https://terrytao.wordpress.com/2022/01/27/masterclass-on-mathematical-thinking/ [cropped-co] What's new Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao * Home * About * Career advice * On writing * Books * Applets * Subscribe to feed Masterclass on mathematical thinking 27 January, 2022 in advertising | Tags: Masterclass About a year ago, I was contacted by Masterclass (a subscription-based online education company) on the possibility of producing a series of classes with the premise of explaining mathematical ways of thinking (such as reducing a complex problem to simpler sub-problems, abstracting out inessential aspects of a problem, or applying transforms or analogies to find new ways of thinking about a problem). After a lot of discussion and planning, as well as a film shoot over the summer, the series is now completed. As per their business model, the full lecture series is only available to subscribers of their platform, but the above link does contain a trailer and some sample content. Share this: * Print * Email * More * * Twitter * Facebook * * Reddit * Pinterest * * Like this: Like Loading... Recent Comments [] Anonymous on Masterclass on mathematical... Masterclass on mathe... on Masterclass on mathematical... [94a] David Fry on Masterclass on mathematical... [0d4] mathedaone on Masterclass on mathematical... [] Anonymous on Masterclass on mathematical... [8c8] alfagaffel on Masterclass on mathematical... [5e4] achraf on Masterclass on mathematical... [5e4] achraf on Additive combinatorics [0d4] mathedaone on Masterclass on mathematical... [3c7] Terence Tao on Masterclass on mathematical... [3c7] Terence Tao on Masterclass on mathematical... [255] Rex on Masterclass on mathematical... [] Anonymous on Masterclass on mathematical... [] Anonymous on Masterclass on mathematical... [3c7] Terence Tao on Masterclass on mathematical... [ ] [Search] Articles by others * Andreas Blass - The mathematical theory T of actual mathematical reasoning * Gene Weingarten - Pearls before breakfast * Isaac Asimov - The relativity of wrong * Jonah Lehrer - Don't! - the secret of self-control * Julianne Dalcanton - The cult of genius * Nassim Taleb - The fourth quadrant: a map of the limits of statistics * Paul Graham - What You'll Wish You'd Known * Po Bronson - How not to talk to your kids * Scott Aaronson - Ten signs a claimed mathematical proof is wrong * Tanya Klowden - articles on astronomy * Timothy Gowers - Elsevier -- my part in its downfall * Timothy Gowers - The two cultures of mathematics * William Thurston - On proof and progress in mathematics Diversions * Abstruse Goose * BoxCar2D * Factcheck.org * FiveThirtyEight * Gapminder * Literally Unbelievable * Planarity * PolitiFact * Quite Interesting * snopes * Strange maps * Television tropes and idioms * The Economist * The Onion * The Straight Dope * This American Life on the financial crisis I * This American Life on the financial crisis II * What if? (xkcd) * xkcd Mathematics * 0xDE * A Mind for Madness * A Portion of the Book * Absolutely useless * Alex Sisto * Algorithm Soup * Almost Originality * AMS blogs * AMS Graduate Student Blog * Analysis & PDE * Analysis & PDE Conferences * Annoying Precision * Area 777 * Ars Mathematica * ATLAS of Finite Group Representations * Automorphic forum * Avzel's journal * Blog on Math Blogs * blogderbeweise * Bubbles Bad; Ripples Good * Cedric Villani * Climbing Mount Bourbaki * Coloquio Oleis * Combinatorics and more * Compressed sensing resources * Computational Complexity * Concrete nonsense * David Mumford's blog * Delta epsilons * DispersiveWiki * Disquisitiones Mathematicae * Embuches tissues * Emmanuel Kowalski's blog * Equatorial Mathematics * fff * Floer Homology * Frank Morgan's blog * Gerard Besson's Blog * Godel's Lost Letter and P=NP * Geometric Group Theory * Geometry and the imagination * Geometry Bulletin Board * George Shakan * Girl's Angle * God Plays Dice * Good Math, Bad Math * Graduated Understanding * Hydrobates * I Can't Believe It's Not Random! * I Woke Up In A Strange Place * Igor Pak's blog * Images des mathematiques * In theory * James Colliander's Blog * Jerome Buzzi's Mathematical Ramblings * Joel David Hamkins * Journal of the American Mathematical Society * Kill Math * Le Petit Chercheur Illustre * Lemma Meringue * Lewko's blog * Libres pensees d'un mathematicien ordinaire * LMS blogs page * Low Dimensional