Math gets a bad reputation. It’s hard, abstract and, especially the way most professors teach it, feels completely detached from the real world. Since my MIT Challenge involves doing a lot of math (far more than programming) I thought I’d try to explain why I feel math does matter.

**How Useful is Calculus in the “Real World”?**

One of the major criticisms I’ve been getting in my challenge is that I’m learning a lot of theory and math, but doing less practical projects. It raises a valid point, people often complain that what they learned in school is detached from the way the world works. If that’s so, am I just wasting my time, since I won’t even get a degree out of my efforts?

I couldn’t disagree more, but I realize my worldview is different from most people. Learning theory matters. Math matters. Not the symbol manipulation that most people are force fed in calculus classes, but the general principles that help you understand how the world works.

**In Order to Change the World, You First Need to Understand It**

North American culture largely eschews learning theory. We make fun of people who have “book smarts” but lack street smarts. Entrepreneurial wisdom is favored over academic calculations and we distrust anyone who has an idea they haven’t gained from experience.

I think this mentality is dangerous. How can you possibly hope to create positive change in the world if you don’t understand it? No, understanding is not exclusively the domain of textbooks and classes, but if you don’t ever bother to learn how things work, you’ll always struggle to change things, whether that’s in finding a career or improving your life.

I find it interesting that many Asian cultures don’t have the same bad attitude about math and theory, and these are the same cultures that are experiencing the fastest economic growth, higher test scores and whose children succeed more when immigrating to more developed countries.

**Math Isn’t in the Numbers**

The reason people complain about never using the math they learned in high-school, is because math isn’t about equations and symbol manipulation. Sure, that’s a part and it’s the part instructors tend to focus on. Math is really about general truths which help you understand relationships between ideas. Once you have a deep intuition about how a branch of math works, you can use it on any problem which has those same relationships.

Knowing 3×5=15 isn’t exclusive to counting three bags of five oranges. It applies to bank accounts, buildings, people and profits. The same is true for calculus, statistics and other advanced maths. If you get the intuition of how the relationships in math work, then you can use it on any problem, even if it is something you’ve never had any experience dealing with before.

That’s the real power of learning theory. Not that it replaces learning through experience, but that they make it far more powerful. It cuts down trial and error, helps you see patterns and think of new solutions to problems. Because often the best way to change the world is to first understand how it works.

Great post, Scott!

Kalid had a wonderful analogy on this topic, found here:

http://aha.betterexplained.com/posts/174/analogy-intuition–details-are-like-a-bow–arrow

It’s very true, and your article and his analogy link wonderfully – an extremely sharp arrow is good (street smart), but without a good bow (book smart – theory), that arrow cannot fly to its full potential.

I don’t understand how you say you are trying to tackle all these MIT classes and absorb the material well and you still have time to blog and make videos.

Anon,

I do all my business work (which includes this blog) on Sunday. I spend Monday-Friday learning and I take Saturday off.

Although it might be a bit easier on my schedule to give up blogging or making videos, that would completely defeat the point. My career is being a blogger, not a student, so I maintain a balance.

-Scott

Scott,

I can say with great confidence that you CAN learn material well(i.e. absorb it) as you whip by at fast speeds.

An example: I put off studying for one of my midterms until 2 weeks before the class. I didn’t really follow through with lectures and as a result, I would have been so screwed for the course. I have been doing this only for one week, but I am halfway through the material and can still remember the smallest of details that I studied, as well as the major concepts, which just bulge out at me in my mind.

The trick is, as you’ve mentioned, stay focused. HOWEVER, I realized that it’s only because I put all my other courses aside and only focused on this work for maybe 5 hours a day. I sprinkle in another subject if I feel like it but my time is spent relaxing and just doing other stuff.

So this MIT challenge that you’re doing seems downright possible, and then some. It seems totally reasonable. But one of the reasons, among many, that I feel you will accomplish this task is because you’re only doing one course at a time, but diving into the course with all your focus. It engages your mind for that entire week or so and allows you to make as many connections as you can in that one week, then reinforcing the connections as you move on. Whereas, trying to do 5 courses at once in a tightly-packed schedule would render your mind confused and overwhelmed at the amount of information that is striking you.

This ‘one-course-at-a-time’ appeals much more to people like me and I only wish they would implement this in schools.

I really like math, becaz it is more of interesting relationships and application in real life. Your video is exactly pointing on the very basic thing that today students, who cram about most of the difficult topics(not only in maths but other subjects also), should know and realize as to y r they studying any particular topic from any subect.thanks for the video.wish u luck.

