This is such a great quote for everyone! No matter the age. No matter what one wants to do.
> “I’m not able to learn mathematics easily,” Talagrand tells ... “I have to work. It takes a very long time and I have a terrible memory. I forget things. So I try to work, despite handicaps, and the way I worked was trying to understand really well the simple things. Really, really well, in complete detail. And that turned out to be a successful approach.”
Just imagine. You may be super smart who gets things easily and right away. Or, you may be average. Using this philosophy in life, one can excel further.
I had a college friend that's super slow to learn. He would always get behind on classes and would not even get passing grades most of the time.
But! When he finally learned something new, he would never forget it. He would remember it in details, both the whys and the hows. I've always admired his skill.
I’m like this. I barely graduated school and failed out of college in the first year with a GPA whose square root was higher than the actual GPA. I had always been placed in accelerated classes only to be kicked out once I fell behind. I needed time to understand things, but in all modesty once I understand something I seem to understand it better than everyone around me. Until then though my mind is blank and I literally can’t force myself to do anything on the subject. I just stumble and can’t remember anything when asked. Some subjects are faster than others but some took a year or longer to understand. When mathematically inclined friends took algebra they flew through it and graduated high school completing calculus B AP with a 5, but it took me a year of failing it and being tracked before I finally clicked. But once I understood it other math courses were a breeze largely because my algebra understanding was beyond everyone else’s. But I was tracked and getting off the track in math is almost impossible. I likewise had challenges in geometry and trig until I “got it,” all of which meant when I finally hit calculus and got the concepts of differentiation and integration I took off like a rocket and never looked back.
After failing out of college I went out to the valley and was very successful. I went back to college in my late 20’s using a loop hole to transfer into a top CS school. I knew myself better now and studied all the time knowing I wasn’t stupid just learned differently. On things that weren’t yet clicking I would relentlessly keep studying it and practicing and trying until it did. I graduated highest in my class at a top public engineering program - which gives gentleman F’s to 70% of original freshmen unlike private schools.
My daughter is the same way, so I found a private school that is very careful about differentiating learners and letting them move their own pace. I was suicidally depressed about public education growing up as it ground me down for being different. She is thriving at the stages I fell off the rails.
I am a similar learner, though not quite the same. Mostly for me it’s a focus thing. If I’m focused in, I learn very quickly, but if not, I fall behind hopelessly. College lectures were next to impossible for me, as I had such a hard time focusing, ended up in academic probation and managed to turn it around enough to graduate.
Years later, I went back and got my MS online. That was incredible. Recorded lectures meant I could pause and rewind when I lost focus. I really enjoyed my classes because now the most stressful part of it was no longer an issue.
It’s incredible our entire public school system is based on the assumption every student learns things in the same way at the same rate.
But how can it scale if it doesn’t assume that? It really has to cater to some statistical center of gravity and at some point cut off the outliers. Otherwise you need to pay for a private education because essentially you’re asking for custom tailored schooling. The fact that my parents couldn’t afford private schooling is no one’s fault - I don’t blame the public school system for things being the way things are honestly despite the level of abject misery I felt in it. In fact I’m a huge fan of it - I learned more than I would have without it and value the fact that everyone no matter how poor gets access to it.
Some public schools try to do differentiation but it’s really expensive and impractical at scale. The quality of teacher, resources, and teacher training required if very high. I think every effort to try is worth doing, but the more you try without increasing the amount of funding, training, and selectivity in teacher hiring (which is impractical given the scarcity of high quality teachers relative to the population size) the worse you do for everyone.
I don’t agree vouchers and school choice helps this fwiw. The issues don’t go away by diffusing administration of schools to more organizations, you just end up spending a lot more tax payer money on a lot more administrative staff at a lot more schools with a lot less focus on that center of mass outcome.
The reality is despite how intolerable my childhood was I found my way - and I know many who do. People are resilient and overcome adversity all the time in many shapes.
The (US) academic system is not set up to accommodate anyone, really. It's designed to get someone just below average through their standardized testing and not much more. If you don't fit that mold you're shit outta luck. You either suffer through it like "normal" people, or you find it utterly intolerable and fail or drop out.
Personally, I learn best backwards from everyone else. Building up very slowly from fundamentals and basically starting over with basic algebra every semester is actual hell. I need to see the goal concept fully formed and functional, and then work backwards to derive the fundamentals I'm missing.
Generally speaking, once I understand a concept I have it forever. I usually only need the briefest of refresher on mechanics and formulae as I use them. Spending the first month of calculus class going over 9th grade algebra is an unbelievable waste of my time.
My final attempt at college was a CS degree. I made it through one semester and did not even get to a single CS concept. It was at least a year and a half of bullshit prerequisites that I had to pay for. I dropped out when I had to write a presentation to the board of my hypothetical company on the benefits of upgrading their printers. I'm not kidding. I paid real money for this.
