In our math research we make countless choices. We chose a problem to work on, decide whether its claim is true or false, what tools to use, what earlier papers to study which might prove useful, w…

When you spend all day sitting in your office thinking about difficult abstract problems, it’s wonderful to take a break and do something intensely physical, like aerial acrobatics.

https://mathoverflow.net/questions/143309/how-do-you-not-forget-old-math/143335#143335 …if I were trying to remember everything in a particular book, I might start by memorizing the table of contents, and then I’d work on remembering the theorem statements, and then finally the proofs.

Summarized in this last piece, Rosenthal determines the cause of death: Lack of anti-trust enforcement, pervasive short-termism, driven by Wall Street’s focus on quarterly results, and management’s focus on manipulating the stock price to maximize the value of their options Without this understanding of how it all interacts, attempts to recreate a single piece of the 1960s without the supporting context are doomed from the start.

I've had a lot of conversations with students lately that start with disclaimers like "I'm sorry, I'm not really good at math, so..." and since it's not so easy to give a pep talk in-person with the whole pandemic and everything, I thought I'd give the pep talk here. (Just keep in mind that I'm not a very good mathematician, so... KIDDING! I'm a perfectly capable mathematician!) ^-- If you felt like you wanted more about being stuck, click some of these --v - Ben Orlin has a conversation with Andrew Wiles, one of the GOATs of mathematics, about being stuck: https://mathwithbaddrawings.com/2017/09/20/the-state-of-being-stuck/ - Kate Poirier asks students to reflect on belonging in mathematics: https://openlab.citytech.cuny.edu/poiriermat1575fall2020/2020/10/23/assignment-are-you-bad-at-math-really/

Dropbox mirror: https://www.dropbox.com/s/bosace9japm3s5j/Gian-Carlo%20Rota%27s%20Lessons%20I%20Wish%20I%20Had%20Been%20Taught.pdf?dl=0

Kevin Buzzard's invited talk at CICM arguing that getting undergraduate mathematics formalised in theorem provers is useful and important. Slides at http://wwwf.imperial.ac.uk/~buzzard/one_off_lectures/ug_maths.pdf

In startups, roles are fluid. Everyone wears many hats: what’s important isn’t one’s job description but the problems which need to be solved. ​ If you’re going to have a team with continuously negotiated roles, you need a context for that continuous negotiation. These demos unified the “tests” with the real work. Eventually, I came to understand that they put themselves into these terrible situations as a way to force themselves to innovate, that the desperation was productive, not destructive. It was desperation, but by design. ​ We worked from deep desperation, but as Vaughn describes, it was absolutely one of the most exhilarating and dynamic periods of my life. But these big-picture problem statements shatter fractally into a hundred sub-problems, and most of the progress in my work comes from identifying and improving articulations these sub-problems.

It may be quite hard to find a reviewer that both knows the math and can deal with the code.

I asked everyone what a successful outcome for them would look like…and what they would focus on, if they were doing my job. I want to gain some understanding of the choices that were made before I was employed at the company, but not to make any judgements about those choices. I might not necessarily be the smartest engineer in the room, and that’s OK. I know it takes a mixture of skill sets to build a great product. One manager admitted to me she was itching to see results, but admired my ‘maturity’ to do thorough research first.

These wrongs are part of why I talk about my practice the way I do - I want to “bring more rigor to people’s curiosity.”

In the third episode of The Torch of Progress, we sit down with Patrick Collison, the Co-founder and CEO of Stripe. We discuss progress studies, his perspective on the sciences, Effective Altruism, on being a self-described 'fallibilist,' and the entrepreneurial mindset. Key Topics: - The rate of scientific progress and whether it's slowing down. - Progress Studies at large and Patrick's views on Effective Altruism - On being a self-described 'fallibilist' and the entrepreneurial mindset. - Q&A from students and attendees, and much more. In this episode we discuss: (0:15) Intro to Progress Studies for Young Scholars (0:50) Past guest speakers - see the replay on Youtube (1:00) Upcoming guests - Max Roser, Deridre Nansen McCloskey, Joel Mokyr (2:00) Introductions: Jason Crawford with Roots of Progress and Patrick Collison, CEO & co-founder of Stripe (3:00) Patrick talks about Stripe, an online payment system (5:42) Fast Grants for Covid-19 research: What have you learned and what does the future of Fast Grants look like? (13:00) The great corporate research labs (Bell Labs, Xerox PARC) - are they a thing of the past? If so, was that natural? Is there something new we should move to? Should we try to bring it back? (15:55) If you were asked to write a report on the future of science and research, like the Endless Frontier Memo by Vannevar Bush in 1945, what would you say? (18:50) - If you had to give society a progress KPI (key performance indicator), what are the key metrics? (23:40) what are the metrics people use to argue if science is slowing down? Scott Alexander said, "Constant progress in science in response to exponential increases in inputs ought to be our null hypothesis." What is your take on this? (29:45) Compare/contrast effective altruism and progress studies (33:28) If we just run full throttle ahead with progress, what about the risk that we are not careful enough and we get some global catastrophe? (36:05) Your twitter bio describes you as a fallibilist optimist. What does this mean and why did you choose those terms? (39:50) What advice that is commonly given to teens is actually wrong? (43:10) Follow Patrick on twitter @patrickc and online patrickcollison.com Q&A (43:50) What do you think about the future of the internet as the rate of adoption is slowing? Do you see it becoming increasingly zero-sum / less spending on r&d? (46:00) Some people have suggested a Manhattan Project for Covid-19. Is that what Fast Grants is doing? If not, is something like that even feasible anymore? (47:19) You mentioned the existential risk that comes with more progress can be mitigated. What do we need to do to mitigate it? (48:10) You gave the advice to keep learning another 5-10 years, but that is not what you did (started a company at a young age). Why? (50:35) Big companies need an effective organizational structure to avoid getting more inefficient and less innovative. What have you done with Stripe to keep it innovative and nimble? (54:06) How did you found a company? How did you know where to start and what steps to take? (55:40) What do you think about studying liberal arts if in college for technology? Links: Progress Studies for Young Scholars: progressstudies.school The Academy of Thought and Industry: thoughtandindustry.com The Roots of Progress Blog: rootsofprogress.org/ Higher Ground Education: tohigherground.org Guidepost Montessori: guidepostmontessori.com

