Benn, great post. My degree at UCLA was in economics and, as a tech CTO, I've used my skills in logic, reasoning and writing infinitely more than math. I have 2 sons pursuing a career in computer science and I take issue with their math-heavy curriculum. Our industry's over-rotation on math discourages a whole population from considering a career in CS and under prepares those who do for life in the real world.
Great point Dave. An analogy that just came to mind is transfer learning. A technical major may feel comfortable with many data tools, as concepts repeat. In addition, a coziness in playing with different ways of solving the same task leads to faster evolution of tools and best practices. Without a sound technical foundation I observe less ease and longer onboarding times.
My point: The more fundamental the education, the easier appears transfer learning for a technical specialisation to me. I would welcome a playful approach to teaching math, improving its image.
Thanks. And yeah, I think your last point is the one that I really wish we could fix. By branding things as highly technical, a lot of people don't even look at analytics jobs because "they aren't computer or math people." But they have all of the other (much more valuable, much rarer) skills.
Benn, excellent article; one which describes how I arrived in math from a desire to be a history professor. My parents were convinced that I would starve in my desired profession, and they had the means to enforce their beliefs. By my SAT and National Merit scores (there used to be separate tests), I was equally competent, and proved to be so. They were, sadly, correct! Far better to explain the outcomes of relatively simple math to those who were afraid of symbols, than to change an engineer's mind, even (maybe especially) when they were wrong. I can now enjoy my retirement in the knowledge that I can figure out a plausible answer to current problems/questions across a broad spectrum, and have the ability to see the flaws in the arguments of the many poltroons and idealogical statisticians among us. And I am still prepared to learn from real experts. Including about fishing and cooking.
As one of those poltroons and idealogical statisticians, please don't read this blog too closely, and gloss over the many flaws in its arguments. For I am not yet retired, and have to keep up the illusion of being a real expert for a little while longer.
Jan 11, 2023·edited Jan 12, 2023Liked by Benn Stancil
I'm a mathematician (MS in applied math) turned data scientist. The biggest benefit to me of going further in math wasn't learning the "advanced methods." It was everything else: how to structure an argument; the humbling experience of often being wrong; the importance of definitions and clear terminology; and, yes, written and verbal communication, because I had to teach a course, write papers, and give presentations.
I hope I'm not guilty of the gatekeeping you warn about here, because I know the other person has expertise that I don't. There isn't one discipline to rule them all. Everyone has something to bring to the table.
Although, if you try to abuse math words to sound smart or win an argument...I will catch you lol
That seems to be the rough consensus in the pro math camp - it's not about the math per se, but the various things around it that make it worthwhile. Which, I can mostly see? My guess is that applies to other fields too, but I'm sure math has its own unique advantages there too.
“The predominance of measurable exploitability marks the current reign of technology that Heidegger abhorred. The German philosopher holds that we have become unable to appreciate beauty and wonder in the world. Everything, including us, is perceived as potential input to industrial production.”
Excellent post. It reminds me of a perceptive article by Paul Romer a few years ago of the perils of "mathiness" in economics (https://paulromer.net/mathiness/).
Paul Romer would not like this post: "Mathiness is a symptom of this deeper problem, but one that is particularly damaging because it can generate a broad backlash against the genuine mathematical theory that it mimics."
Paul Krugman periodically makes the same point (https://archive.nytimes.com/krugman.blogs.nytimes.com/2011/02/02/models-plain-and-fancy/), and is a big advocate of simple toy models instead of these really fancy ones. I think it's a good point, especially in non-scientific fields, where we're looking for directionally correct rather than exactly precise.
Jan 6, 2023·edited Jan 6, 2023Liked by Benn Stancil
deeper topic hides here. What cultures is math useful for? If you're an Egyptian Pharaoh, your math skills (or even the math skills of your commanders) mean less than the sheer strength and numbers of your army. On the other hand, if you're in a former Soviet Union and you're building a train system that needs to support a hundred million people, math becomes very important.