Hi Scott, I disagree.

The world is run by people, not maths. If you want to learn how the world works, learn psychology. Sure, basic maths is useful, but can you give me any significant examples where calculus in particular (and not any other academic topic) has singularly changed your life?

Maths is good for introducing deep logic into one’s way of thinking, but it does not explain how the world operates and isn’t actually as useful as you make out.

Mike

Mike,

They aren’t mutually exclusive. Psychology is definitely important, but math can be incredibly useful too.

I can say with confidence that understanding Bayes’ Equation singularly changed my life, causing me to rethink how I approach uncertainty. The basics of statistics shape how I run personal experiments and debug my life. Calculus provides beautiful metaphors for describing many theories–if you have a good intuition of math you can start using it as a way of creating analogies about things.

The world is run by people, yes. But the universe is run with math.

-Scott

Scott,

Thanks for your reply.

Nobody really lives their lives via maths. It just isn’t the way things are done, not will it ever be.

The universe is not run by maths. We use maths and physics etc to better understand the universe, but often our theories fall flat on their faces, given enough time. E.g. E=mc2 etc?

So, the question of “why do maths” isn’t answerable in the over-arching manner in which you do so above.

Take it steady dude.

Mike

Mike,

Everything you use in your everyday life came about because people studied maths, and later used that to build physical theories and then everyday products.

Let me give you some examples:

Calculus-electromagentism-electricity

Trig-newtonian mechanics-rocketry, aircraft, guns, shipping

Hermitian functions-quantum physics-computers (yes, your computer requires quantum mechanics to function), lasers, nuclear power and bombs

Tensor theory- relativity- gps.

Dont be so quick to dismiss the study of math. It is relevant in your everyday life as well, for example, to calculate an acceleration you use calculus ( the rate if change). You know math, you can get a technical job which is highly paid and less prone to outsourcing.

The universe is modelled using mathematics, and those models were used to build the world you take for granted today.

How did calculus change my life? It opened the doors to further study which has given me a job I live. I can understand the stock market and economic theory. I could if I wanted design my own models of how something is working, use that to make predictions of the future and use those predictions to my advantage.

I’d like some more depth here. You make some casual references in the comments section that make me curious:

“I can say with confidence that understanding Bayes’ Equation singularly changed my life, causing me to rethink how I approach uncertainty. The basics of statistics shape how I run personal experiments and debug my life. Calculus provides beautiful metaphors for describing many theories–if you have a good intuition of math you can start using it as a way of creating analogies about things.”

If you would elaborate further, I could get a greater sense of your point of view.

I’m sorry Mike, I have to disagree. E=mc^2 fell flat on its face? No, it just won’t apply for the neutrinos that the physicists at CERN have observed. That formula, and Einstein’s theory of relativity still applies to most particles. That’s not a theory falling flat on it’s face, that’s us admitting that there are always exceptions to the rule. I mean, that would be like saying because Newton’s Laws of Motion don’t apply to small particles, that they must not work. Except we both know that’s not true.

And people do live their lives via math. We use it all of the time, and we use objects that use math. I want to try something: go through an entire day without doing math or using something that does math. No counting, no basic computation like addition or subtraction, nothing. You can’t do any of it. But wait, you can’t use things like a microwave, oven, cellphone, computer, etc., because all of those things, at some level, do a form of computation. How much do you think you’ll get done? Not a lot, right? We are use math a lot more than we think we do, and we use objects that are constantly doing math.

I get what you’re trying to say. Not everyone needs to know differential equations or linear algebra. But just because people don’t need to have a detailed knowledge about various branches of a subject doesn’t mean that you shouldn’t have a general knowledge about a subject. I mean, who other than meteorologists have a detailed knowledge about how weather works? Very few. But I’m pretty sure you’re going to teach a kid the difference between rain or sunshine.

I couldn’t agree with you more Scott. Understanding mathematical concepts allows you to understand how things relate to one another in the real world. Furthermore, pushing your mind to grasp these difficult concepts will only make learning easier in the future – for that reason alone maths is worth pursing in my opinion.

I totally understand why you’re doing what you are – I have the same hunger to learn and I wish you all the best.

Keep up the good work and good luck!

- David

Mike,

Nobody is a false generalization, because I personally use math a lot in my thinking–so at the very least there’s one weirdo out there who does so.

Math and its cousins philosophy and logic are the basis of the universe. E=mc^2 has never failed any studies I’ve ever heard of, but physics is just one framework for math.

