How to Understand Math Intuitively?

How to prepare for math competitions? How to understand math intuitively? How to learn math? How to practice your math skills? These are all questions I address in this video!

▬ In this video ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
I explain why most people struggle with mathematics, despite not lacking intelligence or knowledge. This video is not limited to students in school or university, but rather applies to everyone interested in using the full potential of math intuition. I created this video together with my friends at MIT, who all attended and won different math competitions/olympiads during high school.

▬ Resources from the video ▬▬▬▬▬▬▬▬▬▬▬▬▬

For all ages and educational backgrounds:

Intro level resources:

More advanced high school and above:

▬ Follow me for more tips ▬▬▬▬▬▬▬▬▬▬▬▬▬▬

▬ Credits ▬▬▬▬▬▬▬▬▬

Also, thanks to my friend and colleague, Emily Mu, for helping me with with this video!

If you don’t have Instagram, feel free to watch the solution to the London underground tunnel problem here: Solution to London subway problem from Instagram

▬ Timestamps ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
0:00 - Intro
0:53 - Why most people don't get math?
2:17 - How to learn math intuitively?
4:38 - Best math resources and literature
6:30 - Practice problem
7:57 - Outro

[SHARPUIQ]

My mom has a master's in math, and she can solve complex math problems, but later, I learned how difficult it was for her to apply this knowledge to solve real-life problems. After I became an engineer, I realized how difficult it was to figure out what mathematical approach you can use to solve problems. That is when math becomes exciting and fun.

[kondojunagaraju]

"The key to the learn anything"
Step-1 Understanding
Step-2 Remembering
Step-3 Practice

[kummer]

Math for me is the greatest endeavor of human kind. Pencil, paper, handwork, life commitment and the greatest adventure on the search of beauty.

[seaturtle]

I am 71 and starting the furtherance of my math journey.

[jyvvidx]

I definitely agree that learning mathematics needs a proper mindset. One just needs to understand the concepts when it comes to solving problems.

[mikebritza]

As 73 year old studying math for the first time and having a mechanical background your analogy is crystal clear and very logical. Thanks for taking the time to put your thoughts on line. With the tube question I would telephone the org’s engineering section and ask them for the total length.

[Wllbam]

Absolutely fantastic recommendations, literally the best, I am in fact now going through these books and it's incredible how much it differs from the standard education I had

[ATFofficial.]

Thank you brother. I went to a rural highschool with teachers who were poor at their jobs, and therefore put me behind. Im re teaching myself math from algebra all the way up through calculus currently so i can hopefully get into school for engineering next fall. This helped tremendously

[shimrrashai-rcfq]

Math is actually at least two skills or disciplines. One is understanding the concepts. The other is being able to solve problems involving them. I would argue that the former is not quite as difficult in terms of sheer work required to develop as the latter. A lesson I learned much later than I would have liked to, owing to my personal history. Learned from bitter experience. Which also shows that luck counts, too. Hard work and luck are not totally independent variables. They can influence each other.

[StephanHaloftis]

I think intuitively understanding probability is the most useful specifically, understanding the compliments of probabilities, which is super easy honestly. Understanding the compliment of a probability will completely change your mindset when coming across a statistic.

[laurencevanhelsuwe]

For the London Underground problem I would first of all aim for a rough ball-park figure. I'm also too lazy to take any train speeds as inputs. Looking at the Underground map, I'd like to simplify it further by imagining the network as a set of pure horizontals and verticals. The total length is then just the sum of H horizontals plus V verticals. Let's also consider the map's rectangular shape, so a horizontal is e.g. 1.25 the length of a vertical. How wide is London? Let's say 20 miles? So a horizontal is 20 miles, a vertical is 16 miles. For our "raster" Underground, let's pick 5 for the number of horizontals, and 7 for the number of verticals. Total? 5 x 20 + 7 x 16 = 212 miles. I still don't know what the true figure is, but I expect the real length to be closer to 212 than 21, 2 or 2120 miles. Quick Google check.. 249 miles.

[rafaelavieira]

Thank you for explaining in a calm and friendly way. It really makes difference in how we can view mathematics as something helpful and not just bunches of information to be decorated. Hope you can keep spreading acknowledge and helping many people like me who is trying to relearn this amazing topic. Take care x

[snackentity]

Yep, this resonated with me. I did pretty average/crappy in my engineering undergrad because I didn't know how to learn. Like you said, it just felt like memorizing procedures and very little of it stuck with me in a way that could be extrapolated to novel situations. Too many concepts immediately obscured by dozens of symbols and pages of rearranging equations. That was intimidating and prevented any confidence in thinking that I was grasping any of it at all. In retrospect, after figuring out how to learn new things, the underlying concepts of the stuff that used to terrify me are embarrassingly simple to understand. I think a lot of professors are super smart in their field of study, but very little of their brain power goes to thinking about teaching and how people actually learn things. I can say that because I also had a few professors that were really good teachers and I remember everything I learned in those classes.

[lucaskoroljow]

Amazing video, another one. So I think it's not my discipline but I'm highly impressed by this skills. Great work.
I see forward to a video about your fitness routine! Keep going, it's great!

[whatever]

Your analogy on the tooltips was really interesting and helpful, thanks a lot!

[kmjohnny]

I've recently got interested in math again, and I find it amazing how it appears in many areas. There's also many solution to one problem, but I like to think with simplicity. If not only I can solve a problem, but explain it to others, then it's a simple solution. I feel like if math is taught correctly, people can see a form of beautiful art in it too. The best if you can find answers logically and intuitively as well.

[nosferatu]

Ich war auch nicht gut in Mathe, aber tada, bin ein theoretischer Physiker geworden. Ich habe erst ab der 8.Klasse gemerkt, dass wenn man sich hinsetzt und übt und übt, dann merkt man in der Klasse wie weit fortgeschritten man ist und wie sich das bemerkbar macht in Form von Lob eines Lehrers. Erst im Studium merkte ich, je mehr Mathe ich mache, desto mehr Spaß macht es. Das war davor für mich nicht so denkbar, dass das Freude in mir auslöst :).

[michael]

Thank you for your inspirational message and friendly presentation. I'm already in my 40's but I hope by picking up the textbook you recommended, and doing some of the problems in the book and online, I can refresh some knowledge and learn new ideas!

[Qai_]

Great Video! I love the idea of gaining an intuitive understanding of math.

[kal]

Your brilliance, dedication and enthusiasm are shown in your work. Keep on doing great jobs for everyone, you're a legend