What I think you're hinted at is not a world wide phenomenon, but a one centric to the United States tech. And maybe not the type of tech that gave us TCP/IP, Wi-FI, and Routers, but the kind of tech that gave us Facebook, Twitter, and (maybe even) Amazon. And here, if I can jump to some conclusions, finding a way to convince everyone that you're a modern version of Egyptian Pharaoh maybe played a bigger role than being good at Math. So, basically, high EQ coupled with engineering? But not Math.
But, again, this is a very US-centric argument. And as a counter argument, I can reference my own upbringing - a highly math-centric culture, in which businesses die or grow based on how well the math works out on the backend - and much less dependent on one's charisma, emotional EQ, etc.
Then there is a question of time. Math was much more important in the US 60-70 years ago, when there were massive country-wide construction projects going on (including Nuclear). Each mistake is catastrophic. Fast forward to today, and the math problems are about optimizing a Taxi's drive path. A complex problem, but one that, even if it fails, can be fixed with a refund, a customer support ticket, or a simple rebooking/retry.
The real question then is not whether Math is important universally. But is Math going to be important in the future, in the United States?
I think the hard question is whether we are willing to separate the very valid utilitarian function of good math, from the important yet problematic role of math skill as a cultural signifier of intelligence.
don't think Math has been that signal in the US for a long time (if ever). With the exception of maybe Wall Street, the popular signifiers for intelligence have been: PhD, University degree tier, Company/Job Combo, but not math on its own
You and I live in completely different realities. In my world, Math SAT is half the reason you get into a good colleges, advanced math classes in high school are the gateway to a technical degrees, and Computer Science is built around higher math. Would you disagree? Or do you claim that all that is purely for its utility?
I realize I sound like some sort of radical anarchist for suggesting we could fulfill all of those roles without any math beyond (at most) Algebra I. But that’s kinda the point...
Don't disagree because the majority of college admission tests are evaluating not someone's Math skills, but ability to prepare for the tests. The difference being maybe at the graduate level, where you do actually have to be good at Math on GREs.
Sciences/CompSci are built around higher math at Universities - as they should be. Universities, at their founding were not meant to be Vocational training schools. If the goal is to teach kids to write code, then there are community colleges where Algebra 1 is enough.
In the context of jobs, as someone who had a 98% on most Math exams, who had studied Statistics in graduate school, etc, I can tell you that the industry cares a lot less about Math than it seems. And someone with a PhD in Theology, with virtually no Math skills, can get just as far up in a career related to Data or Analytics.
And I agree that most Data roles can be filled with Algebra I math. However, someone's willingness to study beyond Algebra I signals significant interest in Data. And this very signal is maybe what we're all after.
So, it sounds like you agree Math SAT is useless on other grounds, but feel Math is a valid signal for data analysis, and a genuine utility for computer science. Is that a fair summary?
To your first point: yes, it is a “useful” signal, but I hope you would agree that it is possible (and perhaps even socially desirable) to find a better one. Right now, I feel there is a religious attachment to math that makes it impossible to even have a rational discussion about alternatives.
Secondly, I am precisely arguing that Math is the wrong basis for Computer Science, for roughly the same reason: it gives us a superficial sense of rigor without directly addressing the real issues. Specifically, that Turing Machines, Lambda Calculus and the Chomsky hierarchy are great solutions to Less Important Problems, and we would be far better off dissing Math and starting over from something like Wolfram’s cellular automata.
I have a marvelous proof of this, but alas it is too long to fit in a blog comment. :-) Email me at ernest.prabhakar@gmail.com if you’re interested!
My experience (US-centric as it is) is much closer to Ernest's. It's not that everyone whips out their math SAT scores to show off how smart they are, or that companies hire you based on how you did on your AP Calc exam though; it's that there's a strong association with "math people" and "smart people." Someone who's a very good historian, or a clever lawyer, or a great therapist typically isn't seen as inaccessibly smart as someone who's a mathematician. It's like a low key rocket scientist - there's almost a connotation to math where it's seen as hard and done by smart people.
