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In life, we strive to always be right. In our work, relationships, and even our hobbies, we learn from a young age that being wrong is a mistake. But, constant correct thinking is a concept that seems almost impossible, right?

Well, actually, and somewhat ironically, wrong. “How Not to Be Wrong” by Jordan Ellenberg discusses ways to think mathematically and make life simpler through this mindset.

A mathematician and a highly regarded intellectual, Ellenberg keeps his work (mostly) simple so that everyone can get a taste of the true power of mathematics.

Read on to understand the ten key takeaways from Ellenberg’s in-depth work.

## 1. Think In a Nonlinear Way

Ellenberg encourages his readers to consider the following; “where you should go depends on where you are.” This nonlinear way of thinking creates a platform in your mind to develop critical thinking and avoid being wrong. This is essentially the book overview. Learning is everything.

Think of it in simple terms. If you are standing at a crossroads waiting for the light to turn red so you can cross the road ahead, you’ll cross straight over to the other side when the light changes.

You won’t cross to the opposite side, then cross diagonally through the middle of the road to get to the street you want to be on. That wouldn’t make sense.

Ellenberg discusses the mathematical concept of linear regression, especially in the first chapter of his work. While this is a complex mathematical idea, Ellenberg uses the basics of this theory to allow his readers to see the power of mathematics.

The idea looks at the relationship between two variables. And you are a variable, and the life that follows you is another.

Nonlinear thinking means thinking logically about what you can and cannot control.

If you consider life and existence in this way, then thinking in a nonlinear way is the only option that makes sense. You can change at any point through your own choices. But the life surrounding can also change very quickly, without you being allowed any control over it.

By thinking in a nonlinear way, you will free your mind from the constant need to be in control of things you can’t be in control of. This will offer you more freedom, and prompt more questions in your life.

And with more questions comes more answers. The more answers you have, the less likely you are to be wrong. Which, ironically, seems like a linear way of thinking.

## 2. Understand That Math is a Part of Everything That You Do

Your teachers weren’t lying when they told you that you would use math every day. And you probably aren’t even aware of when and how you use it. Calculating the length of your work commute, assessing the budget for your next night out, and even the timing of your French press coffee requires basic math.

With this thought in mind, Ellenberg clarifies how being right constantly is possible. At least theoretically. The book overview suggests that if math is at the heart of everything we do and math lives by a set of fixed rules, then following these rules should always lead to the correct outcome.

Of course, this idea doesn’t necessarily always work. Ellenberg is not naive about this fact. But it is a concept that offers an element of comfort because of its simplicity.

If you spend your life focusing on the rules of math and following these step by step, being wrong could pass you by completely.

The problem is that people tend to guess and estimate rather than look at the cold, hard facts. Here is where mistakes begin to appear, and it’s why people are sometimes wrong.

So, how does Ellenberg address this issue? He argues that by making problems easier a conclusion can also occur more simply. By taking the problems of your life and considering a simpler version, you may come to a solution for the simple problem that ultimately can act as a solution for your bigger one.

Math is a powerful tool at the heart of almost everything we do. By promoting the idea that math is at the forefront of life, Ellenberg shows how it is vital to increase critical reasoning skills.

This leaves you the chance to be right more often than you’re wrong. Through a basic application of simple math, more accurate conclusions become clear. And you can increase the chances of being consistently correct in everything you do.

## 3. Consider the Triumph in Mediocrity

Ellenberg asks his readers to question their desire to be right all the time and be perfect. A perfect outcome cannot always occur or be guaranteed. But his thoughts are by no means self-defeating.

Instead, Ellenberg offers an insight into how mediocrity can, and should, receive praise. Normality leads to many of the theories and math questions Ellenberg discusses. Some math is born out of a simple need to solve a problem. The resulting theorems have shaped our world for decades.

And what is normal? Do any of you experience a normal life? You might not be very rich or famous, but why would these concepts make one life more or less ordinary than another? Ellenberg promotes math as normal and central to everything else as life itself.

Mediocrity rarely encouraged in the modern world, especially for the younger generation. But what might be understood as a “normal” life almost always has the extraordinary attached.

Even the rarity of life itself means it has some innate value.

Ellenberg’s work helps us understand mediocrity as a superpower that can often lead to the most extraordinary creativity.

