How to Set Up a Chess Board—Explained

How to Set Up a Chess Board Step-by-Step

Your Quick Guide to a Correct Chess Board Setup

How to Set Up a Chess Board the Correct Way (Image: Mashup Math via Getty)

Have you ever been confused about where to start when setting up a chess board? If so, you are not alone, as it is extremely common to forget the positions of a correct chess board setup, especially when you don’t play very often. Luckily, correctly setting up a chess board is a relatively easy task. If you can apply a few simple rules, then the entire setup process can be easy and straightforward.

In this short guide on how to set up a chess board, we will walk you through setting up your board step-by-step so that you can position all of your pieces in the correct spots on your chess board and be ready to play a game of chess in just a few minutes. This guide also includes a link to download a free PDF reference sheet that you can print out and use as a guide whenever you need it.

In addition to the written directions below, this guide also includes image diagrams that you can reference while setting up your chess board. You may want to have this guide handy while you are actually setting up your board. Are you ready to get started?

How to Set Up a Chess Board

The Standard Chess Board

Before we learn how to set up the pieces on a chess board, let’s take a look at the features of an actual chessboard. The board is an 8x8 grid with 64 squares, alternating between light colors and dark colors. There are an equal amount of light squares as there are dark squares: 32 of each.

Now that you are familiar with the chess board, are you ready to learn how to correctly set up a chess board?

The first step is to make sure that the chess board is facing in the right direction. Whenever playing chess, the lower-right square must always be a light-colored square. To make sure that your board is aligned correctly, make sure that, from the player’s perspective, that the right-most square in the first-row facing you is light-colored. If it is not, then rotate your board clockwise by 90 degrees.

The diagram below shows a chess board that is correctly oriented and one that is incorrectly oriented.

View fullsize

Chess Board Setup Step One: The lower-right square must always be light-colored.

Chessboard Setup: The Pieces and Their Names

Once your chess board is oriented correctly, it’s time to set up the pieces.

View fullsize

Chess Board Setup: Know the Pieces and Their Names (Image: Mashup Math FP)

Each player starts a game of chess with 16 total pieces:

• 8 Pawns

• 2 Rooks

• 2 Knights

• 2 Bishops

• 1 Queen

• 1 King

Each piece has a specific starting spot on the chess board. All of the pieces go on the bottom two rows (the first player’s pieces) and the top two rows (the second player’s pieces).

The following instructions are the same for both the dark set of pieces and the light set of pieces. For the sake of simplicity, the diagrams below will show you how to set up both players chess pieces so that both players pieces are correctly positioned before you start playing a game.

Chess Board Setup: Player Perspective

How to Set Up a Chess Board Step #1: Position the Queens

The first step to setting up a chess board is to correctly position the Queens.

Position the Light Queen on the center-most light square and the Dark Queen is positioned directly across from her on the center-most dark square, as shown in the figure below.

It is very important that the Queens are facing each other and are on a colored square that corresponds with the color of the game pieces (i.e. the light queen goes on a light square and the dark queen goes on a dark square).

How to Set Up a Chess Board: The light queen goes on the center-most light square and the dark queen goes on the center-most dark square. The queens should be directly across from each other.

How to Set Up a Chess Board Step #2: Position the Kings

The entire process of setting up a chess board gets easier once you have correctly positioned the queens.

The next step is to place the King at the Queen’s side at the center of the board.

Chess Board Setup: The Queen will always go on the center-most square that matches her own color and the King goes on the remaining center-most square at her side.

How to Set Up a Chess Board Step #3: Complete the First Row

Now that the King and Queen are correctly positioned, the third step is to complete the first row by placing the remaining non-pawn pieces in height order (tallest to shortest) from the center of the first row outwards.

This positioning means that Bishops come first, then the Knights, and finally the Rooks. A good way to remember this positioning is: Bishops next to royalty, then Knights, and Rooks in the corners.

Bishops next to royalty, then Knights, and Rooks in the corners.

How to Set Up a Chess Board Step #4: Complete the Second Row

The fourth and final step to setting up a chess board is to complete the second row by positioning the Pawns in front of the first row pieces.

The Pawns are your smallest pieces, and lining them up across the second row is simple. Once you have completed this step, your chess board is successfully set up and you are ready to play!

How to Set Up a Chess Board: The final step to setting up a chess board is to complete the second row by positioning the Pawns in front of the first row pieces.

