Oliver Cairn three years before that I was in my final year of high school I got a distinction inthe state Maths competition. He was 9 and topped the state, against 17 year olds. 1.8 million population in the state too.
Fun fact about Terence Tao: when getting his PhD, he almost failed his “general” exam, which is the most important test of your PhD. If you fail the generals you get kicked out. He was in his early 20’s at the time and expected the test to be way easier than it was so he studied pretty lightly and spent a lot of time, I kid you not, staying up late playing video games. Even the smartest mathematician in the world once almost failed a test because he wanted to play video games.
@@ashishkumarjha3851 yea, really motivating indeed, reading tao's writes in his blog :-D can't argue anymore, seems at other perspective things like myths must perish ._.
Prof. Tao once walked to my linear algebra class on the first day of school thinking that he is supposed to teach that class. He actually had prepared a syllabus not knowing that it was not his class. The look on his face was priceless when the actual professor walked in. Later I took a PDE class with him. He is brilliant teacher. He loves math and teaching math and he doesn't do it for the money
@@vulcrums I feel lucky too, thank you for the kind words. I honestly believe in today's world going to college is overpriced and overrated. We can learn a great many deal online, just like we are able to watch Mr. Tao here, giving a lecture. For me the main thing is to see people that are best in what they do, observe them in real life, and understand we are not that different and they are all human, which translates into inspiration. For some reason we are inclined to perceive them as almost mythological, super creatures and nothing like us. Which is in fact could not be farther from the truth. I am not lying when I say you can achieve anything and be who you are without going to college, or without doing a lot of stuff people see as requisites. All one needs is a plan, a determination to stick to it, and reach out to others that could help.
I think the title describes very well... Basically, this addresses two related questions: How small is the minimum gap between consecutive primes that occurs infinitely often (i.o.)? How large is the gap between consecutive primes that occurs infinitely often? As to the first question, the best result so far is on the order of hundreds, but there is an conjecture (known as the "Twin Primes Conjecture") that it goes all the way down to 2. Zhang really started this ball rolling back in 2013 with his result that the answer must be < 70 million (BTW, this story appeared in the New York Times). As to the second question, there is an open conjecture that the strongest answer is K * log^2(p_n), but the best result is smaller than that (yet funnily enough, involves more logs). The conjecture comes from pretending that primes occur randomly.
I made about 40 seconds in and he lost me.... and then he said "this is almost the most basic questions you can ask" and I lol'd! Terence Tao is my new hero! (I just had to edit this for a simple typo - fml etc)
It's common in people with high IQ's. Terence just happens to be one of the top 3 people with the highest IQs in the world. With people with high IQ, their brain processes so much so fast that you will often find them saying "um" and "uh," because that is their brain trying to process words and their thinking process.
Eh.. some people say that Albert Einstein couldn't tie his shoes for the life of him, but that didn't stop him from building the atomic bomb. Therefore, I don't think that it is a hindrance, rather a gift.
+Lee Ketteringham You're being too general in saying hinderance. A fairer statement would be that sometimes the lapse between objective mental function and expression of said objective is hindered by the difference.
@@thedoublehelix5661 Modern mathematics and scientific fields are products of western thinkers... only a seething dishonest anti-white dreg wouldn't admit to this reality.
Years ago when I was a graduate student visiting UCLA. I sat in one of his PDE seminar. I am deeply shocked by the intuition he demonstrated in that one-hour talk. That is the difference between fields medalist and ordinary smart people.
Yes, it’s amazing to see. I think anyone who studies math for a while will have moments of it. It’s like having mathematical dead reckoning - knowing what avenues of arguments will be fruitful.
@@thechemtrailkid yep, I often say it "Math sense". Btw it's also like the sense that some great football players perform such as Messi or Ronaldo, they seem to know where to stand or to run into and make it easy to do. We just can practice it to some levels but can't reach theirs 😢they're born to be the bests
Those of you saying "I can't pass this class", it's not a class. Lecture courses don't consist of running through the history of advances in a subject with only the bare-bones theory. Professors, researchers, and sometimes undergrads, will do open lectures where they'll give the gist of a topic to other mathematicians who may not have knowledge in that area. They won't necessarily go deep into theory, as is the case here. In the first 20 mins he's glossing over a ton of complex heavy machinery used to improve the bounds.
