Masterclass on mathematical thinking
terrytao.wordpress.com
terrytao.wordpress.com
Finally there's a celebrity aspect to Masterclass that's a bit strange. Like these guys are famous, and because they're famous, they are the most worthy to teach you something.
Some series you should check out that are free and IMO provide much better value for time:
Academy of Achievement: https://achievement.org/ * Some good lessons with Eric Lander, Larry Page, Sergey Brin, Bill Gates, Jeff Bezos and Demis Hassabis
3B1B: https://www.3blue1brown.com/
Numberphile: https://www.youtube.com/channel/UCoxcjq-8xIDTYp3uz647V5A
> Finally there's a celebrity aspect to Masterclass that's a bit strange. Like these guys are famous, and because they're famous, they are the most worthy to teach you something.
with the recommendation
> Academy of Achievement: https://achievement.org/ * Some good lessons with Eric Lander, Larry Page, Sergey Brin, Bill Gates, Jeff Bezos and Demis Hassabis
It has a lot of amusingly illustrated insight problems that show you how thinking about a problem differently simplifies getting to the answer a lot. It's probably aimed at advanced teenagers, but in fact the lessons there are some that even many adults probably have not come across before. I mean, I haven't watched the Masterclass, but I imagine Terrence Tao isn't teaching multimanifold group theory or something anyway, so this is the kind of insightful more daily-math problems he's helping people to understand how to think about.
[0] search your favorite, ahem, LIBrary GENeric source of books to find it.
There is another Gardner book, Aha! Gotcha, which has a different emphasis than what I think you're talking about, but is excellent. I loved it as a kid. Gotcha is more about mathematical paradoxes and intuition-breaking concepts. Hotel Infinity, "who shaves the barber who does not shave himself?", the 'unexpected tiger', Zeno's paradox is included I think..., the difference between average and median, Newcomb's problem, etc...
(the unexpected tiger: https://en.wikipedia.org/wiki/Unexpected_hanging_paradox)
I'm going to have to check this out based on how good Gotcha was.
The other one ("Aha Gotcha"), you are right is more about paradoxes that arise when applying logic that seems to lead to contradictory outcomes. But it also has a lot of "change the way of thinking" answers.
The cost is €16/month which is cheaper than Netflix. I just cancelled my Spotify recently so this is affordable for me right now.
EDIT: The problem I see with Master Class as a subcription service is... if you watch Master classes on everything you are getting a broad education rather than a deep dive. I guess it's more for entertainment though.
I held off joining for the longest time because I didn't want twenty hours of each person telling me "You can do this!" The cooks such as Thomas Keller simply aren't capable of staying in affirmation mode that long (think of their kitchens!) and they do get down to business. I learned a lot, even as an experienced cook.
(Math meets Keller: I still don't believe they use a 10% brine in the restaurant. I think he's confused as to what they do.)
Politics and the English language http://www.public-library.uk/ebooks/72/30.pdf
This is a vague question but I'm interested in all kinds of suggestions... including meta suggestions to recommendation sites. I sometimes look at various subreddits like /r/netflix but I don't find much there.
Otherwise, I think the real question is "why just paid?!"
There's an absolute load of amazing free online video content. What topic(s) are you interested in?
Disclaimer: I run it.
I've also heard good things about The Great Courses Plus [1], but have not tried them out yet.
However, the production value is not only visually high, it is generally well done so I find myself watching something I might otherwise not be interested in. It's not like TED talks, which I often find too showy, too heavy on the presentation.
I think Masterclass is a good platform for this kind of thing: get experts to introduce people to watch something they otherwise wouldn't.
> Terence Tao on 27 January, 2022 at 10:31 am The production values of the lecture series given by Masterclass would not be possible for me to replicate by myself. (For instance, the film shoot alone involved well over a dozen people, including makeup, prop design, camera and lighting crew, director, editing, etc., in a custom studio with professional-quality recording equipment. The professional scriptwriting services were also very valuable, improving the selection and arrangement of material in ways I would not have thought of.)
That's possible. It's also possible that Terrance Tao is correct in his judgement that using Masterclass was worth it for him. Personally I'd give him the benefit of the doubt that he's not lying.
Going with Masterclass is probably the path of least resistance for him to create high-quality video content while continuing to spend most time on research and other educational activities.
Another possible factor: Many good mathematicians are quite perfectionistic and would not want to create homemade-quality videos if they can avoid it.
I think you overestimate how commercially viable actual teaching is as opposed to infotainment. Either way, infotainment allows him to earn money and talk about a subject he loves. Good for him and people love infotainment, it tickles their brains just enough but not too much to require actual thinking.
An example: https://www.theguardian.com/world/2015/jan/16/south-korea-te...