So in that, even among the faculties at elite universities, doing hard math has signal value (that may or may not be valid, but is there). As someone else commented, econ has been tilting more mathematical for a while. Though part of that may be because it's more scientific or whatever, the bigger reason seems to be that doing hard math is a form of showing off. People do it for clout that comes with it.
Benn, I think the argument is flawed, as you noted upfront - it was a tough one to defend. Math is hard, and it continues to be exponentially hard when you think about probabilities, equations which deal with sequences, waves and patterns. I was never great at Math, but always above average. From personal experience I can tell you that without math the introduction to Data structures would've been tough, quant would've been tough and physics would've been tough too - particularly mechanics and thermodynamics.
More than that, I think the purpose of a field of study cannot be reduced to the flavor of the decade from an employment perspective and its utility in our jobs alone. As hard math is, its harder to find enough people who will be long term interested in pursuing the field further. It's a sampling problem, if you show the subject to 1MM maybe 10 will be keen to further the field. Without the focus that Math receives, it will be dead under the weight of $'s that young people make solving simple linear algebra through python functions (not easy I admit).
And for the pure progress of the field, let's keep solving.
So I don't disagree that math can be very hard, and that it's useful to keep pushing the boundaries of the field. But my question would be, if you're not someone who's interested in pushing to the edge of field, and do just want a job that pays you some money, is there that much point in learning all of it? Some pieces, sure, but even for data jobs that are ostensibly math jobs, I'm skeptical that any college level math is that applicable. Sure, they "teach you how to think" and they make you more quantitatively comfortable. But it feels like we value the hard math for reasons that go a lot beyond that.
To put it another way, I don't disagree that math is useful and good. My question is entirely around how valuable it is relative to how valuable we act like it is.
Love this post Benn! Like Dave I have a son in college - he loves sports statistics, showing his analysis in Tableau, and is learning R. But he has HATED the fact that the stats curriculum is so math-heavy - he would rather learn data-science tasks like data cleansing, statistical summaries, and how to communicate his analysis to others.
Thanks Josh! And I've obviously got a bias here, but I think doing something like writing a blog, even if very rarely, in which you do analysis on some subject you're interested in is a huge help. By finding a data question you actually want to answer, rather than one that you're answering for the sake of doing the work, people typically push much further than they would with a toy problem. It's in that phase, where you say "wait, that's weird, what about this?," that I think people learn the most. Plus, if it's something you're interested in, you're also trying to interpret the results, and figure out what they mean qualitatively. And that's a much richer version of the job than working with dummy datasets to solve dummy math problems.
Being highly numerate doesn't serve that much daily data practitioners - we all agree. But maths help a lot to comfortably think in guesstimates and understand a problem/solution space.
Imo, that's where maths really shine.
Moreover, there is something full-filling to understand the common underlying concepts between all problems and systems (which maths bring 99% of the time).
I think that's fair, ish. On one hand, I agree from my own experience - reasoning through math problems definitely provides a lot of indirect training for reasoning through other problems, and in a way that's surely useful. On the other hand, I'd imagine a lot of other fields (philosophy, history, the law, etc) would say the same thing. So I'd think math "provides a way to think," but I'm not convinced that it's necessarily a better way than other disciplines.
Good point on other disciplines - probably confirmation bias here, but I tend to think math as a less anthropological field than philosophy, history, litterature, etc. Explaining why it's so powerful to step back on problems.
Anyway, it's not about comparing fields with each other (as you said other fields bring so much thoughts and mental models) and being curious and learning widely is neither about math nor a consequence of it.
On your first point, one other thing that someone said is, unlike other fields, math arrives at the same answer. So, while everything teaches you "how to think" or whatever, only in math (and the sciences, I guess) do those different ways of thinking arrive at the same conclusion.
