William Thurston "On proof and progress in mathematics"

In this interview, Jeremiah Heller and Vesna Stojanoska share their experience of combining math and family life, discuss their ways to get over occasional demotivation in research and speak about social aspects of research. Jokes included! Jeremiah's homepage: https://faculty.math.illinois.edu/~jbheller/ Vesna's homepage: https://faculty.math.illinois.edu/~vesna/ Mike Hopkins’ talk at Paul Goerss’ birthday conference: youtu.be/Ix4pg87LKVk Chapters: 0:00 teaser 0:34 their family and other animals 4:04 kids’ curiosity about math 8:30 wishes for kids’ future 11:04 existential chat about adulthood  13:51 research & relationship 16:13 finding friends outside math bubble 19:26 two-body problem 21:59 math talks as storytelling 27:01 approaches to doing math 31:02 getting over demotivation in research 35:23 mathematics is a social endeavour 37:12 jobmarket pressure 43:24 having kids & academia 47:18 solid advice

Dhruv Ranganathan is a lecturer at Cambridge University, working in algebraic geometry. In this video, Dhruv talks about doing research with undergrads, being tortured by math problems, looking for friends to write math papers, and other cool stuff! Dhruv's webpage: https://www.dhruvrnathan.net Photo: from the webpage 0:00 teaser 0:41 from cricket to air planes 2:16 adventure novels childhood 4:46 what do algebraic geometers do 8:39 experience of undergrad research 12:30 how undergrad research really works 15:35 “now I’m a believer”(c) 18:25 why so much pressure in doing math 21:09 how we create pressure for young people 23:44 doing math as a coping mechanism 27:00 math torture vs intense cartoon watching 28:50 speakers love getting any math questions 30:54 math for extroverts  34:25 teaching students who leave academia 37:33 don’t beat yourself up for math mistakes 39:39 how we try and fail to improve inclusivity 43:44 don’t put people from minorities on every committee 45:45 the advice that’s too hard to follow 48:35 fireplace

Kevin Buzzard is a professor in Imperial College London working in number theory and formal proof verification. In this interview, Kevin shares his views on the role of computers in doing math, tells about his experience of upbringing 3 kids as a researcher and raises questions about the way we approach math education. Lots of glorious laughter and unforgettable facial expressions are included! Kevin's homepage: https://www.imperial.ac.uk/people/k.buzzard Channel podcast: https://anchor.fm/math-life-balance​​​​ Chapters: 0:00 teaser 0:48 Kevin’s t-shirt 3:06 imagination in math 5:36 computers vs humans 10:43 computers and infinity 12:35 math as a zen puzzle 15:19 role of fashion in math 20:06 mathematicians detecting mistakes 24:41 imperfections in our math 29:14 when the dust settles 31:56 not caring what people think 36:01 how to entertain kids in the subway 40:26 babies as the way to understand humanity 42:52 doing math when you have 3 kids 46:09 writing papers with non-mathematicians 48:54 why kids are forced to memorize math? 53:29 doing exams vs learning math 57:16 unusual advice for students 59:15 the answer to the ultimate question

Maria Chudnovsky is a professor at Princeton University, working in graph theory and combinatorics. In this interview, Maria shares her personal experiences: learning Hebrew from math lessons, giving a talk at NASA, using math at her own wedding, and many more! Maria's homepage: http://web.math.princeton.edu/~mchudnov/ Photo: from Maria's homepage The essay we mentioned: W.T. Gowers "The two cultures of mathematics" https://www.dpmms.cam.ac.uk/~wtg10/2cultures.pdf 0:00 teaser 0:29 respect for math at home 2:43 math helps when you don’t speak the local language 6:42 building a world around a research problem 11:37 explaining math to a broad audience 16:00 giving a talk at NASA 19:42 applying graph theory to your wedding 23:16 problem solving vs learning 27:58 being bad at math olympiads  30:40 working with your own students 33:23 experience of doing a PhD 36:02 memorizing math  37:55 studying physics vs math 43:43 maintaining a work-life balance 49:08 everyone has self-doubts 50:54 first time teaching a class 55:46 final advice