“Teaching pays: Cha said he earned $8m last year. “I’m madly in love with maths,” he said, looking the height of trendiness in his crimson shirt and trousers and tweed jacket, in his office in Gangnam – a wealthy part of Seoul famous for its conspicuous consumption and featured in the song Gangnam Style.”
There is a reason the PISA results of some countries stay consistently near the top: https://factsmaps.com/pisa-2018-worldwide-ranking-average-sc...
A lot of these youtubers who put out fantastic videos do essentially all the same things as the Masterclass production crew, but just on a smaller scale. Countless hours are poured into producing these youtube videos that are maybe just as short as 10 minutes.
And even if Terrance Tao wants to make some infotainment, what's wrong with that?
Whether or not something's infotainment and whether or not it could be done more cheaply are orthogonal. There's no reason for him to make this on Youtube, any more than there's a reason for plumbers to do plumbing for nothing in their spare time.
Even cooking would require hundreds -- there's a whole lot of dishes, cuisines, styles and techniques.
May of any subject is likely a years-long endeavor.
I’ve thought for years that netflix could/should really do something interesting with education. I’d love some high quality lectures and courses from them. Like actually legit ones.
It's totally worthwhile, but it depends on your interests.
I originally subbed, for all things, to see Penn & Teller teach the basics of magic. I've since moved on to learning about cooking and how movies are made from the best in the business.
You can get a feel for what is offered here: https://www.masterclass.com/categories
I'm not affiliated with them in any way.
It's a mixed bag, but more positive than the phrase implies. The great ones are great, even if they are just infotainment, but there are some deeper ones as well. At the very least it's a great way to sample different creative fields and find out more about them.
My two main observations are:
1. There's a reason most of them say "So-and-so teaching <vague phrase>". You're not going to learn scales from any musicians, how to make jokes from any comedians, or how to write good from any writers. The craft part is up to you; they'll teach concepts, ideas, abstractions, etc relevant to their field, and ways to apply that craft effectively.
2. They all have elements of "Strong educational content" (EDU) and "infotainment / autobiography / motivational speaking" (TAIN), but some of them swing much harder in one direction than the other.
---
Here's some hand-wavy opinions of the ones I've watched. (Obviously the TAIN value will be higher if you're already interested in that person) -
- Aaron Sorkin teaches Screenwriting (Strong EDU and TAIN)
- Tom Morello teaches Electric Guitar (Strong EDU and TAIN)
- Tony Hawk teaches Skateboarding (Strong EDU and TAIN)
- Daniel Negreanu teaches Poker (Strong EDU and TAIN)
- Niki Nakayama teaches Modern Japanese Cooking (Strong EDU, Medium TAIN)
- Bob Iger teaches Business Strategy and Leadership (Read his book)
- Dan Brown teaches Writing Thrillers (Strong EDU, Medium TAIN)
- Hans Zimmer teaches Film Scoring (Medium EDU, Strong TAIN)
- Neil Gaiman teaches the Art of Storytelling (Medium EDU, Strong TAIN)
- St Vincent teaches Creativity (Medium EDU, Strong TAIN)
- Danny Elfman teaches Music for Film (Medium EDU and TAIN)
- Itzhak Perlman teaches Violin (Medium EDU and TAIN)
- Steve Martin teaches Comedy (Read his book)
- Billy Collins teaches Poetry (Medium EDU, Low TAIN)
- Herbie Hancock teaches Jazz (Low EDU, Medium TAIN)
- Yo-Yo Ma teaches Music and Connection (Low EDU, Medium TAIN)
I've really enjoyed it but as it's already been said it's a lot better to approach the class as an extended interview and reflections from a world-class practitioner about their craft and career. Directing was an especially relevant discipline for the Masterclass formula as it is a mix of hard and soft skills, and there are a lot of resources for the hard skills, especially at an indie level. Ron Howard instead focused more on the soft skills and I gained something from it, especially as some of it is just plain old project management that I could also apply at my (engineering) work.
There was also a long, uncut practical session where Howard directed a scene on a set with an entire team of actors and crew, and I found it really interesting to watch them all work together like I was a fly on the wall.
So if you view Masterclass as a way to pick the brain of a celebrity practitioner you genuinely admire, I think it is 100% worthwhile. If you're instead looking for a regular tutorial about a discipline without having any interest in the instructor themselves, I'm less sure.
It's probably a nice watch, but not for the math value :)
Basically the math equivalent of all those quantum-blackhole-stringtheory videos from the last ~20 years.
The production values are nowhere near what you get with Masterclass (thus, why it's free) but the content can't be beat.
[0]https://learning.edx.org/course/course-v1:UTAustinX+UT.9.10x...
1. https://www.wondrium.com/art-and-craft-of-mathematical-probl...