Roam has a learning curve, but after a few weeks of playing with it I already love it much more than Evernote and Notion. Here's why, and how I'm using it.

All that goes to say, if you just one day got rid of pre-publication peer review entirely – just got rid of it, full stop – there’s no reason to believe that the overall quality of published research would go down, at all. You’re still incentivized to publish your best work; arguably more so because you no longer have the cover of “being peer reviewed” as legitimacy. There will still be good research, and bad research. And post-publication peer review will still be able to pass judgement on anything it wants.

The academic journal business model is a funny one, because the journals themselves don’t actually do much work. The content is produced by PIs, for free, who apply for publication in hope of getting selected. Other PIs who review and curate submissions also work for free: it’s considered a part of academic duty, and prestigious to accept but disastrous to decline. In short, aside from the cost of ink and postage, academic journals deal in one thing only: positional scarcity. The real shame in academic publishing, if you ask me, isn’t Elsevier’s 35% profit margin on journal subscriptions. It’s the much larger amount of money, time and influence that is regressively taxed from the young scientists, to the old ones, in exchange for nothing but brand access.

Only rarely do online-first takes on economics, management theory, cultural theory, and analytic philosophy, among others, make the leap into academia, that other internet of texts. There are perhaps numerous reasons why this is the case. A significant one, though, is the lack of coherent citation and attribution practices on the web.

And I hope we see a renaissance of organizations and individuals step up to support them. Where I want to take Distillations with its upcoming project to write a graph theory toolkit in Swift — a hopeful meeting of engineers and mathematicians.

maybe we should allow people to say they’re just not a math person, and maybe we should find ways they can still support and appreciate math without feeling like they need a Ph.D.

the current mode of team-based mathematics is a relatively new phenomenon. “Mathematics used to be a much more individual activity,” Minsky said. “Maybe in the next year or so, we’ll be back to some solo projects.”

“In research,” said Tom Rivers, “you often need a person like [Harry] around, you know, someone … to encourage people to see what the grass is like on the other side. In other words, a catalyst. Harry Weaver performed that function beautifully.” ​ But it seems to me that we’d be doing a better job fighting COVID-19 if there were someone qualified who believed it was their job to solve it.

Try to ask one question at as many seminars as possible, either during the talk, or privately afterwards. The act of trying to formulating an interesting question (for you, not the speaker!) is a worthwhile exercise, and can focus the mind. ​ The reason for this phenomenon is that mathematics is so rich and infinite that it is impossible to learn it systematically, and if you wait to master one topic before moving on to the next, you'll never get anywhere.

Finally, I am concerned about the state of pure mathematics research. More and more, results depend on theorems whose proofs are unpublished or sketchy (or even, in places, incorrect). We rely more and more on unnamed teams of experts who have a sufficiently broad overview of an area to be able to tell us with confidence which papers can be trusted. Fashions change, people desert areas, and I am genuinely scared that we are leaving a mess behind in some areas. There are some theorems whose proofs might be difficult or impossible to reconstruct in 20 years’ time.

An aspiring research distiller lacks many things that are easy to take for granted: a career path, places to learn, examples and role models. Underlying this is a deeper issue: their work isn’t seen as a real research contribution. We need to fix this. ​ It’s entirely possible to build paths and staircases into these mountains.That is, really outstanding tutorials, reviews, textbooks, and so on. The climb isn’t something to be proud of. The climb isn’t progress: the climb is a mountain of debt.