Chess Board Setup: Quick Reference

That’s all there is to it! We have just successfully set up a chess board with all of the pieces in their correct positions.

If you need some extra help remembering the correct chessboard setup, you can check out the tips below and download and print our free How to Set Up a Chess Board PDF Diagram, which you can keep with your chess pieces and board as a quick reference whenever you want to play.

▶ Click Here to Download Your Free Chess Board Setup Reference Diagram PDF

View fullsize

Click image to preview

How to Set Up a Chess Board: Quick Tips

Many chess players rely on remembering that the Queen loves fashion and always makes sure that her dress matches her square (i.e. she always stands on the color of her piece to start any game). Again, if you can remember to correctly position the Queen, then placing all of the other pieces becomes much easier.

Once you have mastered the proper chessboard setup, you are ready to start playing games! Photo by Tanner Mardis on Unsplash

You can also improve your ability to quickly and accurately set up a chess board simply by practicing the steps as often as possible. The more that you follow the steps, the quicker you will end up memorizing the proper set up of a chess board (and you will also learn how to identify when a board is set up incorrectly). So, if you have the time, go ahead and complete your chess board setup, then clear the pieces and do it again and again until you feel like an absolute pro.

Before you know it, you’ll be setting up your board and starting games in no time. So, now is the time to gather your chess pieces and your board, set up a game, find a friend to play with, and have some fun!

---

Keep Learning:

Is Chess a Sport?

The subject of whether or not chess is considered a sport is extremely polarizing. On one hand, many see chess as merely a game of intense strategy and intellectual skill. For others, chess is clearly a sport due to its competitive nature and high stakes competitive nature.

---

17 Famous Mathematicians in History (and Their Amazing Contributions)

17 Famous Mathematicians in History

From Ancient Greece to Modern Day, Who are the Top 17 Most Famous Mathematicians?

While the study of mathematics is typically focused on learning how to apply mathematical operations and formulas, it is important to also learn about the history of mathematics to truly appreciate the beauty of the subject.

As the famous Isaac Newton Quote goes:

If I have seen further than others, it is by standing on the shoulders of giants.

The giants he is referring to are all of the incredible mathematicians who came before him. Without their contributions to the field of mathematics, he would not have been able to make so many breakthroughs. The field of mathematics as we know it today would not be what it is without countless contributions from various talented mathematicians of various cultural and religious backgrounds, cultures, and genders, who existed during all periods of history.

The stories of famous mathematicians, their discoveries, innovations, and perseverance through adversity serves as an inspiration to math students and enthusiasts around the world, some of whom may seek to make significant contributions of their own.

In this post, we will take a look at the lives and accomplishments of 17 different famous mathematicians from around the world, including famous women mathematicians and famous black mathematicians.

17 Famous Mathematicians in History

---

Famous Mathematicians #1: Pythagoras

1.) Pythagoras (570 - 490 BC)

The ancient Greek, Pythagoras, is one of the most famous and well-known mathematicians in all of history. He is best known for the Pythagorean Theorem, which continues to serve as one of the cornerstones of the field of geometry. His contributions forever changed the way that mathematicians think about and understand triangular relationships.

Fun Fact: In addition to his works as a mathematicians, Pythagoras also founded a school in Croton (the modern day Crotone region of Southern Italy). The attendees of his school were followers of Pythagoras’ teachings and were known as Pythagoreans. They believed that numbers had mystical properties and that the Earth was actually a sphere that revolved around the sun, way before the heliocentric model was introduced.

---

Euclid

2.) Euclid (325 - 265 BC)

As a mathematician in ancient Alexandria, Euclid's foundational textbook, 'Elements', unified and expanded the theories and understandings of mathematics and geometry from his time. He is regarded as the Father of Geometry and many of his theorems are still used today.

Fun Fact: Since there is very little information known about Euclid’s personal life from writings or first-hand accounts, many modern scholars speculate that Euclid may not have been just one person, but rather a school or group of mathematicians publishing their work under one common name.

---

Hypatia of Alexandria

3.) Hypatia (355 - 415 AD)

As the first female mathematician whose life and workings are well-recorded, Hypatia is known for making significant contributions to the fields of mathematics, astronomy, and philosophy. She lived in Alexandria, which was an epicenter of learning and knowledge during the 4th Century, but mathematics was still an incredible male-dominated field. However, despite this adversity, she is remembered for having remarkable perseverance, intellect and courage.