Masterclass is an entertainment company, nothing to do with education.
but also I think that understanding paradigms and thought processes outside your usual comfort zone is education, albeit not the formal one. And this is what Masterclass does great imho.
EDIT: in the comments Prithvi has some interesting suggestions for doing a patreon at a higher level to be released freely. If possible and that eventually exists support that,
1. Masterclass is $20/month. The "masses" can absolutely afford it. It's not really a barrier for entry.
2. There's tons of free lecture content already. Khan Academy is a great example and it'll actually dive deeper than a short episodes.
3. If you're an American, $20/month is laughable for an education. Getting a post-secondary education is like getting a mortgage.
4. Why do we have to knock on highly produced commercial edutainment? It is not a threat to any other form of education by any stretch. At least someone watching this may get inspired or motivated to keep learning more Math.
Agree with your other points, but disagree on this - there are plenty of people who can't afford this kind of subscription (e.g. most materially poor countries in the world, which make up billions of people).
Do you have evidence to support these numbers, or the more general claim of genetic supremacy?
Math education comes up here regularly, and we have lots of smart math people here, but the story is often that some commentator was simply never shown anything interesting in their whole schooling. I'd never have given it much thought were it not for one particular math teacher who put a lot of effort into me and a few other interested kids. I still keep in touch with him.
I'll accept that nobody is, but his mom was a math teacher. Few of us get that kind of leg up, certainly not 600m+. When I was 5, "don't get shot" was already getting a significant share of my brain's power, and I had it better than most. Sure, he's got a brain like gasoline, but don't discount the spark and oxygen that allowed the genius to deflagrate. And don't just throw numbers around like that if you don't have proof. If you respect the mathematics, act like it.
But I have a feeling his success as a professional mathematician involves the interaction of such math talent with hard work and good mathematical taste.
One can read his PhD qualifying exams to observe he was actually not an outlier amongst his peers in his early career.
You are providing questions as a substitute for actual evidence. Your questions are worthy of being asked, but they are still questions.
Basically a variant of "I cannot explain ... therefore it must be Y! How could it not be Y?"
Just because people don't have adequate explanations for nurture doesn't make it an automatic "genetics". All it means is that they don't have adequate explanations. This does not make your stance any stronger or more likely to be correct.
(Disclaimer: I can easily believe genetics is the answer. I won't, however, be sure of it).
> Just because people don't have adequate explanations for nurture doesn't make it an automatic "genetics". All it means is that they don't have adequate explanations.
Your question is the equivalent of "Since you cannot provide evidence, I must be right." This is a fallacy. The other party's lack of evidence does not strengthen your position.
Maybe they don't know how to do it. Maybe TT got lucky.
No formal training in math. Made insane contributions to mathematics including solving "unsolvable" problems.
> A child prodigy by age 11, he had exhausted the mathematical knowledge of two college students who were lodgers at his home. He was later lent a book written by S. L. Loney on advanced trigonometry.[18][19] He mastered this by the age of 13 while discovering sophisticated theorems on his own. By 14, he received merit certificates and academic awards that continued throughout his school career, and he assisted the school in the logistics of assigning its 1,200 students (each with differing needs) to its approximately 35 teachers.[14]: 27 He completed mathematical exams in half the allotted time, and showed a familiarity with geometry and infinite series. Ramanujan was shown how to solve cubic equations in 1902; he developed his own method to solve the quartic. In the following year, he tried to solve the quintic, not knowing that it could not be solved by radicals.
If there was a method of raising kids like this "scientifically" , I bet a good portion of the worlds GDP would be put into this field of research
Our genes encode the layout of physical race tracks on which marbles of matter and information travel. Some people's bodies have a bunch of muscle tracks, so as they grow, their body benefits from the activity on those. They grow up to find it easier to gain muscle than other people.
For geniuses, I imagine that the brain is a perfectly laid out super highway. Any information that comes in gets to where it needs to go because there's signs and signals and traffic cops patrolling. If some piece of information can't find where to go, well, damned if we don't have a construction worker and a navigator jumping in the passenger seat with you to help out.
Ultimately, I think the brain is so plastic that each of us can one day decide to elect a new mayor to our body town. The new mayor can decide to tear up roads and fix potholes etc. Yeah, it would have been great if we had founded the town with a plan and hadn't had that college riot but here we are. Time to pave some roads.
Because it kinda puncture this feel good marketing bull that "you can be anything you want". It could also shut endless flowing money into extra-coaching classes outside normal schools which promise to "help child to reach their fullest potential".
If you will be good at baseball if you have A and B, OK with neither, but terrible with only one, those genes will be identified in most studies as having nothing to do with baseball, maybe even identified as harmful.
I can offer a concrete example. Autism is more often found in high-IQ families, but itself is associated with decreased IQ. That suggests one case where either A and B alone are harmful, having neither makes you fine (and unlikely to bear children with A or B), and having both makes you smart.
I am not sure if we want people to figure out how to make connections involving specific genes, because a lot of us benefit from living in a world where we can game LeetCode by working longer and harder in a way that's unrelated to what Google is looking for.
This dynamic matches what we see in the case of Terrence Tao and his brothers, the Polgar sisters, and other cases of savants/virtuosos that come to mind. Usually one child has extraordinary ability while their siblings are much less remarkable. If the environmental model were accurate, we should see many cases where families produce more than one extreme talent of equal skill. But we don't see that in practice.
[1] https://en.wikipedia.org/wiki/Polygene#Trait_distribution
[2] https://en.wikipedia.org/wiki/Regression_toward_the_mean#His...
> Tao exhibited extraordinary mathematical abilities from an early age, attending university-level mathematics courses at the age of 9. He is one of only two children in the history of the Johns Hopkins' Study of Exceptional Talent program to have achieved a score of 700 or greater on the SAT math section while just eight years old; Tao scored a 760
I think genetics have more to do with this level of achievement than encouragement from an engaged father. Tao has 2 brothers - why aren't they mathematical supergeniuses too? Either he was born with a brain that has extraordinary analytical ability, or he was born with an insane work ethic not commonly associated with young kids. But even then, are there reports of him having to work super hard to understand things? If you can do advanced algebra at age 5, I'd say your brain is something extraordinary. Whether the underlying reason for that extraordinary brain is due to genes or some other trigger, it likely was not mainly due to an "encouraging father", IMO.
The previous sentence from the one you quoted states that
“Tao also has two brothers, who are living in Australia. Both formerly represented the country at the International Mathematical Olympiad”
His (younger) brother, Nigel achieved two bronze medals (placing 132nd and 114th overall) at the age of 15 and 16 [0]. Quite good, specially at a younger age than most participants.
Terence [1] got a gold medal (13th place) right before completing 13 years of age. He achieved a similar feat (28th place) around his 12th birthday and a more humble performance (87th place, but still better than his brother's best) around his 11th birthday. At 11, better than 58% of his competition, some of the best 17 and 18 year olds at competitive math in the world.
He is cited as "the youngest bronze, silver, and gold medalist, respectively, in IMO history." [2]
These are entirely different levels.
[0] https://www.imo-official.org/participant_r.aspx?id=783
[1] https://www.imo-official.org/participant_r.aspx?id=1581
[2] https://en.wikipedia.org/wiki/List_of_International_Mathemat...
He was probably lucky to be the younger brother growing up.
But of course that doesn’t matter. One could equally hypothesize being the oldest allows for most attention from the parents, etc.
But then again, Judit Polgar, by far the strongest chess player among the famous 3 Polgar sisters, was the youngest…
In my opinion, this sort of “human peak” genius performance requires more than small differences in upbringing.
Now, to torture the metaphor, how do I flip on the rest of my switches...
Ask again in 2122.
In the meantime, I guess, we all need to learn that our worth as a person is determined by who we are, not what we are.
Trevor Tao is autistic savant with a double degree in maths and music. He is FIDE International Master in Chess.
Nigel Tao has IQ 180. I think he works with Go language development.
http://math.fau.edu/yiu/Oldwebsites/MPS2010/TerenceTao1984.p...
My favorite part is when he was asked, at age 8 minus epsilon, whether addition distributes over multiplication (after having established that multiplication distributing over addition is an example of a distributive law), and he said, "only for Boolean algebras."
(Disclosure: I was also a child prodigy, so much of this story resonated with me. I'm now a research software engineer at Google, working on lots of mathematically intensive topics in 2D graphics, but obviously nowhere nearly as accomplished as Prof Tao)
At least for me, this also comes with costs. Some of these costs are immediately observable to me (much lower levels of broad-insight / Gordian-Knot-slicing, and I am less patient with others). Other costs are only presumed…I have guesses about associated long-term health risks both direct and indirect.
Anyway, all this to say, I think it can be done artificially. Since these things take time to play out towards mastery, you better hope you can get it right. Just like in software, some things can be a Pareto improvement, but some things can be prematurely optimized, and some things really never needed to be built in the first place.
I agree about inputs. I have a list project I'm working on called "This I Believe". I'm trying to decode my deeply held beliefs so that I understand mself and can change those beliefs. The very first thing I put on it was "Better living through chemistry."
2) Is learning any topic easier for you than for an average person or are you so talented in just a few areas?
300 print "mr. fibonacci is leaving now,"
310 print "and wishes to see you again sometime in the future"
312 print
313 print
315 print "here goes his car!!!!!!!!"
320 print "(brmmmm-brmmmm-putt-putt-vraow-chatter-chatter bye mr. fibonacci!)"I can't seriously believe the alternative.