Topology * M-Phi * Mark Sapir's blog * Math Overflow * Math3ma * Math3ma * Mathbabe * Mathblogging * Mathematical musings * Mathematics Illuminated * Mathematics in Australia * Mathematics Jobs Wiki * Mathematics Stack Exchange * Mathematics under the Microscope * Mathematics without apologies * Mathlog * Mathtube * Matt Baker's Math Blog * Mixedmath * Motivic stuff * Much ado about nothing * Multiple Choice Quiz Wiki * MyCQstate * nLab * Noncommutative geometry blog * Nonlocal equations wiki * Nuit-blanche * Number theory web * Online Analysis Research Seminar * outofprintmath * Pattern of Ideas * Pengfei Zhang's blog * Persiflage * Peter Cameron's Blog * Phillipe LeFloch's blog * ProofWiki * Quomodocumque * Ramis Movassagh's blog * Random Math * Reasonable Deviations * Regularize * Research Seminars * Rigorous Trivialities * Roots of unity * Science Notes by Greg Egan * Secret Blogging Seminar * Selected Papers Network * Sergei Denisov's blog * Short, Fat Matrices * Shtetl-Optimized * Shuanglin's Blog * Since it is not... * Sketches of topology * Snapshots in Mathematics ! * Soft questions * Some compact thoughts * Stacks Project Blog * SymOmega * Tanya Khovanova's Math Blog * tcs math * TeX, LaTeX, and friends * The accidental mathematician * The Cost of Knowledge * The Everything Seminar * The Geomblog * The L-function and modular forms database * The n-Category Cafe * The n-geometry cafe * The On-Line Blog of Integer Sequences * The polylogblog * The polymath blog * The polymath wiki * The Tricki * The twofold gaze * The Unapologetic Mathematician * The value of the variable * The World Digital Mathematical Library * Theoretical Computer Science - StackExchange * Thuses * Tim Gowers' blog * Tim Gowers' mathematical discussions * Todd and Vishal's blog * Van Vu's blog * Vaughn Climenhaga * Vieux Girondin * Visual Insight * Vivatsgasse 7 * Williams College Math/Stat Blog * Windows on Theory * Wiskundemeisjes * XOR's hammer * Yufei Zhao's blog * Zhenghe's Blog Selected articles * A cheap version of nonstandard analysis * A review of probability theory * American Academy of Arts and Sciences speech * Amplification, arbitrage, and the tensor power trick * An airport-inspired puzzle * Benford's law, Zipf's law, and the Pareto distribution * Compressed sensing and single-pixel cameras * Einstein's derivation of E=mc^2 * On multiple choice questions in mathematics * Problem solving strategies * Quantum mechanics and Tomb Raider * Real analysis problem solving strategies * Sailing into the wind, or faster than the wind * Simons lectures on structure and randomness * Small samples, and the margin of error * Soft analysis, hard analysis, and the finite convergence principle * The blue-eyed islanders puzzle * The cosmic distance ladder * The federal budget, rescaled * Ultrafilters, non-standard analysis, and epsilon management * What is a gauge? * What is good mathematics? * Why global regularity for Navier-Stokes is hard Software * Detexify * GmailTeX * Inverse Symbolic Calculator * jfig * LaTeX to Wordpress * Online LaTeX Equation Editor * Sage: Open Source Mathematical Software * Subverting the system The sciences * Academic blogs * American Academy of Arts and Sciences * Australian Academy of Science * Bad Astronomy * National Academy of Science * RealClimate * Schneier on security * Science-Based Medicine * Seven warning signs of bogus science * The Royal Society * This week in evolution * Tree of Life Web Project Top Posts * Masterclass on mathematical thinking * Career advice * Books * On writing * About * Does one have to be a genius to do maths? * There's more to mathematics than rigour and proofs * Why global regularity for Navier-Stokes is hard * Analysis I * 245A: Problem solving strategies Archives * January 2022 (1) * December 2021 (2) * November 2021 (2) * October 2021 (1) * September 2021 (2) * August 2021 (1) * July 2021 (3) * June 2021 (1) * May 2021 (2) * February 2021 (6) * January 2021 (2) * December 2020 (4) * November 2020 (2) * October 2020 (4) * September 2020 (5) * August 2020 (2) * July 2020 (2) * June 2020 (1) * May 2020 (2) * April 2020 (3) * March 2020 (9) * February 2020 (1) * January 2020 (3) * December 2019 (4) * November 2019 (2) * September 2019 (2) * August 2019 (3) * July 2019 (2) * June 2019 (4) * May 2019 (6) * April 2019 (4) * March 2019 (2) * February 2019 (5) * January 2019 (1) * December 2018 (6) * November 