Interesting Fact: In addition to her accomplishments in the fields of math and astronomy, Hypatia is also known for having a tragic death (she was murdered in cold blood by a mob of Christian religious fanatics for being both a pagan and a female intellectual in 415 AD).

---

Famous Mathematicians #4: Al-Khwarizmi

4.) Muhammad ibn Musa Al-Khwarizmi (780 - 850 AD)

The famous Persian scholar, Muhammad ibn Musa Al-Khwarizmi, made countless profound and lasting contributions to mathematical thought, especially in the field of algebra. His work in the formation of algorithms forms the foundation of algebra as we know it today.

Fun Fact: The word algorithm is derived from Al-Khwarizmi’s name as he is credited with introducing algebraic concepts to the Western world. His name in Latin translated to Algorithmi, which became the title of the algebraic procedures featured in his writings.

---

Leonardo of Pisa (also known as Fibonacci)

5.) Fibonacci (1170 - 1240)

Also known as Leonardo of Pisa, little is known about the life of the great Italian mathematician known as Fibonacci. However, his mathematical contributions live on in a tremendous way as his famous Fibonacci sequence continues to illuminate the mathematical structures of nature and the natural world.

Fun Fact: Fibonacci is credited with introducing the Hindu-Arabic numeral system to Europe, which eventually led to its widespread acceptance, simplifying and unifying mathematical formulas, equations, and computations.

---

Famous Mathematicians in History #6: Sophie Germain

6.) Sophie Germain (1776-1831)

Despite facing incredible adversity as a female mathematician in Paris during the late 18th and early 19th centuries, Germain persisted and became one of the most famous mathematicians of all time. Her greatest contributions came in the fields of number theory and elasticity theory.

Fun Fact: Despite living during an era when girls were never encouraged to pursue the field of mathematics, Germain taught herself using her father’s math textbooks. Using a fake male name, she wrote letters about mathematics to famous Germain mathematician (and #7 on our list) Carl Friedrich Gauss, who would not discover the true identity of his pen-pal colleague until years later.

---

Carl Friedrich Gauss

7.) Carl Friedrich Gauss (1777 - 1855)

Often referred to as the Prince of Mathematicians, Carl Friedrich Gauss is one of the most famous mathematicians in history as he made many significant contributions to the study of mathematics including the fields of statistics, differential equations, and number theory.

Fun Fact: Gauss was considered an incredibly talented mathematician from a very young age. When he was only 3 years old, he successfully spotted and corrected an error his father had made while calculating payrolls!

---

Famous Mathematicians #8: Srinivasa Ramanujan

8.) Srinivasa Ramanujan (1887 - 1920)

Despite having no formal math education or training, Ramanujan, an Indian mathematician, taught himself complex mathematics and became one of the most influential mathematicians who ever lived. Despite his short life, he is well known for his incredible contributions to the fields of number theory, analysis, and continued fractions.

Fun Fact: Ramanujan believed that his mathematical abilities were inspired by the divine and claimed the Hindu goddess Namagiri would share mathematical formulas and equations with him while he was dreaming.

---

Emmy Noether

9.) Emmy Noether (1882 - 1935)

Emmy Noether, a prominent 20th-century German mathematician, is famous for her revolutionary work in the fields of theoretical physics and abstract algebra.

Fun Fact: One of Noether’s greatest contributions to the field of mathematics was Noether’s Theorem, which links the properties of symmetry with the laws of conservation. Although she would face tremendous opposition to her pursuit of mathematics because of her gender, she is known today as a true trailblazer for women in STEM.

---

Famous Mathematicians in History #10: Albert Einstein

10.) Albert Einstein (1879 - 1955)

The famous genius, Albert Einstein, is best known for his contributions to the field of theoretical physics, but he made significant contributions to the field of mathematical physics as well, including his groundbreaking theory of relativity, which would forever change the way we think about reality.

Fun Fact: Einstein was a late bloomer in terms of his cognitive abilities. In fact, he did not learn how to properly speak until he was three years old, leading his teachers to believe that he was slow.

---

“I always look forward to getting my Mashup Math newsletter email every week. I love the free activities!” -Christina R., 5th Grade Math Teacher, Dallas, TX

Do YOU want free math resources, lesson activities, and puzzles and games for grades 1-8 in your inbox every week? Join our mailing list and start getting tons of free stuff!

