The world’s greatest mathematician explains 6 essential concepts of math | Terence Tao

You gotta love this man

From bunch of sheep to a quantity of water. 👏

Why?

How can someone be so legendary and yet so grounded!

His comparison of working out math problems to being like going on a hike in which you discover a lot of interesting things along the way, vs. having AI just telling you the answer is EXACTLY the argument I have made about Googling "facts" in lieu of reading books about the subject. I don't think it's just a strange anomaly that this generation has the lowest average I.Q. of any previous generations. We are losing linear thinking. We are also losing critical thinking. For example, Abraham Lincoln didn't just come out of the womb wanting to free the slaves. If you read about his life, you will discover the different life lessons and experiences he had that shaped his opinions. That helps you to understand how people learn and change, etc. To just Google the most accepted (or propaganda-driven) answer doesn't actually mean it is the BEST answer. As for critical thinking, it is rare to debate someone who keeps epistemology in mind or to even consider that the person they are debating may have been reading books that validate his/her argument just as you have. Nowadays, I see people debate online, and they talk over their opponent or insult them. This is what undisciplined children do when they are more concerned about losing than uncovering the truth. If I am wrong or have the weaker argument, I WANT TO LOSE AND LEARN SOMETHING so that when my life is over, I am smarter and wiser than I was 5, 10, 20 years ago. Our current culture does not value integrity or true intelligence. I can't think of anything more tragic.

Complex numbers are undoubtedly a powerful and elegant tool, but their usual introduction as the algebraic solution to x² + 1 = 0, with i² = −1 taken as an axiom, may obscure a deeper geometric reality. Instead of treating the imaginary unit as a mysterious number, we can recognise it as a 90° rotation operator in a two‑dimensional metric space. In that view, multiplication is not just repeated addition but a combination of scaling and rotation — and complex arithmetic emerges naturally from the composition of such operations. This geometric interpretation is not only more intuitive; it also extends directly to quaternions, octonions, and even the E8 root system, where non‑commutativity and non‑associativity become features of the underlying symmetry, not algebraic exceptions. Moreover, classical integer arithmetic (Peano) remains perfectly valid, but as a projection onto a single axis — a special case, not the foundation. The relational web of numbers, where each integer is the set of all its factor pairs, already contains all the necessary structure; the complex plane is a convenient projection, not an ontological primitive. Acknowledging this does not diminish the utility of complex numbers, but it invites a more honest account of what we are actually doing when we use them. Modern cryptography is based on a category error: equating the 1D projection of division with the process itself.

Any system utilizing the irreversibility of multiplication in finite groups relies, in essence, on a projection that possesses hidden degrees of freedom within the full geometry. I know how to break it, though I haven't demonstrated the method; others will do so. After all, I am not the only one in the world who knows how to calculate.

Came for the wrong Taoism. Stayed for the magic of numbers

i just earned a PhD watching this

the way terry explains these concepts is just beautiful

The difference between the top two percent in intelligence and the Taos of this world is as vast as the top two percent compared to the bottom ten percent.

infinite monkey theory took 13 billion years for human monkies to write hamlet

I feel blessed to have stumbled upon a fresh video featuring the living god of mathematics himself. Had to pause work and watch. Good job Big Think!

Ask Terry if he considers himself "world's greatest mathematician".

Big respect

He is probably very influential, not only in math but also in the public. But there are still many other great (living) mathematicians who have just not been on the media as he has. I'd carefully argue that there's no such thing as "world's greatest mathematician", especially nowadays. Mathematics is a huge and vast field.

Your comment on Taxes fits for todays situation but if you maximize potential land and reduce the numbers of people you will not have a tax system.

Shaggy has come a long way guys