2018 (2) * October 2018 (2) * September 2018 (5) * August 2018 (3) * July 2018 (3) * June 2018 (1) * May 2018 (4) * April 2018 (4) * March 2018 (5) * February 2018 (4) * January 2018 (5) * December 2017 (5) * November 2017 (3) * October 2017 (4) * September 2017 (4) * August 2017 (5) * July 2017 (5) * June 2017 (1) * May 2017 (3) * April 2017 (2) * March 2017 (3) * February 2017 (1) * January 2017 (2) * December 2016 (2) * November 2016 (2) * October 2016 (5) * September 2016 (4) * August 2016 (4) * July 2016 (1) * June 2016 (3) * May 2016 (5) * April 2016 (2) * March 2016 (6) * February 2016 (2) * January 2016 (1) * December 2015 (4) * November 2015 (6) * October 2015 (5) * September 2015 (5) * August 2015 (4) * July 2015 (7) * June 2015 (1) * May 2015 (5) * April 2015 (4) * March 2015 (3) * February 2015 (4) * January 2015 (4) * December 2014 (6) * November 2014 (5) * October 2014 (4) * September 2014 (3) * August 2014 (4) * July 2014 (5) * June 2014 (5) * May 2014 (5) * April 2014 (2) * March 2014 (4) * February 2014 (5) * January 2014 (4) * December 2013 (4) * November 2013 (5) * October 2013 (4) * September 2013 (5) * August 2013 (1) * July 2013 (7) * June 2013 (12) * May 2013 (4) * April 2013 (2) * March 2013 (2) * February 2013 (6) * January 2013 (1) * December 2012 (4) * November 2012 (7) * October 2012 (6) * September 2012 (4) * August 2012 (3) * July 2012 (4) * June 2012 (3) * May 2012 (3) * April 2012 (4) * March 2012 (5) * February 2012 (5) * January 2012 (4) * December 2011 (8) * November 2011 (8) * October 2011 (7) * September 2011 (6) * August 2011 (8) * July 2011 (9) * June 2011 (8) * May 2011 (11) * April 2011 (3) * March 2011 (10) * February 2011 (3) * January 2011 (5) * December 2010 (5) * November 2010 (6) * October 2010 (9) * September 2010 (9) * August 2010 (3) * July 2010 (4) * June 2010 (8) * May 2010 (8) * April 2010 (8) * March 2010 (8) * February 2010 (10) * January 2010 (12) * December 2009 (11) * November 2009 (8) * October 2009 (15) * September 2009 (6) * August 2009 (13) * July 2009 (10) * June 2009 (11) * May 2009 (9) * April 2009 (11) * March 2009 (14) * February 2009 (13) * January 2009 (18) * December 2008 (8) * November 2008 (9) * October 2008 (10) * September 2008 (5) * August 2008 (6) * July 2008 (7) * June 2008 (8) * May 2008 (11) * April 2008 (12) * March 2008 (12) * February 2008 (13) * January 2008 (17) * December 2007 (10) * November 2007 (9) * October 2007 (9) * September 2007 (7) * August 2007 (9) * July 2007 (9) * June 2007 (6) * May 2007 (10) * April 2007 (11) * March 2007 (9) * February 2007 (4) Categories * expository (292) + tricks (11) * guest blog (10) * Mathematics (826) + math.AC (8) + math.AG (42) + math.AP (112) + math.AT (17) + math.CA (179) + math.CO (182) + math.CT (8) + math.CV (37) + math.DG (37) + math.DS (85) + math.FA (24) + math.GM (12) + math.GN (21) + math.GR (88) + math.GT (16) + math.HO (12) + math.IT (13) + math.LO (51) + math.MG (43) + math.MP (28) + math.NA (23) + math.NT (182) + math.OA (22) + math.PR (102) + math.QA (6) + math.RA (41) + math.RT (21) + math.SG (4) + math.SP (48) + math.ST (9) * non-technical (166) + admin (45) + advertising (43) + diversions (5) + media (13) o journals (3) + obituary (15) * opinion (31) * paper (223) + book (19) + Companion (13) + update (21) * question (125) + polymath (85) * talk (67) + DLS (20) * teaching (188) + 245A - Real analysis (11) + 245B - Real analysis (21) + 245C - Real analysis (6) + 246A - complex analysis (11) + 246B - complex analysis (5) + 246C - complex analysis (5) + 247B - Classical Fourier Analysis (5) + 254A - analytic prime number theory (19) + 254A - ergodic theory (18) + 254A - Hilbert's fifth problem (12) + 254A - Incompressible fluid equations (5) + 254A - random matrices (14) + 254B - expansion in groups (8) + 254B - Higher order Fourier analysis (9) + 255B - incompressible Euler equations (2) + 275A - probability theory (6) + 285G - poincare conjecture (20) + Logic reading seminar (8) * travel (26) additive combinatorics almost orthogonality approximate groups arithmetic progressions Ben Green Cauchy-Schwarz Cayley graphs central limit theorem Chowla conjecture compactness compressed sensing correspondence principle distributions eigenvalues Elias Stein Emmanuel Breuillard entropy equidistribution ergodic theory Euler equations exponential sums finite fields Fourier transform Freiman's theorem Gowers