---

Katherine Johnson

11.) Katherine Johnson (1918 - 2020)

Katherine Johnson was a true trailblazer for women and people of color in STEM. Her mathematical talents and calculations played a crucial role in NASA’s success for several decades, making her one of the most well known and famous mathematicians in history.

Fun Fact: Johnson’s work so well respected and trusted that famous astronaut John Glenn personally requested for her to double-check and verify all computer calculations related to his historic ride into orbit around Earth in 1962.

---

Alan Turing, despite facing rampant homophobia during his time, made foundational contributions to computer science and cryptography. His work on the Enigma machine during WWII played a crucial role in the Allied victory, making him a true war hero.

12.) Alan Turing (1912 - 1954)

Alan Turing is known as the Father of Modern Computing and his work blazed a trail for modern computers as we know them today. Turing introduced the concept of a universal machine, also known as a Turing machine, that could perform thousands of calculations based on predetermine rules/instructions. Also, Turing is credited with helping the Allies to defeat the Nazis in World Word II, when he helped to decode the German Enigma code.

Fun Fact: Turing developed a test for artificial intelligence, known as the Turing Test, which evaluates whether or not a machine can trick a human into thinking it is human as well.

---

Famous Mathematicians in History #13: Shakuntala Devi

13.) Shakuntala Devi (1929 - 2013 AD)

Devi, an Indian mathematician and mental calculator, is known as the Human Computer. She belongs on our list of famous mathematicians due to her incredible mental math abilities, which have earned her a place in the Guinness Book of World Records!

Fun Fact: Known for being able to perform incredibly complex mathematical calculations mentally in mere seconds, Devi famously multiplied two randomly chosen 13-digit numbers in her head in under 30 seconds, which was a world record in 1982.

---

Famous Mathematicians #14: Grigori Perelman

14.) Grigori Perelman (1966 - Present)

Perelman, an accomplished Russian mathematician, is famous for solving the Poincaré conjecture, which was one of the 7 Millennium Prize Problems in 2002. The conjecture essentially states that any finite 3D space that has no boundary is the topical equivalent of a 3D sphere.

Fun Fact: After Perelman’s solution to the Poincaré conjecture was confirmed in 2002, he was awarded a one million dollar prize in addition to the prestigious Fields Medal. However, he declined to accept either award stating that he did not care about money or fame.

---

Maryam Mirzakhani

15.) Maryam Mirzakhani (1977 - 2017 AD)

Mirzakhani, an decorated and celebrated Iranian mathematician, is the first and only woman to ever win the prestigious Fields Medal for her work in mathematics, namely in the fields of Riemann surfaces and hyperbolic geometry.

Fun Fact: Mirzakhani becoming the first female to win the Fields Medal in 2014 was no small feat, as the award is often considered the Nobel Prize of mathematics.

---

Terence Tao

16.) Terence Tao (1975 - Present)

Arguably the most famous modern famous mathematician on our list, Terence Tao is known for his substantial breakthroughs and research on the topics of representation theory, harmonic analysis, combinatorics, and partial differential equations.

Fun Fact: Tao, an Australian-American mathematician, won a gold medal in the International Mathematical Olympiad when he was just 13 years old. He would go on to be awarded the Fields Medal for his mathematical contributions in 2006.

---

17.) Sir Isaac Newton (1643-1727)

Did you really think we weren’t going to include Sir Isaac Newton? Widely considered one of the most influential and famous mathematicians and scientists of all time for his revolutionary contributions to the fields of calculus and astronomy, Newton is most famous for developing the laws of gravity and motion. He is often credited with the development of calculus and is celebrated to this day for paving the way for modern mathematics and physics as we know it today, making him arguably the most famous mathematician in history!

Fun Fact: In addition to his studies in physics and math, Newton also devoted his time to studying alchemy—the ancient practice of trying to turn common medals into gold—and he wrote often on the subject. While the exact cause of his death remains unknown, many believe that it was due to mercury poisoning he incurred while working on an alchemy experiment.

---

Conclusion

These famous mathematicians and their inspirational stories remind us that mathematics is field of study that has been shaped by the brilliance and perseverance of a diverse and courageous group of thinkers from all walks of life. While this list only featured a small handful of history’s prominent mathematicians, the true history of math includes a rich and forever-growing collection of individuals who have made incredible and lasting contributions to the field of mathematics and STEM as a whole.