## 4. Learn That Public Opinion Doesn’t Exist and Doesn’t Matter

What would you do with your life if your fear of public opinion was suddenly removed? Learn a new skill? Try to get famous on social media? Insist on a raise?

Through the power of mathematics, Ellenberg seeks to prove that public opinion does not exist. Therefore, there is no way that it matters, which is one of the key takeaways of the book. He does this by looking at forums in which public opinion seems to matter most. These include examples from election statistics.

Ellenberg focuses on one example to make his readers understand this controversial way of thinking. He believes that there are no answers. He writes “If there is no such thing as public opinion, what’s an elected official to do? The simplest answer: when there’s no coherent message from the people, do whatever you want” (p 369). And that is the beauty of this way of thinking.

Ellenberg is essentially saying that everyone is different, and therefore everyone has their own opinion, so public opinion itself cannot exist. Sure, there might be popular opinions amongst groups of people, but the fact that there are always those with contrasting and adverse opinions proves Ellenberg’s idea true.

Ellenberg looks into the mistakes that come from statistics, and how public misunderstanding can affect particular outcomes. In doing so, he offers an insight into how public opinion shouldn’t matter, as it can come from inaccurate information.

Of course, we all know that is not the way of the world. Public opinion may always have an impact on politics and other areas. Ellenberg rightly suggests that knowing your math can help you through.

## 5. It’s Okay Not to Know Everything

It’s more than okay; it’s impossible. Ellenberg points out that humans do not yet know everything there is to know, about our world and others. Therefore, knowing everything is a goal that can never be met.

And that, Ellenberg, insists, is okay. After all, if we were to be born knowing everything, wouldn’t life be incredibly dull? To know nothing is truly power, because it offers the chance to ask questions. And questions lead to one of two things: direct and conclusive answers, or the need to find out the answer through experimentation.

It is the latter that has resulted in human advances in science, technology, and even art. Without questions, there could be no answers. Answers lead to further questions, and the cycle inevitably continues. And it is important for humans as a species that it does. And so, to know everything would mean no discoveries.

What is better, Ellenberg argues, is the hunger for knowledge that is likely present in every person. They say that true geniuses amongst us listen more than they speak, and there’s a reason for this; active listening offers a consistent way to learn new information.

Of course, you can and should form your conclusions based on the new information you learn. But Ellenberg argues that the power of math should help base these conclusions on logic, and therefore offers a chance to be right more often than not.

## 6. Anything Can Be Proven From a Contradiction

Let’s say you make a statement. You assert that “it is October.” Therefore, next month, it must be November. Both of these statements are true.

But further truths become clear through contradiction. If you tell me that “it is October” then I can’t reasonably hold the belief that next month will be January or that the previous month was July. Logic dictates that if it is currently October, November must follow, and to argue anything else is foolish.

There is, of course, a degree of the math behind this concept. Ellenberg does get into the nitty-gritty of it all for those who are that way inclined. But the true takeaway is that being wrong has value because it has the power to offer us a new conclusion.

Science and math rely on contradiction to research and prove (or disprove) new theories. So, the contradictions we experience every day can go far in teaching us valuable life lessons.

Being right means facing the things you do not know to understand them better. This can, of course, be daunting, but Ellenberg argues that through math and the power of contradiction facing these uncertainties can be both freeing and informative.

Ellenberg’s work accurately displays how the parts of math we don’t quite understand can land us in trouble, especially in the pursuit of being right all the time. So, he offers the thought that studying life through contradictions can help to strengthen other ways of thinking.

Thinking in terms of contradictions will also increase your critical analysis skills. Being able to ask “well, what is the other side of this coin” can help you explore new possibilities in your life that you never thought possible. And all with the simple power of math.

## 7. “How Not to Be Wrong” by Jordan Ellenberg Teaches That You Will Learn from Failure

It’s an age-old saying, but failure is the making of a man. As discussed above, if your goal is to learn everything, then the only way this could come to pass is by failing. And this book review discusses how Jordan Ellenberg understands this concept through math.

Ellenberg points out that learning almost always comes from making mistakes. And, when you think about it, this has been true since your first lesson.

Being right about everything all the time is a pleasant idea. But it makes for a far more valuable life to fail occasionally. If you had only ever passed exams and had never studied for them before, you would have no experience of the value of the study.

So when the time comes for a test you are not ready for, failure could come very easily and quickly, knocking you out of your upward trend with devastating results.