Tomer Schlank is a professor at the Hebrew University of Jerusalem, working in homotopy theory and arithmetic geometry. In this interview, Tomer shares his experience of advising a big group of students, speaks about the importance of embracing the struggle, and explains how to get unstuck in a math problem. Tomer's homepage: https://mathematics.huji.ac.il/people/tomer-schlank Photo: from Tomer's homepage 0:00 teaser 0:31 astronaut’s dreams 4:06 enjoying the struggle 8:27 top-down thinking 11:35 seminar with physicists 14:52 math dream with Vesna Stojanoska 19:24 taking breaks in projects 22:32 advising 11 students 26:47 doing math & drinking arak 31:14 being stuck is good for you 34:49 how to get unstuck 38:08 don’t worry about talent 42:33 why people hate math 45:36 run towards the problem 48:25 don’t look down on other parts of math 51:43 final advice

Saul Glasman worked in homotopy theory and K-theory, and now works as a software engineer. In this interview, we discuss the hardships of academic jobmarket, fears around leaving math, and the fundamental problems in academia. Saul's homepage: http://www-users.math.umn.edu/~sglasman/ Photo: from his website #mathematician​​​​​​ #mathlife​​​​​​ #interview​​​​​​  #academiavsindustry #leavingacademia #jobmarketacademia 0:00 teaser 0:44 always loved math 2:04 why left academia 8:55  the fears of leaving 14:02 staying in touch with math 20:33 send greetings to Saul :) 21:55 stigma around leaving academia 25:13 problems in academia 30:11 we aren't taught to teach 35:50 there's freedom in industry 37:36 and you feel productive! 42:44 social interactions: academia vs industry 45:19 learning effective team work 49:15 you can learn to enjoy a job 52:20 why can't we do internships 55:47 what you wish you knew 59:02 advice for those who have doubts

Giulia Saccà is an assistant professor at Columbia  University, working in algebraic geometry. In this interview, Giulia gives jobmarket advice for mathematicians, contemplates some of the struggles that minorities in math get to deal with, and tells about books that resemble math research.  Giulia's homepage: http://math.columbia.edu/~giulia/ Photo: Allegra Boverman Women in Math program at IAS: https://www.ias.edu/math/wam 0:00 teaser 0:27 interests in history in philosophy 6:51 jobmarket advice 11:37 talking about our insecurities helps 16:23 struggles of minorities in math 20:05 what to do with impostor syndrome 27:01 how to find role models 30:48 Women in Math program at IAS is great 35:57 the future of online seminars 41:06 how to keep track of math projects 47:27 which music helps to do math 49:31 alpinism resembles doing research 52:21 Proust writes about math 58:44 the joy of cooking 1:00:40 a wish for young mathematicians

In this [episode], I read a piece from Thurston's essay "On proof and progress in mathematics", where he reflects on the importance of seeing mathematicians' progress and contributions much broader than just in proving new theorems. William Thurston on Wikipedia: https://en.wikipedia.org/wiki/William_Thurston Cover photo: from this Wikipedia page The full essay: https://arxiv.org/pdf/math/9404236.pdf Thurston's lecture "Knots to Narnia": https://youtu.be/IKSrBt2kFD4 Thurston's answer on MathOverflow about contributions in mathematics: https://mathoverflow.net/questions/43690/whats-a-mathematician-to-do/44213#44213

This sarcastic [episode] is dedicated to my family and all my friends of the last 10 years. They will see why. A special thanks to Nicole R. for the help with the video(s)! And to my brother for the T-shirt: there’s a tiny cute bug that says "I have giant problems". 0:00 Prologue 0:53 Inclusivity statement 1:24 How to build an abusive relationship with your research 3:00 How to suffer from doing research 5:10 How to be unproductive   7:01 How to compare yourself with others 8:38 How to feel worse from reassurance 9:33 Epilogue

Irakli Patchkoria is a lecturer at the University of Aberdeen, working in homotopy theory. In this interview, he speaks about math-tennis balance, shares his experience of moving from Georgia to Western Europe and admits taking part in illegal actions on university exams. Irakli's homepage: https://www.abdn.ac.uk/people/irakli.patchkoria Photo: Irakli's private photo collection 0:00 teaser 1:13 epic story of family math 6:21 father’s advice 10:25 don’t work too much 14:41 experience in collaborations 19:02 Georgians and assimilation 21:47 making new friends (hey, Zurich!) 25:47 cheating on exams 28:38 you will have ideas for papers 33:48 don’t be afraid of stars in math 38:16 partying hard 41:25 drinking with mathematicians 43:41 math and the meaning of life 46:22 please make jokes in talks 48:53 helping young mathematicians