---

Continue your celebration of Math History with following free resources:

• Who Invented Math? A Quick Explanation of the History of Math for Students

• 11 Famous Women Mathematicians and Their Contributions!

• 11 Famous African American Mathematicians and Their Contributions!

---

More Math-Related Posts You Will Love:

---

Free Addition Chart—Printable PDF

Download a Free Addition Chart (Printable PDF)

Free Addition Chart for Students

In math, being able to add numbers is a core foundational skill that every student must master in order to be able to perform many complex calculations later on.

Whether you are an elementary teacher helping your students to learn their addition facts or an adult looking to refresh previously learned math skills, an addition chart can be an extremely useful visual tool.

So, if you are looking for an easy visual reference for adding numbers up to 20, then you’re in the right place!

You can use the link below to download your free addition chart as an easy-to-print PDF file. And keep reading to learn more about addition charts and how they are used to practice and master your adding skills.

View fullsize

Addition Chart Preview

• Click here to download your free Addition Chart

---

How to Use an Addition Chart

An addition chart, also known as an addition table chart or addition facts chart, is a visual aide that shows the math facts from 1 to 10 organized in a grid that works like a bing board where the value inside of each interior box represents the sum of the corresponding column and row.

For example, if you wanted to find the sum of 7 and 4, you would find 7 along the top row and 4 along the left column and then use your fingers or a pencil to find the corresponding interior box. Since the value inside of this box is 11, you could conclude that 7 + 4 = 11.

This process is demonstrated in Figure 01 below. Repeat this process with as many practice problems as needed.

Figure 01: How to Use an Addition Chart

Why You Should Use a Printable Addition Chart

An addition chart is most effective when it is printable and given to students to have a physical copy of and to use as a hands-on tool whenever they are working on addition problems.

Printable addition charts, like the one you can download above for free, are great because they can be used offline and in-person as often as you need them. Many parents and teachers opt to print our addition chart in color and either put it in a plastic binder sleeve or, even better, have it laminated for continual use day after day.

You can also print a copy that can be posted somewhere in your home or classroom to serve as a reference guide (such as on a refrigerator door or on a classroom bulletin board).

Addition Chart Printable Version

Moving On From Using an Addition Chart

Since the addition chart is only a temporary tool that will help students become more comfortable with practicing and learning their basic addition facts, you should be prepared to stop using the chart once you have mastered the addition facts up to ten.

Once you feel comfortable with your understanding of addition up to ten, you can continue progressing you math skills by moving onto working with larger numbers.

An addition chart is a great visual aide for helping students to master the basic addition facts before moving onto more complex math skills.

Photo by Natasha Hall on Unsplash

Read More Posts About Math Education:

Who Put Letters in Math?—Solved

Who Put Letters in Math?

Who Added Letters to Math and Why the Heck Did They Do That?

Who put letters in math?

We’ve all been there before. You’re sitting in math class staring at an equation that is filled with not only numbers (which are to be expected in a math equation), but freaking letters as well (what gives?). Feeling frustrated and confused, you can’t help but to scratch your head and wonder, “who put letters in math, and why?”

And now you’re here, looking to figure out exactly who put letters in math and why it is even necessary in the first place (this isn’t English class, after all).

While the concept of working with letters in math may seem silly, it is actually also pretty brilliant, given that the “invention” of using letters is a foundational part of the field of algebra.

So, who put letters in math? The bulk of the credit goes to one man. Are you ready to learn his name?

What Do Letters in Math Mean?

Before you learn about the man who added letters to math, it is important that you understand why letters are used in math and what they actually represent.

In math, letters, more commonly known as variables, are used to represent different values in various expressions and equations.

You can think of variables as place holders that represent unknown values or quantities and they are most prominently used in algebra. Without variables, you would not be able to form equations or solve problems!

View fullsize

Diophantus of Alexandria is often credited as the Father of Algebra.

Who Put Letters in Math?

Answering this question will require a short tour through the history of math, starting in Ancient Greece. The first recored use of letters in mathematical equations and expressions is credited to the Ancient Greek mathematicians, most notably Diophantus of Alexandria, who is considered the “Father of Algebra.”

In his famous textbook Arithmetica, Diophantus used an abbreviated notation system and symbols to represent unknown quantities and values. And while his work put the field of mathematics on the path of including letters in math, Diophantus’ system of using symbols was very different from the algebraic notation that you are seeing in your math classes.

So, if it wasn’t Diophantus who added letters to math, who was it?