I'm not really sure what to make of that, but seems like an interesting point.
And this is probably why nothing will ever really change here - at this point, the hierarchy has become self-reinforcing that nothing will ever emerge as an alternative.
“ever” is a long time :-) From my perspective, the hierarchy had a great run, but is starting to collapse under its own weight. It’s a matter of when, not if. Which means the real challenge is creating new tools that embody the right values BEFORE that happens...
I agree that if we did have good data visualisation courses that built skills over a number of years, then those people would likely be well suited for roles as analysts. Maths is a long term learned skill, like music, art, and writing. Most buzzword courses are weeks or months long at most. They are not long term, difficult, or challenging…and I suspect knowledge is not always well retained. I know people who are good musicians who are very capable analysts, but I’ve seen many more fail, for their inability to understand and grow in the field.
I hire people into data roles, from many backgrounds, but I find those with a maths/science/eng background pick things up faster, and grow in the role quicker. Those without are still capable but they find it much more challenging.
Is that because they know math though? (That's a real question.) Someone else messaged me about this post and said they disagreed because math teaches you logic and how to reason. Which I think is a fair criticism - you probably do get more comfortable in thinking in certain ways by studying math. I don't think other fields don't teach that too, but everything has their own bent. So it's not math per se that's all that valuable, but the way of thinking it encourages.
I think that’s right! I deleted a whole paragraph around how maths helps you understand functions, logic and fitting things together creatively. Things like nesting functions in excel come much easier to those that have covered similar concepts in maths.
I often joke that most advanced maths I used as an analyst was revenue growth…but even this simple equation needs rearranging- and we see students starting science degrees not even knowing how to rearrange equations (let alone economics or commerce)!
Benn, great post. My degree at UCLA was in economics and, as a tech CTO, I've used my skills in logic, reasoning and writing infinitely more than math. I have 2 sons pursuing a career in computer science and I take issue with their math-heavy curriculum. Our industry's over-rotation on math discourages a whole population from considering a career in CS and under prepares those who do for life in the real world.
Great point Dave. An analogy that just came to mind is transfer learning. A technical major may feel comfortable with many data tools, as concepts repeat. In addition, a coziness in playing with different ways of solving the same task leads to faster evolution of tools and best practices. Without a sound technical foundation I observe less ease and longer onboarding times.
My point: The more fundamental the education, the easier appears transfer learning for a technical specialisation to me. I would welcome a playful approach to teaching math, improving its image.
Thanks. And yeah, I think your last point is the one that I really wish we could fix. By branding things as highly technical, a lot of people don't even look at analytics jobs because "they aren't computer or math people." But they have all of the other (much more valuable, much rarer) skills.
Benn, excellent article; one which describes how I arrived in math from a desire to be a history professor. My parents were convinced that I would starve in my desired profession, and they had the means to enforce their beliefs. By my SAT and National Merit scores (there used to be separate tests), I was equally competent, and proved to be so. They were, sadly, correct! Far better to explain the outcomes of relatively simple math to those who were afraid of symbols, than to change an engineer's mind, even (maybe especially) when they were wrong. I can now enjoy my retirement in the knowledge that I can figure out a plausible answer to current problems/questions across a broad spectrum, and have the ability to see the flaws in the arguments of the many poltroons and idealogical statisticians among us. And I am still prepared to learn from real experts. Including about fishing and cooking.
As one of those poltroons and idealogical statisticians, please don't read this blog too closely, and gloss over the many flaws in its arguments. For I am not yet retired, and have to keep up the illusion of being a real expert for a little while longer.
Once again, Benn does a fantastic job of roasting himself and barbecuing our sacred cows. Great sequel to last week's post!
Hmm, when you put it that way, my career prospects might need to reconsider my editorial strategy.