I've totally given up on the educational system. I don't fit into the cookie cutter ideal of the average idiot grinding out a degree. I just can't do it.
I think probably the ideal way for me to learn is to spend a lot of time one on one with a domain expert that can show me the final concept and work backwards with me to fill in the gaps in my knowledge. I don't want or need, nor can I tolerate spending time going over things I already know for the 30th time. I need to learn the things I don't know. School just doesn't work that way.
>Personally, I learn best backwards from everyone else. Building up very slowly from fundamentals and basically starting over with basic algebra every semester is actual hell. I need to see the goal concept fully formed and functional, and then work backwards to derive the fundamentals I'm missing.
Same, and at work too. I think it's because we think big picture and conceptually. Tell me the outline, and I'll seek out missing information and fill in puzzle pieces, until I can grok it. It's a slow process but learning from first principles I find absolutely boring and unengaging.
I found math in high school utterly meaningless, a set of drills and exercises to do again and again without explanation.
If you go to the gym and you want to do some exercises, you'll generally get a list and try to learn them correctly.
If math teachers taught sports, no one would ever do anything because they would never understand what the goal was. What's the end result? The complex end result should be made known so that we know why we're doing something.
With math it's, shut up and do your drills and if you don't you'll be punished with bad grades. See that guy in the corner with his head down and protractor? He loves it, be like him.
That's one area where I think LLMs will shine outside of the hype zone: they could boost a student's ability to make progress without supervision.
And I understand that there are great teachers out there and an LLM cannot replace that, but at the same time there are a lot of bad teachers wasting everybody's time.
Yup, I've actually gotten pretty decent results out of an LLM for subjects I'm already pretty familiar with. If we ever figure out the hallucination problem, LLMs could revolutionize education overnight.
I think that almost everyone would benefit enormously from having a focused and dedicated one-on-one tutor. Just imagine if you could call up the leading world expert in any field at any time to ask any question you could possibly have. We as a species would get so much more done.
At least that's what I want AI to be in the next decade or so. A tool to push humans to a much higher potential where we can solve our own problems more effectively. I'm afraid we'll skip that step, though and go straight to worshiping the AI that makes the most paperclips.
Anyway, I'm still experimenting off and on with local LLMs to get me closer to where I want to be. I'm not sure it's much faster to use an LLM and continually verify its output, but it does at least provide structure and guidance for my own self-teaching.
A bit reminiscent of John Carmack's method too; not only does he work for 10 hours a day (preferably uninterrupted) he also secretes himself away at some random location for a week at a time.
It's not the same, I know, but to remember things you have to establish and remember entire trains of thought. Not just remember individual milestones.
There's a story that an American football coach, after gathering the best players he could, would start each season just working on the fundamentals, saying you cannot do the simple easy you can't do complex.
One of his Hall of Fame players said that he woukd begin with "Gentlemen, this is a football"
This is true but players understood the goal - play better football.
With math it's what exactly?
If someone worked backwards from code on DAY 1 of high school math, I'd have been engaged... Instead it was mindless repetitive drills. Later as an advanced thing they'd ask you a real-world question: "Let's say you wanted to circumnavigate the Earth and you started here and had to blah blah". I think they should start and not end with that type of thing.
The world needs more recognition of good mathematics and mathematicians. Really love the work quantum magazine does on covering mathematics. So many implications for the rest of the world.
For those who don't know, Quanta Magazine is financed by Jim Simons (from Chern-Simons theory) who became known as a very successful hedge fund manager. I just love the idea that he's using a portion of his billions to fund a little non-profit math magazine.
I agree. Quanta is the sort of material I like to read during my morning coffee ritual before I start a day of screen time.
Are there any quality print magazines like it? I used to get Physics World a long time ago and have been looking for something in print to scratch that same itch.
It doesn't even need to be altruistic. One would expect that out of sheer self-interest, one would look into propelling humanity forward by elevating and liberating as many people as possible, enabling the brightest of our species to solve the hardest problems and elevate humanity. Though accepting that one needs others to solve problems one does not understand, that they play a supporting role, takes a great deal of humility.
I don't associate myself with that particular group of people, nor did I in any way condone such behaviour, nor do I support long-termists and so on.
My comment was mostly calling out the hypocrisy of some EAs, Long-termists, and the likes. It points out the myopic, self-centered, irrational, and too self-important view, the often exhibited messiah complex, and of course the absence of humility.
The issue is that we've setup the system to require people like this, which more often than not exposes us to people the opposite of Jim Simons, like Robert Mercer, Peter Thiel, etc. Instead having a proper tax structure, we rely on altruistic wealthy individuals, which are rare, and mainly get people who want to drive us into libertarian hellscapes.