If you’re curious as to how someone could use math (and logic) as a principle for life, read LessWrong: http://www.lesswrong.com/

Alan,

Bayes’ Rule describes how to update your knowledge of something when you find new evidence. People talk about uncertainty and risk in casual ways all the time, but if you actually understand Bayes rule then you can understand how it’s possible to reason about *anything*. There are tons of counterintuitive and amazing implications of this rule, but it all stems from one equation.

Statistics, particularly the concept of sampling and the methodologies of choosing the pattern you’re looking for before testing it are the basis of all empirical science, but most people have never heard of them. We rarely need the full rigor of a chi-squared test, but having some grasp of the basic ideas keeps us from avoiding the common human biases.

Calculus, including its even more useful generalization, differential equations, allow you to model systems. If you understand autonomous systems, you can reason why, for example, when you spray mosquitoes with DDT, that actually *increases* the mosquito population.

The problem is that math is about fully general truths, not specifics. So it’s not so much about informing you on a specific practical instance, but reshaping your entire paradigm of viewing life, which causes you to look at decisions completely differently.

-Scott

Look scott I studied computer science and automatic control 7 years ago and I’m working now as a developer/designer/consultant in a bank.

I have studied math, calculus, statisitics, accounting,and probability.

I can tell you that sometimes I was wondering why we are studying this untill I saw a real example (like differntial equation).

But I dont feel that it makes a big different in understanding life, Yes sometime it help in tactical situations.

What I can say is that it makes your mind think differently , think better like usig binary search in large address book. But still it is scattered situations.

Scott,

Let’s face it, maths is needed in all different walks of life, but not to the extent to which you have said in the article above.

Life is not about advanced maths. Simple maths anybody can do, even illiterate people can do simple arithmetic, which allows them to do everything they will ever need to do. There are billions of people on this planet – of which only a small fraction are good at advanced maths – are the rest not living a decent quality life?

Let’s break out from this “my way is the only way” mentality. Sure maths is useful, but it isn’t essential. Electricity, mobile phones, etc are all not essential to life. Life is far more than just the gadgets and gizmos modern man has invented. People have lived for millennia without any of this stuff.

Learning maths as fast as possible will get you nowhere. Sure, you’ll get good at it and might even be the best, but it’s only useful for goals which you have chosen that absolutely require such an end result. You could quite easily live a life without any hardcore learning and enjoy it much more so.

Adios amigos.

Mike, no one is telling you that you HAVE to learn maths. Scott is merely pointing out that doing so has benefits which are often ignored by American society, and that having a good understanding of maths will help you in the world that exists today. If you don’t want to learn maths then it’s your decision. Maybe you didn’t realise that.

About the CERN experiment: The experiment would prove that Einstein’s theory is incomplete, but not inaccurate. Think about the implications. We have verified over and over again it’s truth in the frame of reference of the lab, but what if there were more than the four dimensions we knew about? What if time and space were wrapped up in other dimensions? Then the experiment would not disprove Einstein’s theory but rather bring about a new set of questions regarding the conditions under which the measurements were made. We know that in fact Newton was correct about his observations. His theory is simply a Taylor expansion of Einstein’s (i.e. v approaches 0).

Scott, your comment about entrepreneurship brings to light why some of the most successful entrepreneurs are engineers and not business majors. Their insight into the theory and practical knowledge with how to make a system work together are why they are able to create high-level products that are deliverable to the consumer.

Mike,

You cannot study/understand psychology without having an understanding of math. If nobody cared about math, then nobody could do anything in psychology because the field itself can’t exist without it.

Logic *is* math, and you HAVE to use logic/math to study relationships of any kind. Math is simply a language that everybody must learn to communicate how things change, interact, and affect each other.

Think about it. What if we never learned the ability to count? Then we’d never be able to evolve into a society that can barter and trade; we would still be living in an every-man-for-himself type of environment, and after a few million years, probably extinct as a species.

Scott,

Thank you for your video. Math has changed my life. Before I studied math, my life was aimless and miserable. When I attended high school, I failed math. I was told, “it’s okay, you’re not good at math”. After years of wandering the country and soul searching, I enrolled in college. Math became absolutely captivating. My new goal was to teach math at the high school level and change the perception. I am about to begin my fourth year of teaching at a New Tech project-based high school. Also, next week I will be attending a AP summer institute for Calculus AB certification.

I have beat the odds and am doing what was believed impossible.

Using math, I have tapped into parts of my mind that I never would have had access to otherwise. I have the ability to realize truths that were obscure. I have even evolved into a fit vegetarian and have tackled the negative obstacles in my life.