uniformity norm Gowers uniformity norms graph theory Gromov's theorem GUE hard analysis Hilbert's fifth problem hypergraphs incompressible Euler equations inverse conjecture Joni Teravainen Kaisa Matomaki Kakeya conjecture Lie algebras Lie groups linear algebra Liouville function Littlewood-Offord problem Maksym Radziwill Mobius function Navier-Stokes equations nilpotent groups nilsequences nonstandard analysis parity problem politics polymath1 polymath8 Polymath15 polynomial method polynomials prime gaps prime numbers prime number theorem random matrices randomness Ratner's theorem regularity lemma Ricci flow Riemann zeta function Roth's theorem Schrodinger equation sieve theory structure Szemeredi's theorem Tamar Ziegler ultrafilters universality Van Vu wave maps Yitang Zhang RSS The Polymath Blog * Polymath projects 2021 20 February, 2021 * A sort of Polymath on a famous MathOverflow problem 9 June, 2019 * Ten Years of Polymath 3 February, 2019 * Updates and Pictures 19 October, 2018 * Polymath proposal: finding simpler unit distance graphs of chromatic number 5 10 April, 2018 * A new polymath proposal (related to the Riemann Hypothesis) over Tao's blog 26 January, 2018 * Spontaneous Polymath 14 - A success! 26 January, 2018 * Polymath 13 - a success! 22 August, 2017 * Non-transitive Dice over Gowers's Blog 15 May, 2017 * Rota's Basis Conjecture: Polymath 12, post 3 5 May, 2017 16 comments Comments feed for this article 27 January, 2022 at 9:25 am Rex [255] Is there any particular reason why you decided to do these lectures through a for-profit company instead of just making the material publicly available (for example through this blog)? Reply 27 January, 2022 at 10:12 am Aditya Guha Roy [d54] This weblog already has many pages where different suggestions for thinking mathematically have been suggested by professor Tao. In fact if you read through his blogposts carefully, you will often find examples of how he changed the odor of a problem by viewing it differently. Reply 27 January, 2022 at 10:31 am Terence Tao [3c7] 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.) Reply 27 January, 2022 at 10:34 am Anonymous [] How many classes? Are the lectures on going, or have they all been finished? Are they target at the general public or professional mathematicians? Reply 27 January, 2022 at 11:39 am Terence Tao [3c7] In the end we produced a series of 12 short lectures, the titles of which should be visible from the web page linked to in the post. The target audience is the general public, without presupposing any exposure to advanced mathematics (or even high school mathematics, really). Reply 27 January, 2022 at 10:59 am Anonymous [] It seems that Masterclass is an online form of "The Great Course" series, which are in DVD format, and you can borrow from local library for free. Maybe one can get free subscription from libraries. Reply 27 January, 2022 at 11:13 am Rex [255] That seems curious to me. Are the scriptwriters knowledgeable about math? If not, how would it be possible for them to know what material is essential, or the optimal way to arrange it (unless they are doing it from the perspective of a student audience)? Reply 27 January, 2022 at 11:37 am Terence Tao [3c7] The scriptwriting process was a collaborative one; I submitted some material on proposed lecture topics, and after many (remote) meetings with the producer and writers we were able to pick out the most promising topics and develop them into a coherently arranged series. One or two of the people involved did have some mathematical training, but actually I think the fact that many of the writers did not have this background was in fact helpful for this particular type of outreach project, as they could tell when a proposed topic was too technical or assumed too much prior exposure to mathematics. As a side note, I did have some very enjoyable discussions with the staff at Masterclass about the analogies between the creative process in mathematics and the creative process in filmmaking. Unexpectedly, a lot of the experiences I had working on a mathematical problem resonated with the filmmakers, and vice versa, despite working in ostensibly very different fields. Reply 27 January, 2022 at 12:28 pm alfagaffel [8c8] Using this blog Professor Tao will certainly reach out to people. However, the people using the Masterclass in not the same. Reply 27 January, 2022 at 