Tao is a very good communicator. Modest, fluent, responsive, considered, honest, and humorous. Very good person, a great scholar and a gentleman to the core.
I use this video to fall asleep comfortably. Listening to someone happily talking about numbers and scientific stuff just soothes me so well even though I do not comprehend the material.
@@scapedrag7893 Not really. If this was said about music, would you reply the same? If I didn't like the music I wouldn't listen to it but not long ago I was listening to something being played and it was a relaxing way to fall asleep.
I hardly do well in math, and yet I understood what he was saying clearly and precisely. Considering the theoretical principles that he is working on, this presentation was very concise, even for novice beginners. You can tell he is thinking about it every moment, the problems and solutions he is trying to figure out, even while giving this presentation. Beautiful, really. And yet, people want to insult his teaching and writing? You've obviously not had very many professors.
Tao’s genius at mathematics began early in life. He started to learn calculus when he was 7, at which age he began high school; by 9 he was already very good at university-level calculus. By 11, he was thriving in international mathematics competitions. Tao, now 31, was 20 when he earned his Ph.D. from Princeton University, and he joined UCLA’s faculty that year. UCLA promoted him to full professor at age 24.
I think you’re in the wrong spot. This is a math lesson, not a documentary. And anyone can check out his wiki without people copying and pasting random factoids for likes.
I'm not a math person. Math was the only subject I failed at in high school and college, but it is a great pleasure to watch a math genius in the works
The point is, people aren't there for him, and this isn't a course. It is a research lecture, and people are there to see what his work is - where it is in the historical context, and where he is taking it. While many disciplines use ppt, mathematicians continue to love chalk (and dislike whiteboard) in the way they tell their stories.
Tao is brilliant and very likable. And happily, the first half of the talk had a lot of Oh, of course! moments. Admittedly, the second half had a few What did he say? moments or Does "cover" mean "include"? Etc. Very informative talk, though, despite an occasional avoidable lack of clarity. It's not that Tao thinks faster than he can talk, as some commentators suggest. I've known Field Prize winners whose presentations are always crystal clear. Still, we shouldn't let an imagined ideal spoil our appreciation of the good. After all, there aren't that many people actively engaged in the research and who could have given us this update (to 2014). Thanks to the UCLA Math Dept. for making this available! Prime number distribution is a tough and fascinating field.
Hmm, good points made here. I will defend him by saying that, without meaning to insult, cover is a fairly commonly used word in university mathematics, for example in compactness. A set of sets cover another set if the union of those sets contains the target set.
Please enumerate the moments of "occasional avoidable lack of clarity" Otherwise we might conclude your Y-Tube name is an accurate characterization of your behavior.
Watching lectures given by Terence Tao, Edward Witten, and Manjul Bhargava has led me to a single definitive conclusion; 99.99999% of us are just meat with eyes.
that's typically how intelligence works. . most of us understand consciously or subconsciously how valuable really, really, smart people are to the survival and advancement of our species.
Because the end equation concludes with “a lot” of Logarithm (Log) which technically the math theorist finds himself into. Aka theres too many (Logs) in which the guy who’s solving the equation is “drowning” in.
Ooorr, maybe they are all dumb, and he is trying to teach them what a prime is but, even with an incredible elaborated argument, they still dont get it .
@Ryan Sun Not that far...just...maybe a year's study to understand properly the surface-level mathematics involved, and many more of specialized study on different parts (distributed across a number of people, as in the polymath group) to effectively apply it...but you might be able to understand what he's saying in a year.
Well some of mathematical thought has practical applications. In this case though, I've gotta say I don't really see the use. Lol. I think its interesting, but what does studying gaps between prime numbers actually accomplish?