I suppose for that to happen, the world needs better math lessons in school. Most have allmost traumatic experiences, so they now don't want to know anything about math at all.
(I also only started to enjoy math, when I could apply it with programming, before it was not traumatic, but mostly boring, but we also did not cover any fun parts like Mandelbrot etc)
I'm always very confused by this. Why are maths lessons more traumatic than, say, history or biology or foreign language lessons? I mean learning lists of irregular verbs is not precisely most people's idea of fun. And yet only about maths do people speak with such dramatic language.
There must be something beyond what's happening in schools themselves that makes people react this way. I just can't work out what it is.
In my mind math learning builds on top of the stuff you have learned earlier on different level than other subjects. If you get ”derailed” at some spot in learning it becomes tough / impossible to learn the concepts that build on top of the stuff that you didn’t understand properly.
This is kind of a rant, but I think we heap a whole bunch of expectations on math progress in school, that are unrelated to math and create a burnout atmosphere. There's a culture of fear surrounding math. Most adults, even people who are in supposedly technical occupations, outwardly hate math. Most can proclaim that they set their math aside after it got them through school.
Yet it's also chosen as an arbitrary measure for ranking children and gating their academic and career choices. Kids are "ahead" or "behind" in math. They're tutored during the summer and sent to cram schools. They're tested at every grade level. Math determines access to many fields of study in college. School districts are ranked by math scores.
We have some vague sense that math is important for something. Maybe it fosters intelligence or diligence, both of which are valuable I suppose. But never math for its own sake.
I loved math in school and was even on the state math team. Sadly much of the math I learned in high school and even college I had to unlearn (the worst example being assuming everything is a normal distribution and reporting mean and standard deviation instead of looking at a histogram).
I'm convinced that the best way to teach stats is to start people with data and graphing. The formal mathematics of statistics is certainly a fascinating discipline (my grandfather was a professor of statistics) but for the rest of us, the formulas are a work-around to the problem of dealing directly with the data and doing repetitive calculations by hand.
The formulas and proofs are certainly valuable, but could come later. And the graphs remain useful (at least for a hack like me) for confirming our understanding of the formulas.
Also, data and graphing would be a way to ease students into programming.
I agree, but have to caution that the abstract and dry stuff is still part of math. It was what turned me on to math. I'd favor a blending of math and science curricula, and use more data analysis when teaching science.
It's a dilemma because math is so broad, and has both pure and applied sides. And a challenge for changing curricula is that the public defines "math" as the precise sequence of topics that they studied in school (and hated).
What about history? Don't people perceive it as even more unnecessary than maths? Shouldn't we expect to see all sorts of theories on how history should be taught in more practical ways if your explanation is correct?
I'm only picking on history or languages as examples. I could have picked literature, or almost anything, really. A lot of what is taught at school isn't necessarily a bunch of super applied skills
There are lots of bad teachers in every discipline, and I'm sure that everything could be taught a lot better. I'm still not getting why maths is singled out.
History is about stories of people in the real world. Learning dates of battles or treaties was and is also hated, but otherwise it is just stories, one can more or less relate to.
Plain math is abstract. No humans involved, just numbers and formulas. Nothing to connect to, unless the teacher brings in the real world. Because math is awesome at describing and predicting real world events. But that is usually applied math, like physics. And I loved physics (and history) in school. But math? My brain refused as it saw no benefit except for the needed grades.
History is not abstract. It does not give you generalizations, abstractions and models, just historical facts. Many of those facts are useful in understanding why things around you are the way they are.
The attempts to make history more "scientific", usually for religious or political reasons (e.g., explaining past events throgh class struggle), end up looking like propaganda.
If you learned history as a set of facts then you did not learn history. History is about the connections between those facts and the overarching story.
Science is also taught as a set of facts to be memorized, but that is also not science. In both science and history, the most important question is not "what do you know?" but "how do you know?".
You can, but the world is still an chaotic place, so making a forcast on human geopolitics, is like making a weather forecast. Likely valid for the next days, but increasingly bad for longer timeframes.
But one can make for example the prediction that the war in Ukraine will be going on for a little bit longer.
Weather forecasts can easily be compared to actuals, and distribution of residuals can be calculated. That’s how weather forecast models are quantitatively evaluated. A seven day weather forecast has 95% confidence interval of around plus-minus 10 degrees Fahrenheit, way better than “it’ll be like today”.
Your prediction about the war in Ukraine is not falsifiable.
Look, I am not going to make a detailed geopolitical analysis here, but there are lots of sites and institutes who do, you can check them out. The difference with weather forcast is only, that human analysis of geopolitical events often hope to influence the outcome. But the weather will come whether we think it will be sun or rain.
