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I agree with the sentiment of this. I think our obsession with innate mathematical skill and genius is so detrimental to the growth mindset that you need to have in order to learn things.

I've been working a lot on my math skills lately (as an adult). A mindset I've had in the past is that "if it's hard, then that means you've hit your ceiling and you're wasting your time." But really, the opposite is true. If it's easy, then it means you already know this material, and you're wasting your time.

> I agree with the sentiment of this. I think our obsession with innate mathematical skill and genius is so detrimental to the growth mindset that you need to have in order to learn things.

I would argue something different. The "skill" angle is just thinly veiled ladder-pulling.

Sure, math is hard work, and there's a degree of prerequisites that need to be met to have things click, but to the mindset embodied by the cliche "X is left as an exercise for the reader" is just people rejoicing on the idea they can needlessly make life hard for the reader for no reason at all.

Everyone is familiar with the "Ivory tower" cliche, but what is not immediately obvious is how the tower aspect originates as a self-promotion and self-defense mechanism to sell the idea their particular role is critical and everyone who wishes to know something is obligated to go through them to reach their goals. This mindset trickles down from the top towards lower levels. And that's what ultimately makes math hard.

Case in point: linear algebra. The bulk of the material on the topic has been around for many decades, and the bulk of the course material,l used to teach that stuff, from beginner to advanced levels, is extraordinarily cryptic and mostly indecipherable. But then machine learning field started to take off and suddenly we started to see content addressing even advanced topics like dimensionality reduction using all kinds of subspace decomposition methods as someting clear and trivial. What changed? Only the type of people covering the topic.

> I agree with the sentiment of this. I think our obsession with innate ~~mathematical~~ skill and genius is so detrimental to the growth mindset that you need to have in order to learn things.

I strongly believe that the average human being can be exceptional in any niche topic given enough time, dedication and focus.

The author of the book has picked out mathematics because that was what he was interested in. The reality is that this rule applies to everything.

The belief that some people have an innate skill that they are born with is deeply unhelpful. Whilst some people (mostly spectrum) do seem have an innate talent, I would argue that it is more an inbuilt ability to hyper focus on a topic, whether that topic be mathematics, Star Trek, dinosaurs or legacy console games from the 1980’s.

I think we do our children a disservice by convincing them that some of their peers are just “born with it”, because it discourages them from continuing to try.

What we should be teaching children is HOW to learn. At the moment it’s a by-product of learning about some topic. If we look at the old adage “feed a man a fish”, the same is true of learning.

“Teach someone mathematics and they will learn mathematics. Teach someone to learn and they will learn anything”.

So you're saying success at maths isn't an inbuilt ability. Instead, it depends on an (inbuilt) ability to hyper focus... Which you are just born with?

Not even that. It depends on the learned ability to stop pushing yourself when your focus is wavering. That's how you develop aversion towards the topic. Let your natural curiosity draw you to particular topics (that's why you might have a winding road through the subject).

I've had some success converting people by telling them others had convinced them they were stupid. They usually have one or two things they are actually good at, like a domain they flee to. I simply point out how everything else is exactly like [say] playing the guitar. Eventually you will be good enough to sing at the same time. Clearly you already are a genius. I cant even remember the most basic cords or lyrics because I've never bothered with it.

I met the guitar guy a few years later outside his house. He always had just one guitar but now owned something like 20, something like a hundred books about music. Quite the composer. It looked and sounded highly sophisticated. The dumb guy didn't exist anymore.

But also, some people are stupid, right?

When I was a young adult, i spent a lot of time on math and physics.

I was initially celebrated for the mathematical talent.

But as life progressed, I my family started seeing me as an academic loser.

Basically, no girls would be interested in me because "mathemetical talent" doesn't help you with that.

And i seen handsome men had more respect from society than spending countless time on math.

So, i later gave up because my family kept pressuring me to attain real success, girls, money and car and i became a programmer.

Funny enough, I was still a loser in societal view doesn't matter I started clearly half a million a year.

So most people don't try hard at math because math is not rewarding, for most people.

It's much better to build physique, music talent, comedic talent, this helps you get girls and respect from peers.

Most people don't try hard at the gym. Most people don't try hard at music. Most people aren't comedians.

This reads like the foreword to the incel handbook.

This perspective has discouraged so many people from exploring their potential

easy_things -> comfort_zone

I'm not a math teacher, but I do enjoy math, and I have helped several family members and friends with math courses.