And, as you’re sure to know, when learning math, failure is somewhat guaranteed at first. They say talent is born from pursuing an interest, and the same is true for math. But the key word here is ‘pursued.’

Ellenberg’s honest relationship with failure as a mathematician will teach you that clever people fail often. They can strive forward toward success, and come up with new and creative ways to resolve their initial problem that marks their intelligence.

You will gain much more through failing, and often have more satisfaction when you are successful than you would if you continually passed every test in your life, both in reality and metaphorically.

## 8. Mathematics is Just Common Sense

People may sometimes feel intimidated by mathematics, but that is because they can’t see just how common it is. Math is, at its core, the study of following rules to lead to an accurate conclusion. And it follows if you correctly follow these rules, the correct answer will find you and help you.

Ellenberg makes the point the rules of math are just common sense, and, therefore, anyone can learn them. The difficulty seems to come because math is rarely viewed objectively. The reason for this is that whenever we are using math, it is generally for something pressing in our lives that requires an immediate answer.

But take a step back. It makes sense that two plus two is four, doesn’t it? You have two of something. When you get two more, you will always have the same number of items at the end. And the same rules are seen in almost all areas of math.

This is one of the key takeaways from “How Not to Be Wrong.” It’s why you learn addition, subtraction, multiplication, and division at such an early age; you will use it as you grow up. What five-year-old wouldn’t want to work out how many years it will be until they’re ten? When you understand math as a common-sense concept, it becomes less intimidating. You can then employ it in your life to always keep you on the right track.

Maybe it gets a little more complex when dealing with high-end physics and complex numbers, as these can be difficult concepts for many people to grasp. But in everyday life, the math you find yourself using makes sense, even if you can’t always see it.

## 9. Don’t Use Probability Alone to Assess Risk

Risk and probability have somehow become interchangeable. However, the two are more different than you might expect. Using probability to calculate the outcome is helpful, but using this alone to assess the risk of any particular decision is foolish.

The issue arises because the risk relies on factors other than probability alone. Generally, more factors come into play. Physical circumstances, random luck, and even the kinds of people involved in whatever risky situation are going down all contribute to the outcome.

If you’re having your appendix removed by a group of trained and highly educated surgeons, you’d probably believe your chances of survival are good. But, if you’re having your appendix removed by a group of nine-year-olds, you’d probably run from the hospital at full speed.

The chance of death comes from the quality of the surgeon, not probability itself because appendix removal is generally quite a safe, secure procedure.

Probability can be a vital tool for various problems, both mathematically and in the wider world. But using it to assess risk without considering other factors that influence this leaves you open to getting things wrong. And to danger.

Use probability with the other factors that influence the danger to determine the outcome of an event or situation as closely as possible.

## 10. Question Everything

Question everything, not just in areas of maths, but in life. Your goal is to seek the correct answer, so you need the answers to particular questions. And you can’t get answers without asking. You should be asking two questions: what assumptions are being made, and are they justified?

Ellenberg argues that this is particularly true of scientific and statistic-based conclusions. The public tends to hear a statistic on the news and believe it without question. But errors are made more often than we’d like to think, which is why asking difficult questions is so important.

Human error is also a highly significant issue. People mess up, which is a fact of life.

But Jordan Ellenberg is not suggesting that you should treat everyone like they will mess up. Ellenberg believes that when something seems wrong, you should question it. That way, you can find the correct answer in time.

Observed data might experience changes and edits that alter it to suit the person or organization using it. Language can also prove deceptive, as words insinuate one idea while neglecting another.

That is why questioning everything and being open to the solutions you come to can have real, positive implications for your own life.

Try it for yourself. Begin to question everything you know, and do your research to draw conclusions that make the most sense. You’ll be amazed what you can teach yourself simply by asking, “could this be wrong?”

And as stated above, questions lead to answers. This allows you to find conclusions that lead you on the right track more often than not.

You might never be right all the time, and you will almost certainly make mistakes. But Ellenberg’s work teaches us the value of being wrong. It also teaches us how mathematics can get us just a little closer to the real answers we’re seeking. If that is, we know how to use it.

## So, Can You Truly Be Right All the Time?

“How Not to Be Wrong” by Jordan Ellenberg offers insights into the power of math. By understanding how often you use math in everyday life, you can apply it to various situations. And find the correct answer as a result.

Following the rules of mathematics will always lead you to the correct conclusion.

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