I'm diploma student in chemical engineering currently watching phd math and the way he teach them is very straight-forward and easy to understand with his voice tone
Being locked in a psych ward for like 80-some days with a rubber pen and sheets of notebook paper, I came up with a few factors of primes by using my triangle or my building square. They fizzle out though. :( Still, Tao is my hero. I hope to one day pass calculus. It's my dream. I love math. I just suck at it.
What is astonishing and cute is that Terry Tao, despite his fame and accomplishment has stayed humble. And despite teaching for so many years, he still cannot maintain eye contact, which is a typical trait of a genius who are usually introverts. It comforts me because, I too struggle to maintain eye contact, although I manage to get above average grades. I have learnt some social skills by closely observing behavior of others and learning gradually from them. It is self-reassuring in a way to know that there are other people like me, who are much more accomplished in their lives. It is OK to be an introvert, as long as you still care about people and are passionate about your work and your family. I wish everyone who is reading my message to have a nice day, a happy week, and a wonderful year. 🙂
I was a math undergrad at UCLA... I had and still have so much respect for this man. He makes analytic number theory look like elementary algebra. This video is probably one of my favorites of all time on RU-vid. I don’t think people realize how important the twin prime conjecture really is. Together w the Riemann hypothesis they can change our world so much once proven.
Alpha Centauri honestly his video lectures I have only found on RU-vid, he doesn’t upload them himself you can go on his personal website and he has like a blog where he updates his current research and things like that!!!
Yitang Zhang's story is an inspiration in itself, and the collaborative extension is a delightful coda. Mathematicians like to work by themselves to solve problems, look at Andrew Wiles' story for example. But Terry rejects that kind of thinking and he wants to make Mathematics research collaborative like Erdos did. Kudos to him.
Beginning was about prime numbers: it is really important for humanity to know a lot about prime numbers, because we use them everywhere. For example, cryptography of internet(security), debit-credit cards. For this we need to know very big prime numbers, so normal people cannot guess it. The theorem he was improving was the spaces between prime numbers. If we found 1 prime number, how many more steps minimum we need to make to find the next prime number in the sequence.
@@iamalive2826 if one listens to music's for hours, that individual possesses a worrisome habitual behavior. Very unhealthy, and (uncalled for but..) stupid.
When the teacher is teaching and you don't understand anything. You don't even know what questions to ask in order for you to grasp. This is how I feel while watching this video.
What is his primary focus in mathematics? Because whatever it is, eventually he will be remembered as the one who advanced it forever. Truly an exceptional teacher too!!
He’s made valuable contributions to many areas. Not sure he really has *the* primary focus, but you can guess he’d like to solve the Riemann Hypothesis and the Twin Prime Conjecture. However these days you don’t solve big number theory problems by doing number theory, you take detours into equivalent problems in algebra etc.
@@eddie-xx Your comment is rather interesting, because instead of containing an emoji character, it contains an svg referring to an image on youtube's servers. Did you make this comment on your phone? If so, it would be an interesting experiment to see if one could edit the package sent to youtube when making a comment to potentially upload any image as a comment.
Why do people comment that they didn't understand a single sentence? Like, I understand that they probably watched this video because they want to understand it, but why not realize immediately that you don't understand particular crucial concepts and then go look them up or something? It just feels really weird to me to comment that
I know this guy, he's from Australia, Adelaide South Australia if I remember correctly. He's a math prodigy who won medals at the math olympics When he was only around 12-13, everyone else in the competition was around 18. But as a kid he went by the name of Terence not Terry.
Bipolar dissorder type I (mainly manic)/II (mainly depressive)¨, ADHD Combined Type¨, though. ADHD is the umbrella term, and ADD is now called ADHD Predominantly Inattentive because later in life it is usually expresses other sorts of hyperactivity that aren't hyperkinetic (e.g. anxiety, aggressiveness, restlessness; if unattended, it usually evolves into a second comorbid pathology, like, GAD and/or BPD-T I or II, but usually II), which means that what was usually called ADHD is now called ADHD Predominantly Hyperkinetic (GAD and BPD can evolve here from untreated ADHD, but it's more commonly type I). The real difference between the three types of ADHD aren't physiological, but behavioural, and urine phenethylamine levels remain fairly similar across the three groups. Which means, more often than not, the following: 1) you don't have BPD, but instead cyclothimia, and can be treated /relatively/ easily. 2) You do have BPD, and it evolved as a behavioural overcompensation of having ADHD in a capitalist society. 3) You were born with a "bipolar" brain, and the "random" fluctuations in mood and motivation made your psychiatrist misdiagnose ADHD on top of the bipolar dissorder, and you don't actually have ADHD. It's not an uncommon mistake, and it's one hard to notice, specially with children (you know, very few kids are actually suicidal).