And the prediction about the war in Ukraine would not be "it'll be like today". The current prediction is, that russia will continue to slowly make ground and move the front lines to the west. There are actually predictions how much and where exactly. I think that gets also falsified in some institutes, but is probably classified.
Are you saying there is some classified science also called history that makes quantitative, testable, falsifiable predictions?
Maybe so, but I have no clearance and have not seen it. And it would be completely different from history I studied in school. There wasn’t a single prediction, let alone quantitative prediction with time horizon and confidence interval in any of the history books I’ve read.
And that is exactly the question allmost never being asked in (my) school. "No time for it. Here are the facts. Accept it and learn them, we will determine your future on how well you memorized them"
But to be fair, some of my teachers tried this approach as much as possible, but within the whole framework of the curriculum, not much was possible.
Because many school Maths teachers are fundamentally bad at teaching the subject and when this abstract subject naturally is difficult for young pupils to absorb, in the end they default to "because it is that's the way it is, and you just have to learn it!", roughly put.
Math is used as an IQ filter in the education system so even the people who are capable of it develop a hate for it.
The math department at my university was viewed very negatively because of this. People doing CS prerequisites and whatnot knew that they weren't there to learn but just to pass a glorified IQ test.
Because in maths one thing builds on another, more so than in other fields.
If you missed multiplication there is no way you can get integral calculus. People drop out at different stages and can never get back on track in the school curriculum.
I don't think aptitude is the reason. A lot of people are physically unfit and have traumatic sports education experiences, probably even more so than math, but athletes remain stars.
The issue is entirely cultural. Entrepreneurs, celebrities, socialites are venerated, scientists aren't. There's no mainstream cultural recognition of scientists and science itself, at best people get attention who monetize research.
The "issue" is entirely about money. Sports make so much money because so many have fun watching them. And it's an issue only if you want fame so badly as to make an issue of the fact that what you do is anonymous.
As a European who was unfit for sports, the social stigma is much worse. It is socially acceptable to be bad at maths, but you are looked down upon if you are overweight, lack coordination or are otherwise unfit.
For me it was a self enforcing effect where it also impacted how I viewed myself and I did not feel confident enough socially.
Obesity is one of the few remaining social stigmas that are "acceptable" to joke about. I don't think the average person know how it makes you feel when people passing you in the street look at you and make comments or try to avoid you.
There are so many micro aggressions that happens where each stare, laugh or comment just breaks you down mentally and isolates you socially.
"It is socially acceptable to be bad at maths, but you are looked down upon if you are overweight, lack coordination or are otherwise unfit"
Yes, that is sadly often the case.
My advise if you want to change something, find acticities that are fun. Everything with water is good, if you are overweight, but it seems, you likely would not like the public swimming pool. But there are offerings for water exercises especially for obese people. Being in a group helps ignore what others think. Otherwise there are hidden lakes for example. (Or get a private swimming pool if you have the funds)
Maybe credit him in the title would be a good thing to start. In the title, there is neither its name nor the price he won. His nationality is not even mentioned in the article.
They could have written a better head line and mentioned the name of the mathematician. Leaving the mathematicians name out of the head line is a click bait technique, and tends to devalue the whole article.
"Michel Talagrand wins Abel Prize for his work on randomness/stochastic processes" would have been a good headline to have, but they chose theirs deliberately to not reveal the import information at a glance.
I've found his work on inequalities, but the article mentions in passing that he did some good work on the teavellimg salesman problem and I can't seem to find anything about it. Does anyone know where I could find it?
My problem was always I took on too much so I had surprising breadth. I could find connections between many areas. I wish I had just focused on one or two things and gone very very deep. I would probably be a more fulfilled academic today if I was able to do that instead of an engineering manager.
Weird that neither his name (Michel Talagrand) nor his nationality (French) are mentioned in the title. His nationality is not even mentioned in the article. I'd be pissed if I were him, doing something that important, and not even getting your name in the title.
I imagine that people like Talagrand are more concerned with the substance of the article than the title, where all this and more are unambiguously detailed.
Yes, it’s the equivalent to the Nobel in that it’s yearly with a big monetary prize, but the most prestigious award in the field remains the Fields medal, which is only awarded every four years.
The Nobel prize is usually awarded to old (around 60) researchers at the end of their career whereas the Fields medal is only awarded to researchers under 40 (and since it's only awarded every 4 years, the cutoff age can even be 36 if you're not lucky). In that sense the Abel prize is more of a Nobel equivalent than the Fields medal.
The age limit of 40 kind of ruins the Fields medal as the top prize tho. Sure, getting it is absolutely huge, but what about the people whose work's value is apparent only after decades?