I've long thought that almost all have the capability to learn roughly high school level math, though it will take more effort for some than for others. And a key factor to keep up a sustained effort is motivation. A lot of people who end up hating math or think they're terrible at it just haven't had the right motivation. Once they do, and they feel things start to make sense and they're able to solve problems, things get a lot easier.

Personally I also feel that learning math, especially a bit higher-level stuff where you go into derivations and low-level proofs, has helped me a lot in many non-math areas. It changed the way I thought about other stuff, to the better.

Though, helping my family members and friends taught me that different people might need quite different approaches to start to understand new material. Some have an easier time approaching things from a geometrical or graph perspective, others really thrive on digging into the formulas early on etc. One size does not fit all.

Effort, combined with the right motivation, can overcome most perceived barriers

It sounds like trivial insight, but at least in my experience many adults and even teachers have this "it's hard so it's ok to not want to do it" attitude towards math. And I think that is very detrimental.

I totally agree! The barriers many of us face with math are less about ability and more about how we've been taught to approach it. All it took was for me to change my math teacher at school, and boom. Love, but at second sight. And curiosity and persistence can unlock more than just numbers

A nice sentiment but clearly a large % of people never do learn even basic mathematical thinking and seem very confused by it. So is there some scientific study backing up the claim that all these people could easily learn it or are we just making it up because its a nice egalitarian thesis for a math popularization book?

That certain countries both now and in the past have had significantly higher mathematical ability among the general population and much higher proportions going on to further study suggests that ability isn’t innate but that people don’t choose it. In the Soviet Union more time was spent teaching mathematics and a whole culture developed around mathematics being fun.

I do not think that Bessis's argument is entirely "made up"

> So is there some scientific study backing up the claim that all these people could easily learn it [emphasis added]

Who said it would be easy?

>A nice sentiment but clearly a large % of people never do learn even basic mathematical thinking and seem very confused by it

Any healthy/able individual could learn to deadlift twice their bodyweight with sufficient training, but the vast majority of people never reach this basic fitness milestone, because they don't put any time into achieving it. There's a very large gap between what people are capable of theoretically and what they achieve in practice.

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I studied math hard for several years in college and graduate school—purely out of interest and enjoyment, not for any practical purpose. That was more than forty years ago, but Bessis's description of the role of intuition in learning and doing math matches my recollection of my subjective experience of it.

Whether that youthful immersion in math in fact benefitted me in later life and whether that kind of thinking is actually desirable for everyone as he seems to suggest—I don't know. But it is a thought-provoking interview.

I also studied it and got several degrees, but I don't think that it actually benefited me. I think high school math is incredibly important to be able to think clearly in a quantitative way, and one university-level statistics course, but all the other university math... I dont think it helped me at all. I am disappointed by it because I feel that I was misled to believe that it would be useful and helpful.

Have you ever ascribed numbers to real life personal problems? I find that managing to frame something bothersome into a converging limit somehow, really dissolves stress.. A few times at least.

That’s an interesting approach. I don’t think I’ve done that myself, but I can see how it could be helpful.

One positive effect of having studied pure mathematics when young might have been that I became comfortable with thinking in multiple layers of abstraction. In topology and analysis, for example, you have points, then you have sets of points, then you have properties of those sets of points (openness, compactness, discreteness, etc.), then you have functions defining the relations among those sets of points and their properties, then you have sets of functions and the properties of those sets, etc.

I never used mathematical abstraction hierarchies directly in my later life, but having thought in those terms when young might have helped me get my head around multilayered issues in other fields, like the humanities and social sciences.

But a possible negative effect of spending too much time thinking about mathematics when young was overexposure to issues with a limited set of truth values. In mainstream mathematics, if my understanding is correct, every well-formed statement is either true or false (or undecided or undecidable). Spending too much time focusing on true/false dichotomies in my youth might have made it harder for me to get used to the fuzziness of other human endeavors later. I think I eventually did, though.

Thanks for sharing. The reverse direction here, I'm trying to go from fuzziness to the exactness of those true/false dichotomies, haha. The way I've been attacking mathematics, it's like a tree in the forest, one could start with the axioms and from the base reach each branch and the leaves and fruits. But I've just been walking around the tree, looking at the leaves and fruits and branches from different directions to see ways of climbing without doing a whole lot of climbing. What I mean is I've been thinking and reading in an imprecise way a whole lot without actually juggling symbols with pen and paper, haha. Or a roadtrip analogy, I've done little driving and a lot of map ogling. At least I won't miss the turns when I pick up some speed.