If you are undecided - this is very approachable and interesting. Though he speaks very quickly he makes sure to write everything down and the concepts are straightforward enough to follow with just a High School level understanding of math. It's pretty cool.
@Alex Lee calc 1 is high school level stfu. At least in europe. All calc classes should be taught in high school bc they arent really math. “Real” math starts with analysis, set theory and linear algebra. Its crazy how the math undergrad level in the US is so low. In Europe we start freshman year straight away with real analysis and what they call in the US “abstract” linear algebra. In the US they learn it on the 3rd year of undergrad. Its embarassing. While on my second year in Europe I learn measure theory, measure theoretic probability theory, etc. and on my 3rd year undergrad i learn functional analysis
Law student checking in: It sounds like homeboy is speaking a foreign language. STEM are the wizards of our society. My cuz is studying engineering. I don't get any of it. That's okay though. I think you're all awesome. Total respect! You folks will all deal with many lawyers in your careers. I hope they're chill. Just don't ask them to do any complicated math! XD
To be fair, it's not like this lecture is from a course. He is talking about cutting-edge research in mathematics, so it's obviously going to be many levels more complicated than what people learn in school.
@@astro_penguin_ Oh, there was no offense intended. It's just a reality that most professions will intersect with the legal profession in one way or another. That same cousin I mentioned in my previous comment from 4 years ago is now a civil engineer. He often vents to me sometimes about his dealing with lawyers whenever we hang out 😂
I understand the logic and the process... maybe is because I don't speak English or maybe is because I'm not a mathematician, but there are some bits that I couldn't comprehend. Still, this is really fascinating, he seems to enjoy it a lot. I love this kind of content... some subtitles would be welcome. In the meantime I'll practice my English.
don't tell the woke leftie types that. remember, IQ is a social construct created by the cisgender white male patriarchy in order to keep "marginalized" people oppressed. the woke crowd will tell you that Tao is just a product of hard work and dedication. nothing to do with genius
There's a stereotype out there of the genius who can't communicate with "regular" people. I think it's mostly false. I've been to a number of math talks and, in my experience, the best mathematicians give the best talks. I think it's a combination of genius lending itself to all aspects of life, including public speaking, and the idea that if you've thought about something deeply and understood it profoundly, you can figure out the simplest and most appropriate way of explaining it. That's certainly how I feel every time I listen to Tao talk or read his blog. Mind, this is a heuristic and not an absolute rule! Some mediocre mathematicians are great speakers, and some brilliant mathematicians are almost indecipherable.
I'm very mesmerized by your ability to write so smoothly on a chalkboard. I usually whiteboard everything but I love the smoothness of chalk and when you have noticeable symmetry in your alignment of words / numbers on the board... AH i'm just sitting here in the dark LOVING it lol.
I truly think his mind just goes very fast and his words can't keep up. You can see that in his behaviour and speech itself. He is too smart. He was born a genius, you can't just develop similar brain functionality as him if you don't have natural gift.
9:21 "If you want to get to anything below 6 to get down to 2 you will need a new method" Well If you get the 6 right and you minus 4 off it then that equals 2. *_I AM LOOKING FORWARD TO RECEIVING MY NOBEL PRIZE_*
No matter how good you were, your theory of time was invalid. Einstein's theory of relativity proved your theory of time wrong. You stated that if we were able to locate each particle, its direction and its speed we will be able to time travel. That statement was proved wrong. Explain your self.
