Famous Vietnamese hackers do not have a university degree and love Math

From the perspective of a security maker, Duong Ngoc Thai, a security expert from Google, shared his interesting story with mathematics.

Duong Ngoc Thai, a famous hacker in Vietnam, currently works for Google. Here is the article on his blog, shared with Zing.vn, to answer the question “What to study math for?”.

A wall of my office is used as a board. On it is always chattering math symbols. The problems written here are not complicated, freshmen can understand, but sometimes the solution affects the safety of hundreds of millions of Internet users. In this room, no one asked what math to do, because everyone understood that doing no math would do nothing.

I used to like math

I like to study mathematics from a young age, but I’m not good at math. I studied mathematics at level 2, and at grade 9, I failed the 3rd grade math class. In grade 10, I still tried to study by myself, borrow your notebooks to study mathematics and still work hard on the articles for the journal Math and Youth.

A corner of the room to solve the problem of Duong Ngoc Thai.

If anyone has a good and beautiful solution, they will be named. I still remember you Tran Vinh Hung, whose name also has a name. Recently I learned that Hung was a math professor in America.

I was named once, not in a magazine, but a math teacher named in front of the school as a mirror … hard to post to the magazine, even though it was never named.

If anyone has a good and beautiful solution, they will be named. I still remember you Tran Vinh Hung, whose name also has a name. Recently I learned that Hung was a math professor in America.

I was named once, not in a magazine, but a math teacher named in front of the school as a mirror … hard to post to the magazine, even though it was never named.

My biggest luck is probably not afraid of math. In a world where many people are afraid of math, like to learn math to create a competitive advantage, making me have a different identity

– Duong Ngoc Thai, Google’s security officer in Canada.

In the middle of 11th grade I had a computer and started to spend all my time on the Internet. I was at school more and more ignorant because I didn’t want to go to school. So sometimes I was given a “team” at risk of graduation.

Until the second half of the 12th grade, I went to school more seriously for fear of dropping college. I was no longer interested in math, and studying was just to take high scores.

Incredible college, the first two-year general program taught a lot of math, but I did not study. At 6:30 in the morning, I stuffed rice ribs, boi tiu didn’t know if it was empty, but how to stuff the matrices with the rim, the school, the group.

I don’t understand what to do and no one is sad to explain. I skipped school, stayed at home to learn how to hack and work.

What I just said is nothing new, many people have experienced similar stories. Yet after 20 years, I am still learning math with an indescribable joy. What happens next for me is true.

The luckiest of my life is not afraid of math

I do security at a bank. The first few years of good work, lots of things to do and they paid well. I manage a small group, gradually people do all the work, I have nothing to do, so I plan to take a break.

I told my boss, but the boss called me to stay, my legs in the outer legs, no need to take a break.

I study math because math is so beautiful.

I opened the company, then closed it without selling any product. I realized that I lacked business knowledge so I bought a bunch of books to read, then tried everything, but none succeeded.

I did not feel discouraged, but I did not want to waste time. The question of what to do is still not answered.

I read on Professor Ngo Quang Hung’s blog about the vicious cycle of his career. Great things like what I like, I will do a lot, I will be good and good at many things, the more I like, the more I do it, and repeat it. So finding and jumping into this vicious circle is the key to success.

What is my vicious circle? Thinking back, I found that I was the best and liked the most. I kept searching for a long time but not realizing my greatest competitive advantage was the job I was doing. So I went back to making security, “to see how far I can go.”

Hacker Duong Ngoc Thai, currently working for Google

It was a great time. Just like the person who walked in the tunnel for a long time, he thought it would be forever, but then he saw the light gleaming at the end of the road, I spent all the strength of youth to run toward the light, the more everything ran, the more clear , the clearer the faster I run. Within 3 years, from far away, I catch up and go with the world. Perseverance is because of me, luckily, it is heaven.

My biggest luck is probably not afraid of math. In a world where so many people are afraid of math, like learning math creates a small competitive advantage, making me have a different identity, different from many people.