I'm a mathematician (MS in applied math) turned data scientist. The biggest benefit to me of going further in math wasn't learning the "advanced methods." It was everything else: how to structure an argument; the humbling experience of often being wrong; the importance of definitions and clear terminology; and, yes, written and verbal communication, because I had to teach a course, write papers, and give presentations.
I hope I'm not guilty of the gatekeeping you warn about here, because I know the other person has expertise that I don't. There isn't one discipline to rule them all. Everyone has something to bring to the table.
Although, if you try to abuse math words to sound smart or win an argument...I will catch you lol
That seems to be the rough consensus in the pro math camp - it's not about the math per se, but the various things around it that make it worthwhile. Which, I can mostly see? My guess is that applies to other fields too, but I'm sure math has its own unique advantages there too.
Wow! That entire section "Shape Rotators sell words"
https://benn.substack.com/i/95079164/shape-rotators-sell-words
That's really awesome and yes, I'm guilty of using math-y jargon as rhetoric thus the vibe to convince people as well.
Only when it's done to me, do I realize something's off.
Thanks! I absolutely love this article (https://www.vulture.com/2020/02/spread-of-corporate-speak.html), and want a full sequel to it about our math jargon. One day, one day.
have you been reading Heidegger, Benn? 👀
https://www.thecollector.com/martin-heidegger-science-cannot-think/
“The predominance of measurable exploitability marks the current reign of technology that Heidegger abhorred. The German philosopher holds that we have become unable to appreciate beauty and wonder in the world. Everything, including us, is perceived as potential input to industrial production.”
I haven't, but this dude sounds like he'd be in the trailing comma club.
https://mode.com/blog/should-sql-queries-use-trailing-or-leading-commas/#:~:text=Some%20might%20call,we%20contain%20multitudes.
Excellent post. It reminds me of a perceptive article by Paul Romer a few years ago of the perils of "mathiness" in economics (https://paulromer.net/mathiness/).
Paul Romer would not like this post: "Mathiness is a symptom of this deeper problem, but one that is particularly damaging because it can generate a broad backlash against the genuine mathematical theory that it mimics."
Paul Krugman periodically makes the same point (https://archive.nytimes.com/krugman.blogs.nytimes.com/2011/02/02/models-plain-and-fancy/), and is a big advocate of simple toy models instead of these really fancy ones. I think it's a good point, especially in non-scientific fields, where we're looking for directionally correct rather than exactly precise.
HBS to Math: “If I were married to you, I’d put poison in your coffee.”
Math to HBS : “If I were married to you, I’d drink it.”
Great writing Benn!
And all of us to HBS: We don't care what you do, here's $100,000 for a good party and lots of LinkedIn connections.
deeper topic hides here. What cultures is math useful for? If you're an Egyptian Pharaoh, your math skills (or even the math skills of your commanders) mean less than the sheer strength and numbers of your army. On the other hand, if you're in a former Soviet Union and you're building a train system that needs to support a hundred million people, math becomes very important.
What I think you're hinted at is not a world wide phenomenon, but a one centric to the United States tech. And maybe not the type of tech that gave us TCP/IP, Wi-FI, and Routers, but the kind of tech that gave us Facebook, Twitter, and (maybe even) Amazon. And here, if I can jump to some conclusions, finding a way to convince everyone that you're a modern version of Egyptian Pharaoh maybe played a bigger role than being good at Math. So, basically, high EQ coupled with engineering? But not Math.
But, again, this is a very US-centric argument. And as a counter argument, I can reference my own upbringing - a highly math-centric culture, in which businesses die or grow based on how well the math works out on the backend - and much less dependent on one's charisma, emotional EQ, etc.
Then there is a question of time. Math was much more important in the US 60-70 years ago, when there were massive country-wide construction projects going on (including Nuclear). Each mistake is catastrophic. Fast forward to today, and the math problems are about optimizing a Taxi's drive path. A complex problem, but one that, even if it fails, can be fixed with a refund, a customer support ticket, or a simple rebooking/retry.