Who Put Letters in Math?

Answer: François Viète

Much later on, towards the end of the 16th century, a French mathematician named François Viète first introduced the concept of using letters to represent unknown numbers and quantities when solving math equations. Viète’s work truly revolutionized the field of algebra and algebraic notation. In his initial works, he developed a notation system where consonants were used to represent known quantities and vowels were used to represent unknown quantities. This system would gradually morph into the modern algebraic notation system that we use today.

Now that you have your answer, here are some fun facts about this relatively unknown 16th century French Mathematician:

• Viète is most famous for being known as the first mathematician to use a letter-based algebraic notation system for solving equations, which laid the foundation for algebra as we know it today.

• In addition to being a mathematician, Viète was an extremely talented codebreaker. He spent time serving as a cryptanalyst and decoding secret messages sent by rival nations for King Henry IV.

• He was also a licensed private attorney and travelled all around France working as a lawyer. Viète would eventually become a respected legal advisor to the King.

• Viète's famous algebra textbook, Canon Mathematicus, was not published until fourteen years after he died.

• Viète also made major contributions to the field of trigonometry. Most notably, he developed a formula for the relationship between the angles and sides of any triangle, which is still used in modern mathematics and is known as Viète's Formula.

Who Added Letters to Math? 16th century French mathematician, François Viète, is credited as being the first to introduce the concept of using letters to represent unknown quantities.

Why Were Letters Added to Math?

Finally, now that you know who added letters to math, its important that you really understand why they were put there and why they are so useful in algebra.

The greatest impact of adding letters to math is that it made the subject more universal and accessible. Since math principles and theorems are universal, the use of letters as placeholders for specific values or inputs allowed mathematicians to represent general mathematical facts which are applicable to a wide range of values.

From a historical perspective, the introduction of using letters to represent unknown values in math equations was truly groundbreaking and it changed the field of mathematics forever. This revolutionary concept sparked the evolution of algebra from a field of study that was primarily focused on calculation to one of manipulation and generalization—which led to countless advancements and breakthroughs in the fields of science, technology, mathematics, and engineering.

Einstein’s famous theory of relativity equation, E=MC^2, would not be possible if not for the use of letters in math. Photo by Artturi Jalli on Unsplash

For example, consider Albert Einstein’s famous theory of relativity equation, E=MC^2.

In this famous equation involving mostly letters, E is used to represent energy, M is used to represent mass, and C is used to represent the speed of light. In a nutshell, Einstein’s equation states that mass (M) can be converted into energy (E) and vice versa. The concept itself is truly groundbreaking and it would not be possible without the use of letters in math.

As for being relevant to algebra students in the modern day who are not concerned with developing their own theories of relativity, it is important to know that letters in math allow you to simplify abstract and complex mathematical situations, making them much easier to conceptualize and solve. The use of letters in expressions and equations allows you to see patterns, make generalizations, and develop new problem-solving methods that are applicable to a vast array of scenarios and problems.

Conclusion: Letters in Math

It’s totally normal to be surprised and confused when you are first introduced to letters symbolizing values in math. Exploring who is responsible for adding letters in math as well the why behind their introduction has taken you on a journey through the history of math that ranges from Ancient Greece to 16th century France to the modern day. So, who put letters in math? In terms of crediting one person, the award goes to François Viète and his initial use of letters to represent quantities in algebraic expressions and equations. Without this contribution, algebra as we know it today would be a very different field of study.

More Free Resources You Will Love:

Who Invented Math? A Quick Explanation for Students

The history of math runs deep and spans across a variety of ancient cultures and civilizations, which leads many to wonder who invented math?

Let’s explore who gets the credit and why!

---

What is the Last Number?—Explained

What is the Last Number?

To Infinity and Beyond: Is There a Final Number?

What is the last number? Photo by Mika Baumeister on Unsplash

When you were a child and learning how to count, values like 50 and 100 were considered large and perhaps, at that time, you wondered when you would be able to count from one all the way until the very last number, whatever that number may be.

And while “what is the last number?” is a seemingly simple question, the answer is actually extremely complex, controversial, and even philosophical.

Searching for an answer to the question “what is the last number?” will take you on a journey through the nature of numbers and the incredible concept of infinity. If you are ready to take this fascinating mathematical journey with us, continue reading as we will explore the concept of infinity, the largest known numbers known to man, and the idea of a “last number.”

