from a glyph in the Voynich manuscript, an early-15th-century collection of illustrations and text that no one seems to understand.



W. Hugh Woodin has been researching infinite numbers for many years. His favorite number is an infinite one, called 2aleph_0, or 2 raised to the power of aleph-naught. When describing the sizes of infinite sets, a alemph number is used. A set of size 3 can be formed by the numbers 2, 4 and 6.

He said that Woodin chose the number because he realized that there are different sizes of infinite. The conception of 2aleph_0 is special.

In other words, there is always something bigger, because the Infinite Cardinal Numbers are infinite.

Apéry's constant

Atomic nucleus with orbiting electrons.

(Image credit: Ian Cuming/Getty Images)

Oliver Knill, a Harvard mathematician, told Live Science his favorite number is the Apéry's constant, because there is still some mystery associated with it. The beginning is 1.2020569 and the end is infinitely. When you plug in the number 3, the constant is written as Zeta (3).

One of the biggest problems in math is the Riemann hypothesis, which makes a prediction about when the Riemann zeta function equals zero and would allow mathematicians to better predict how the prime numbers are distributed.

Riemann's Zeta function_Furfur

Riemann's Zeta function. (Image credit: Furfur)

If I woke up after a thousand years, I would ask if the Riemann hypothesis had been proven.

What is it about this constant that makes it so cool? It turns out that the constant Apéry shows up in fascinating places in physics, including in equations governing the electron's magnetism and orientation to its angular momentum.

The number 1

Floating 3D number 1s.

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Rafi Letzter's father, Ed Letzter, a mathematician at Temple University in Philadelphia, had a practical answer.

I suppose this is a boring answer, but I would have to choose 1 as my favorite, both as a number and in its different roles in so many different more abstract contexts.

One is the only number that all other numbers share. It is the only number that can be divided by one positive number. It is the only positive integer that is neither prime nor composite.

One hundred percent is a fancy way of saying 1 in math and engineering. It is complete and whole.

Throughout the sciences, 1 is used to represent basic units. A single particle has a charge of +2. In logic, 1 means yes. It is the atomic number of the lightest element and the dimensions of a straight line.

Euler's identity

leonhard euler

(Image credit: Jakob Emanuel Handmann/Wikimedia Commons)

The mathematical jewel of the late physicist Richard Feynman is the identity of Euler, which is actually an equation. It was also compared to a Shakespearean sonnet.

A number of mathematical constants, including pi, natural log e and the imaginary unit i, are tied together by the identity of Euler.

The three constants are connected with the multiplicative identity of elementary arithmetic: ei*Pi + 1

The number 0

If we are already talking about how awesome 1 is, why not include the even weirder and cooler number 0? The concept of zero was unimportant for most of human history. According to the University of St. Andrew in Scotland, clay tablets from ancient Babylonian times did not always distinguish between numbers.

The ancient Greeks began to develop the idea of using zero as an empty place indicator to distinguish numbers of different magnitudes, but it wasn't until roughly the seventh century that Indian mathematicians began describing the modern idea of zero. The Maya had independently derived the concept of division, which is what the modern answer is.

Zero is useful, but it is difficult for many people to wrap their heads around. We have examples such as 1 horse or 3 chickens in our day-to-day lives, but using a number to represent nothing is a larger conceptual leap. Without 0o, we wouldn't be able to represent all of the digital code that makes our world run. The data on computers is represented by strings.

The square root of 2

The square root of 2 is said to have led to the first mathematical murder in history. According to the University of Cambridge, Hippasus of Metapontum is credited with discovering it in the fifth century B.C. Hippasus stumbled on the fact that an isosceles right triangle with two base sides that are 1 unit in length will have a hypotenuse, which is an irrational number.

Hippasus was thrown into the sea by members of the Pythagoreans after they heard about his discovery. The universe only contained whole numbers and their ratios because the Pythagoreans believed that all is number. Irrational numbers such as and pi, which can't be expressed as a ratio of whole numbers and go on forever after the decimal place, were seen as an abomination.

We are a little calmer about Pythagoras these days. It begins as 1.4142135623 and goes on forever. The constant of Pythagoras has many uses. It is used to prove the existence of irrational numbers and to define the A paper size. The A paper's length should be divided by its width, according to the 216 definition. A piece of A1 paper divided in half by width will yield two pieces of A2 paper. If you divide an A2 in half again, you will get two A3 pieces of paper.

Live Science contributor Adam Mann updated the article on March 4, 2022,