> the provocative claim

Leibniz made that claim centuries ago in his critical remarks on John Locke's Essay on Human Understanding. Leibniz specifically said that Locke's lack of mathematical knowledge led him to (per Leibniz) his philosophical errors regarding the nature of 'substance'.

https://www.earlymoderntexts.com/assets/pdfs/leibniz1705book...

I’m far from being any kind of serious mathematician, but I’ve learned more in the last couple years of taking that seriously as an ambition than in decades of relegating myself to inferiority on it.

One of the highly generous mentors who dragged me kicking and screaming into the world of even making an attempt told me: “There are no bad math students. There are only bad math teachers who themselves had bad math teachers.”

Sadly, when I was a postdoc, an eminent mathematician I was working under once shared a story that he found amusing that one of his colleagues was once asked a question in the form: "This might be a stupid question, but..." and the response was "There are no stupid questions, only stupid people."

Run into too many people like that, who I daresay are common in the field, and it's easy to see how people become dispirited and give up.

I think we can recognize Pauli for his identification of one of the few magic gadgets we accept around spin statistics without accepting his educational philosophy: “Das ist nicht einmal falsch.”

He was right on the nature of the universe, he was wrong on making a better world. I for one forgive him on the basis of time served.

How much of math aversion stems from a chain reaction of ineffective instruction

> everyone can, and should, try to improve their mathematical thinking — not necessarily to solve math problems, but as a general self-help technique

Agreed with the above. Almost everyone can probably expand their mathematical thinking abilities with deliberate practice.

> But I do not think this is innate, even though it often manifests in early childhood. Genius is not an essence. It’s a state. It’s a state that you build by doing a certain job.

Though his opinion on mathematical geniuses above, I somewhat disagree with. IMO everyone has a ceiling when it comes to math.

> IMO everyone has a ceiling when it comes to math.

Yes, but it's higher than you think: https://www.justinmath.com/your-mathematical-potential-has-a...

Statistical (Bayesian) thinking is an extremely underrated way of thinking of almost everything.

Agree. I’ve been trying to learn ML and data for a few years now and, around 2021 I guess, realised Maths was the real block.

I’ve tried a bunch of courses (MIT linalg, Coursera ICL Maths for ML, Khan etc etc) but what I eventually realised is my foundations were so, so weak being mid 30s and having essentially stopped learning in HS (apart from a business stats paper at Uni).

Enter a post on reddit about Mathacademy (https://www.mathacademy.com/). It’s truly incredible. I’m doing around 60-90 minutes a day and properly understanding and developing an intuition for things. They’ve got 3 pre-uni courses and I’ve now nearly finished the first one. It’s truly a revelation to be able to intuit and solve even simple problems and, having skipped ahead so far in my previous study, see fuzzy links to what’s coming.

Cannot recommend it enough. I’m serious about enrolling in a Dip Grad once I’ve finished the Uni level stuff. Maybe even into an MA eventually.

I used to get very frustrated that others could not intuit information the way I could. I have a lot of experience trying to express quantities to leaders and policymakers.

At the very minimum, I ask people to always think of the distribution of whatever figure they are given.

Just that is far more than so many are willing to do.

Waste of time. Just talk in terms of what they want to hear. They are just interested in the payoffs (not in the details).

As info explodes and specialists dive deeper into their niches, info asymmetry between ppl increases. There are thousands of specialists running in different directions at different speeds. Leaders can't keep up.

Their job is to try to get all these "vectors" aligned toward common goals, prevent fragmentation and division.

And while most specialists think this "sync" process happens through "education" and getting everyone to understand a complex ever changing universe, the truth is large diverse groups are kept in sync via status signalling, carrot/stick etc. This is why leaders will pay attention when you talk in terms of what increases clout/status/wealth/security/followers etc. Cause thats their biggest tool to prevent schisms and collapse.

This guy is unbelievably French (I mean in his intellectual character). Here I was expecting a kind of rehash of the 20th century movements of pure math and high modernism[0], but instead we get a frankly Hegelian concept of math or at least a Hegel filtered through 20th and 21st century French philosophy.

[0]https://news.ycombinator.com/item?id=41962944

I was actually thinking Jean Paul Satre when I read his answers

Gentle Reminder that the author of this article used to have a wonderful math channel: https://www.youtube.com/c/pbsinfiniteseries

Everyone? Even retards?