What is the last number in the world? (Image: Mashup Math FP)

To Infinity and Beyond: What is the Last Number?

In math, any conversation about determining the “last number” will involve the concept of infinity.

In fact, many will say that infinity is the final answer to the question “what is the last number?” But, infinity isn’t actually a number. Instead, infinity is an abstract concept that describes a quantity that never ends and is unbounded. In math, you can think of infinity like a highway that goes on forever. No matter how far you travel along this highway, there will always be more road ahead.

With this in mind…

What is the last number?

Answer: There is no such thing as the biggest number or last number. Why? Because the concept of infinity exists.

Simply put, numbers continue on and on indefinitely and they never end. So, there could never be a final number.

Just like the highway that never ends, when we count numbers, no matter how high we go, there will always be another number that is larger than the number you have counted to. This idea is the very definition of the concept of infinity.

If I asked you to present me with the largest number you could think of, I could simply take that number and add one to it. And then you could take that number and add one more to it, and so on forever and ever!

Therefore, while infinity is not actually a number that can be counted, it is an abstract concept that represents the idea that numbers are infinite and that a last number can never be reached. And while infinity cannot be called the “last number,” it can be used to explain why a last number does not exist.

The concept of infinity: Imagine a highway that goes on and on forever in both directions. No matter how far you travel along this highway, there will always be more road ahead.

Photo by Amanda Sandlin on Unsplash

What is the Largest Number?

While there is no final number or last number, there are still some extremely large numbers out there.

Despite the infinite nature of numbers, mathematicians have identified many exceptionally large values and numbers. For example, a googol is a name for the value that starts with 1 and followed by 100 zeroes.

Mathematicians and scientists use the word googol to represent this value so they don’t have to ever write the number out in long-form, which would look as follows:

• 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

And, because of the concept of infinity, we can not say that a googol is the last number, because numbers go on forever. Because of the nature of numbers, there also exists a googolplex, which is a 1 followed by a googol’s worth of zeroes (OMG!).

Do you want to see what a googolplex would look like written in long-form? Well, so would we, but this number is so big that there is actually not enough room in the observable universe to write out a googolplex in long-form, even if every digit were written in the smallest possible font (OMG!).

And even though a googolplex is so mind-bogglingly large that it exceeds the total number of atoms in the universe, it is still not considered the last number.

What is the largest number in the world?

While there is no last number, the largest number ever named is called Rayo’s Number.

Discovered in 2021 and named after Agustin Rayo, this value is considered the largest number that can be named with an expression using googol symbols.

However, despite being the largest named number, Rayo’s Number still can not claim the title of the
"last number in the world,” which further demonstrates why a final number does not exist.

What is the largest number in the world? Photo by Jeremy Thomas on Unsplash

What Would Happen if We Knew the Last Number in the World?

Now, let’s pretend that there actually was a last number and that our proverbial infinite highway of numbers did come to an end. What would this mean for math and human’s understanding of the world?

Simply put, the existence of a last number would change math and science as we know it forever. But how? For starters, it would completely change our understanding of the concepts of space and time, both of which depend on the concept of infinity and the never-ending nature of numbers.

While it’s fun to play with the question “what is the last number?”, it is even more interesting to think about why we are intrigues by this question in the first place. The answer is likely due to the human desire for completeness and closure (we are finite creatures after all).

But, what makes subjects like math and science so mysterious and awe-inspiring is there limitless nature and concepts that extend beyond the limits of human understanding. The concept of infinity and the never-ending nature of numbers gives the human mind access to a vast world of exploration, expansion, and possibilities.

What is the largest number? Exploring this question will not give you a definitive answer, but it will give you an appreciation for the mysterious nature of numbers and why mathematics is such a profound field of study. Photo by Alexander Sinn on Unsplash

Conclusion: What is the Last Number in the World?

While exploring the questions “what is the last number?” does not lead us to a definitive answer, it does take us down along a fascinating journey through the concept of infinite and the never-ending nature of numbers. This journey illuminates the magic of mathematics and the beauty of numbers.

Given the nature of infinity, there can be no last number because numbers never end and every value is followed by another forever and ever—stretching on towards the often incomprehensible concept of infinity,

And while many seek the final number out of curiosity and a human desire for closure, it is the fact that there is no final number that reminds us that it is the mysterious and never-ending nature of mathematics that makes the subject so profound, inspiring, and helpful to our understanding of the universe.

---

Keep Learning: