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Masterclass on mathematical thinking

305 points| harmonicseq | 4 years ago |terrytao.wordpress.com | reply

130 comments

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[+] imranq|4 years ago|reply
This is nice initiative and any attempt to make mathematics more accessible is a value added to society in my book. However, saying you will learn "mathematical thinking" by watching 1.5 hours of passively watching, even Professor Tao, is quite an overpromise. I don't think there's a subject that requires more hands on practice and thinking than math, especially higher level math, so this is more along the lines of edutainment. So in my mind, how valuable this course is depends on what this content replaces for you. If watching this series replaces something distracting then its great, but if it replaces actually doing problems and working out proofs, then it's not worth it.

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

[+] ramblerman|4 years ago|reply
I fully agree on the celebrity worship, but am a bit confused with how you then align

> 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

[+] supernova87a|4 years ago|reply
The 3B1B videos on 1) the Fourier transform, and 2) the determinant were eye-opening for me to understand what all the math actually meant physically, 20 years after learning about that stuff in a book. Sometimes it really does take explaining it from a different angle.
[+] lanstin|4 years ago|reply
on the other hand, i took a general relativity class solely because Prof Penrose was teaching it, did none of the homeworks, and still walked away having learned a lot from the many comments Penrose made that conveyed a big picture understanding; an experience of illumination that so many maths classes fail to provide. and unlike the famous business people you cite, Prof Tao has done a lot of actual maths.
[+] aiilns|4 years ago|reply
I've taken a course by Dr. Keith Devlin (professor at Standford) through coursera: _Introduction to Mathematical Thinking_, which I found quite interesting. However, I studied medicine, so perhaps it may be too basic for someone who has studied mathematics in university.
[+] supernova87a|4 years ago|reply
Watching the trailer, makes me think that people who may enjoy this series will also enjoy a book called "Aha" by Martin Gardner (from probably 40 years ago)[0].

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.

[+] wging|4 years ago|reply
Do you mean Aha! Insight? I don't see a book just labeled "Aha".

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.

[+] agumonkey|4 years ago|reply
Them russian librarians have well furnished shelves.
[+] Graffur|4 years ago|reply
My first reaction to this blog post was kind of negative because Master Class is not free. I watched the teaser video and it's actually pretty inspiring. As someone who has done undergraduate Computer Science level Math, but completely forgotten most things about Math except for simple Algebra, I am going to try this.

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.

[+] dfdz|4 years ago|reply
In case anyone missed the response to a similar comment on the blog:

> 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.)

[+] forgotmyoldacc|4 years ago|reply
Seems like motivation porn more than education. Not that there's anything wrong with that, just knowing which one is which is useful.
[+] zwieback|4 years ago|reply
We've had Masterclass for a bit over a year now. It's not deep, for sure, not going to replace any kind of study or exercise.

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.

[+] codezero|4 years ago|reply
Same for me, I also appreciated that he responded to the question on his blog of why it is paid - production value / editing / professional equipment etc... it makes sense.
[+] cloudedcordial|4 years ago|reply
I had a similar negative knee jerk reaction upon learning that Yo-Yo Ma gives one of the courses from MasterClass. The whole MasterClass business seems like entertainment as you've noted. Music could be entertainment but there's some deep subjects just like mathematics. One cannot just sit back and gain deep understanding.
[+] chubot|4 years ago|reply
On that note, I wonder if anyone has suggestions for paid video content that is good? That is, "non fiction" or educational stuff like this series is supposed to be. I feel like I spend too much time watching YouTube (mostly free) and Netflix (very cheap, quality varies).

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.

[+] kinghtown|4 years ago|reply
Which actually adds value to Masterclass because really what kind of an education could one get from Netflix?

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.

[+] ahahahahah|4 years ago|reply
There's some good comments on the blog post about why he thinks doing it through MasterClass brought a lot of value that wouldn't be there otherwise.
[+] paulpauper|4 years ago|reply
You are not going to go from high school math to graduate level competency with this course, obviously.
[+] mindcrime|4 years ago|reply
I've never seriously considered subscribing to Masterclass, but this has gotten the gears turning in my head a little. So I'm curious: does anyone here subscribe, and could you comment on whether or not you feel like it's worthwhile, given the available content?
[+] DavidPiper|4 years ago|reply
I subscribe, but will probably be ending my sub at the end of this year.

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)

[+] Darkstryder|4 years ago|reply
Cinematography is a hobby of mine and I got gifted the "Ron Howard teaches Directing" Masterclass a few years back. I did not check the other Masterclasses, although I've considered watching a few others.