It is because of not accounting, I have the opportunity to come to the code, the main tool of the security industry. I discovered that the world has very few security engineers who know the code. I think there must be about 20 new security engineers who have 1 person who knows the password. Simply because you want to learn cryptography, you need to learn math first, but mentioning math is that many people have dizziness, dizziness, and no energy to learn.

I’m the opposite. When I realized the math that I used to be used to protect the Internet, I rushed to learn to forget to eat and sleep.

I don’t have any special talent, I have to work hard to learn things that for many people are just basic math. There are books I have read for 10 years, but I still don’t understand. Only thing, I never wanted to stop. I was like the one who conquered new lands, the more difficult it was, the happier it was.

Learning math is like exercise. You can live without exercise, but exercise will help you stay healthy and thus improve the quality of life.

What is interesting is that my math knowledge is nowhere near and the code that I have learned does not need the advanced math knowledge. Just use a few maths that level 2 math students can understand, cryptography can protect the Internet.

Just knowing a little bit of the math that the code used, I had a competitive advantage over many people and became an expert in my field.

Imagine if I knew a little more, what else could I do?

But that’s because your job needs to use math, and my work and my daily life don’t need math?

Thank you for asking. I also asked that.

Math is very beautiful

Some people say learning math is like exercise. You can live without exercise, but exercise will help you stay healthy and thus improve the quality of life.

An American scientist once said that learning math is like upgrading the firmware to the brain, not adding the width will also add vertical. The fact that the natural world is dominated by math and math is a good way to understand more about the world in which we live.

The famous scientist Richard Feynman says that God’s language is calculus. If these ideas still haven’t convinced you, let me tell you the rest of the reason I study math.

I study math because math is so beautiful. Learning math brought me so much joy, making the question study what to do as a child playing in the tenth year to do. Learning for fun, is that not enough?

In fact, people who have a lot of pleasures do not benefit. Admire a picture, read a detective story, watch a movie, listen to a piece of music …

What would you think if I said that math can also bring joy, math is also very entertaining?

What to learn math to do is a question that anyone once in a lifetime questioned

Mathematics comes from very specific problems in everyday life. Greeks do math because they want to measure objects. But then, very quickly, math became a game, the question is no longer to do but is this game fun to play?

How many of the best minds of mankind have played math games, learning math is a way for ordinary people like us to join them. What is more interesting than being able to meet acquaintances with Fermat, Euler or Abel?

The arts or sports that we enjoy, after all, are just games, so we can temporarily escape the tediousness of everyday life.

Mathematics, from this perspective, is the pinnacle of entertainment art, because it takes place entirely in human imagination, not limited by space, time or senses.

Betrand Russel, an eminent British mathematician in the early 20th century, wrote: “Math, looking right, not only the truth, but also the ultimate beauty, a cold and austere beauty, like like sculpture, not depending on our weak nature, not relying on the great traps of painting or music, but great purity and strict perfection like only the greatest art can show.

There is no need to be good at math to see its beauty

You don’t need to be good at math, don’t need to be a mathematician to feel the beauty Mr. Russel describes. I think having knowledge will help somewhat, but there are many dream-like elementary math results that anyone can see.

Get a piece of paper and a pen. You go get it, I’ll wait.

Draw a triangle. Next you connect each vertex to the center point of the opposite edge. What do you see? The three lines you just drew, called the median, intersect at one point. Isn’t it beautiful? Three straight lines that have nothing to do with each other have one thing in common. Why does the triangle have this property? Please save for homework for readers.

Next, draw a circle. My first mathematical memory was to sit up straight, put my hands on the table and read aloud to my classmates: the circumference of the circle is 2 times pi multiplied by a radius, written as C = 2 * π * r.

This formula says that the ratio between the circumference and the diameter of a circle, no matter how large or small, is a constant. If we take half the circumference multiplied by pi again, we will have a circle area, ie A = π * r * r. Is it strange?