12:02 pm mathedaone [0d4] Wow, this master class looks a lot interesting. I am a mathlete competing in the Math Olympiad. I can solve some problems in IMO. I finished top 20 nationally 2020, but didn't make it to the national team. I failed again in 2021, although I think I'm really close to it. I'm currently a freshman in high school and have two years left to make the national team. I'm wondering if this will help me solve the problem better, will it help my journey IMO? By the way, how about your book "Solving Mathematical Problems", what do you think of the book now after you've been doing math for so long? Do you think this will help me prepare IMO? Do you have any other suggestions, book lists, what to do to prepare IMO? I really admire you, you are a role model in my eyes. I am really looking forward to working in mathematics. At the same time competing, I'm also working on university math, but I'd love to win the gold medal, which I think is a stepping stone to becoming a mathematician. Thanks for answering! -Mingdao Zou, from Sweden Reply 27 January, 2022 at 12:24 pm achraf [5e4] Can you provide us a free access to the series ? Because masterclass is a paid platform. Reply 27 January, 2022 at 12:39 pm Anonymous [] Is there a general method to reduce a problem into "natural" sub-problems? Reply 27 January, 2022 at 12:49 pm mathedaone [0d4] Note: I have read your post "Advice on mathematics competitions". And I'm still confused due to my knowledge limitations. I have a study plan for IMO and I am working hard. But there's still uncertainty here, like I can't fathom the minds of people who get perfect socres IMO, it seems to be the best for them. I'm wondering what's to separate best from the rest? Especially after trying again and failing in 2021. Einstein said not only to work hard, but also to be efficient, I don't have as much advantage as you in IQ. And I really want to aim high and aim for a gold medalist and even perfect score. I'd really appreciate it if you have an answer to clear my mind! Reply 27 January, 2022 at 1:01 pm David Fry [94a] Said it before, & I'll say it again: Terry is destined to be on a much larger stage in order to fulfill his purpose. So what if he makes a few bucks for his valuable time to ultimately reach the world stage? Reply 27 January, 2022 at 2:31 pm Masterclass on mathematical thinking by Terrence Tao - The web development company Lzo Media - Senior Backend Developer [...] Article URL: https://terrytao.wordpress.com/2022/01/27/ masterclass-on-mathematical-thinking/ [...] Reply 27 January, 2022 at 2:46 pm Anonymous [] Sounds great! I love Masterclass and the great quality of their videos. Looking forward to watching them! Reply Leave a Reply Cancel reply Enter your comment here... [ ] Fill in your details below or click an icon to log in: * * * * * Gravatar Email (Address never made public) [ ] Name [ ] Website [ ] WordPress.com Logo You are commenting using your WordPress.com account. ( Log Out / Change ) Google photo You are commenting using your Google account. ( Log Out / Change ) Twitter picture You are commenting using your Twitter account. ( Log Out / Change ) Facebook photo You are commenting using your Facebook account. ( Log Out / Change ) Cancel Connecting to %s [ ] Notify me of new comments via email. [ ] Notify me of new posts via email. [Post Comment] [ ] [ ] [ ] [ ] [ ] [ ] [ ] D[ ] For commenters To enter in LaTeX in comments, use $latex $ (without the < and > signs, of course; in fact, these signs should be avoided as they can cause formatting errors). See the about page for details and for other commenting policy. << The inverse theorem for the U^3 Gowers uniformity norm on arbitrary finite abelian groups: Fourier-analytic and ergodic approaches Blog at WordPress.com.Ben Eastaugh and Chris Sternal-Johnson. Subscribe to feed. * Follow Following + [9ecc62] What's new Join 10,415 other followers [ ] Sign me up + Already have a WordPress.com account? Log in now. * + [9ecc62] What's new + Customize + Follow Following + Sign up + Log in + Copy shortlink + Report this content + View post in Reader + Manage subscriptions + Collapse this bar Send to Email Address [ ] Your Name [ ] Your Email Address [ ] [ ] loading [Send Email] Cancel Post was not sent - check your email addresses! Email check failed, please try again Sorry, your blog cannot share posts by email. %d bloggers like this: [b]