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.

[+] EMM_386|4 years ago|reply
I am a subscriber.

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.

[+] olegious|4 years ago|reply
I love their cooking content.
[+] ConnorCallahan|4 years ago|reply
I just watched the first 8 out of 12 episodes and I was disappointed. There were certainly a couple good nuggets but I'm afraid that Masterclass puts too much emphasis on making things simple such that he spends most of the time talking about really simple ideas.
[+] maroonblazer|4 years ago|reply
Have you seen the EdX course Effective Thinking Through Mathematics (free) [0]? I really enjoyed it and found the principles really do transfer beyond the domain of math, as the title suggests.

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...

[+] calf|4 years ago|reply
Is there anything there that you wouldn't learn in the process of college-level STEM classes?
[+] Victerius|4 years ago|reply
Is Masterclass any different from TED?
[+] pumanoir|4 years ago|reply
Looks good. It reminds me of The Great Courses and its streaming service Wondrium [1]. They have (from the top of my head [1]) at least two courses that would be the equivalent to this one. The courses are taught by experts in a field who also happen to be great teachers (usually teaching award winning professors).

1. https://www.wondrium.com/art-and-craft-of-mathematical-probl...

2. https://www.wondrium.com/home

[+] Emphere|4 years ago|reply
I would like to second this recommendation. For a long time I thought their content was low quality edutainment because of the generally 90s website design and the generic stock photos used for courses(admittedly, that's...a pretty shallow line of reasoning). The courses are usually taught by university professors, have a well thought out lesson plan and have helpful accompanying guidebooks (you can also request course transcripts, I believe). For example, the course linked above is taught by Paul Zeitz based on his book, "The Art and Craft of Problem Solving", which is a classic for learning Olympiad-level problem solving techniques. I've also learned a lot from their history courses.
[+] laserlight|4 years ago|reply
> I was contacted by Masterclass (a subscription-based online education company)

Masterclass is an entertainment company, nothing to do with education.

[+] yayr|4 years ago|reply
partially agree, but I also think that it is in many cases worthwhile entertainment compared to many other entertainment options available.

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.

[+] vorhemus|4 years ago|reply
Why does this get so many upvotes? There is no value in the linked post other than saying: Buy my masterclass!
[+] melissalobos|4 years ago|reply
Try not to take this as me being mean, but I can't help but feel that for profit math education grands very hard against the basic concepts of math and math education("No royal road to math" and all that). I understand that someone of Tao's stature in the popular math community is likely very enticing to masterclass. However Tao himself benefited tremendously from being noticed at a young age and having his skills nurtured. It feels a bit wrong for any one in his position to be aiding a for profit institution, especially when the content is not free. I understand that they approached him, and I and everyone haven't to produce a free good quality version of this. But it does still FEEL wrong. I of course say this as a very privileged elite educated person.

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,

[+] beebmam|4 years ago|reply
The more that education becomes monetarily inaccessible to the masses, the more the masses will reject the educated. And then god help us.
[+] lee|4 years ago|reply
This comment bothered me for a few reasons:

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.

[+] paulpauper|4 years ago|reply
probably helps also to have a 1 in 100 million IQ too, but sounds like fun anyway. I am not sure how some of thee masterclasses are useful. Like the one by the astronaut . I don't plan on going into space anytime soon. Maybe Elon Musk would enjoy that one. No amount of videos will make even a typical PhD in math even as close to as good as him. It's 90% genes , 10% other factors.
[+] uoaei|4 years ago|reply
Is it really common opinion that TT is smart because of his genes? I would think having a helpful and engaged math-fluent father and lots of encouragement from an early age has way more to do with it. You can't seriously believe that an introduction into mathematical thinking from an early age and close advision from math-fluent parents is only 10% of the reason that TT is where he is today.
[+] klyrs|4 years ago|reply
> It's 90% genes , 10% other factors.

Do you have evidence to support these numbers, or the more general claim of genetic supremacy?

[+] amznbyebyebye|4 years ago|reply
These are like world class atheletes, gifted and they put in the hard work to get to where they are today. That is what it takes to be one of these once in a decade type of mathematician.
[+] michaelhah|4 years ago|reply
Probably getting to his level is highly genetically dependent but that’s not what watching a Masterclass vid is about. Probably really interesting but I would likely forget to cancel and i am planning on living forever so I’d end up paying an infinite amount of money for this.