There is no reason for the ratio between the circumference and the diameter or the ratio of the area and the square of the radius of every circle to be equal and equal to a number that appears everywhere in mathematics and life. But this is the truth.

The way the ancient mathematicians found Pi.

It is right here on earth, right on the Moon, Mars and right everywhere in this universe. How do people calculate pi? Notice that we can easily calculate the area or circumference of a square or rectangle, simply because the straight line is easier to measure than the curve. Based on this observation, more than two thousand years ago, Archimedes (yes, he himself jumped out of the bath and ran and la Eureka) came up with a very unique way of calculating.

First, he draws a hexagon with a side length equal to a circle radius. The circumference of the hexagon will be 6 x r.

Apparently the circumference of the circle is larger than the circumference of the hexagon, so Archimedes deduces π must be greater than 3.

Archimedes then doubled the number of edges of the polygon. Because the edges are straight lines, Archimedes “easily” calculates the perimeter of each polygon.

“Easy” in quotation marks because Archimedes did not have money to buy a Casio computer, so it had to be calculated manually by a square root. In this way, Archimedes estimated that 3 + 10/71 <π <3 + 10/70.

As the author of Infinite Powers wrote, the number π between the two numbers is almost the same, only different in that the first number has a denominator of 71, the next number is 70. The following number is shortened to 22/7, a very famous approximation of π that every student will learn and some people still mistakenly believe that is the true value of π.

For me, Archimedes’ method is no different from a good story that can be read and read over and over again. After Archimedes, many mathematicians have devised many other “stories” to approximate π.

Now it is known that there is no way to calculate the accuracy π, but it is still possible to calculate. Accurately. I don’t know exactly how much, but how much I can count accurately, is it interesting?

Next, go find a compass and a ruler. Draw any angle, then use the compass according to the instructions in Figure 5 to divide that angle.

The question is how to divide the three corners with the ruler and the compass? From the split into three, it is easy to say, who is more difficult to go to heaven. Two problems at first glance are very similar, but in fact, they belong to two very different worlds.

You won’t be able to divide a corner into three with the compass.

The Greeks began to seek answers from BC, but there was no answer until the end of the 19th century. A very courageous answer: there is no way.

How to prove a problem without a solution? With an extremely ingenious argument as follows. To divide three corners, it is necessary to solve a quadratic equation. By the 19th century, it was known that the quadratic equation solution was represented by the square root.

But with rulers and compasses we can only calculate the square root, infer what must be proved. My heart always has room for proof of impossibility like this.

They are the embodiment of the ultimate beauty that Mr. Russel speaks of. No matter who you are, no matter where you come from, there’s no need to know me the next day, but I won’t be able to divide three corners with a ruler and a compass.

The existence of proofs can no longer give me hope. Whenever I can’t solve some problem, I often sneak out hoping that the problem is wrong or that the lesson can’t be solved.

Is there any other form of artistic entertainment that only within a few minutes, just by the imagination and very elementary knowledge, have you reached the threshold of knowledge of all mankind? Learning math is like having a miraculous door of Doraemon, it is just a moment to be able to travel to places where nobody has ever arrived. What’s more fun.

I write this article for no other purpose than to share the pleasure of the person who perceives the beauty of mathematics. Naturally or badly depends very much on the perspective. Maybe you don’t see what I’m writing here is interesting, it’s okay.

I just want to say that math has completely changed my life and hope that you give math a chance to change the life of you or your children.

I understand that most of us do not have a good experience when studying mathematics in high school or college. I assure you this is a common problem, not only in Vietnam but all over the world.

Mathematics is taught in a hard way, so it is learned mechanically. No problem, be optimistic, school is not the only place we can learn.

I have never had a college degree, if I can study math, anyone can learn it. The only thing we need is an open mind, daring to try new things, leaving the rest to worry.

Good luck and hope you will also see the proofs and say, oh so beautiful!

Source : Zing