The real question then is not whether Math is important universally. But is Math going to be important in the future, in the United States?
I think the hard question is whether we are willing to separate the very valid utilitarian function of good math, from the important yet problematic role of math skill as a cultural signifier of intelligence.
don't think Math has been that signal in the US for a long time (if ever). With the exception of maybe Wall Street, the popular signifiers for intelligence have been: PhD, University degree tier, Company/Job Combo, but not math on its own
You and I live in completely different realities. In my world, Math SAT is half the reason you get into a good colleges, advanced math classes in high school are the gateway to a technical degrees, and Computer Science is built around higher math. Would you disagree? Or do you claim that all that is purely for its utility?
I realize I sound like some sort of radical anarchist for suggesting we could fulfill all of those roles without any math beyond (at most) Algebra I. But that’s kinda the point...
Don't disagree because the majority of college admission tests are evaluating not someone's Math skills, but ability to prepare for the tests. The difference being maybe at the graduate level, where you do actually have to be good at Math on GREs.
Sciences/CompSci are built around higher math at Universities - as they should be. Universities, at their founding were not meant to be Vocational training schools. If the goal is to teach kids to write code, then there are community colleges where Algebra 1 is enough.
In the context of jobs, as someone who had a 98% on most Math exams, who had studied Statistics in graduate school, etc, I can tell you that the industry cares a lot less about Math than it seems. And someone with a PhD in Theology, with virtually no Math skills, can get just as far up in a career related to Data or Analytics.
And I agree that most Data roles can be filled with Algebra I math. However, someone's willingness to study beyond Algebra I signals significant interest in Data. And this very signal is maybe what we're all after.
So, it sounds like you agree Math SAT is useless on other grounds, but feel Math is a valid signal for data analysis, and a genuine utility for computer science. Is that a fair summary?
To your first point: yes, it is a “useful” signal, but I hope you would agree that it is possible (and perhaps even socially desirable) to find a better one. Right now, I feel there is a religious attachment to math that makes it impossible to even have a rational discussion about alternatives.
Secondly, I am precisely arguing that Math is the wrong basis for Computer Science, for roughly the same reason: it gives us a superficial sense of rigor without directly addressing the real issues. Specifically, that Turing Machines, Lambda Calculus and the Chomsky hierarchy are great solutions to Less Important Problems, and we would be far better off dissing Math and starting over from something like Wolfram’s cellular automata.
I have a marvelous proof of this, but alas it is too long to fit in a blog comment. :-) Email me at ernest.prabhakar@gmail.com if you’re interested!
My experience (US-centric as it is) is much closer to Ernest's. It's not that everyone whips out their math SAT scores to show off how smart they are, or that companies hire you based on how you did on your AP Calc exam though; it's that there's a strong association with "math people" and "smart people." Someone who's a very good historian, or a clever lawyer, or a great therapist typically isn't seen as inaccessibly smart as someone who's a mathematician. It's like a low key rocket scientist - there's almost a connotation to math where it's seen as hard and done by smart people.
So in that, even among the faculties at elite universities, doing hard math has signal value (that may or may not be valid, but is there). As someone else commented, econ has been tilting more mathematical for a while. Though part of that may be because it's more scientific or whatever, the bigger reason seems to be that doing hard math is a form of showing off. People do it for clout that comes with it.
Benn, I think the argument is flawed, as you noted upfront - it was a tough one to defend. Math is hard, and it continues to be exponentially hard when you think about probabilities, equations which deal with sequences, waves and patterns. I was never great at Math, but always above average. From personal experience I can tell you that without math the introduction to Data structures would've been tough, quant would've been tough and physics would've been tough too - particularly mechanics and thermodynamics.
More than that, I think the purpose of a field of study cannot be reduced to the flavor of the decade from an employment perspective and its utility in our jobs alone. As hard math is, its harder to find enough people who will be long term interested in pursuing the field further. It's a sampling problem, if you show the subject to 1MM maybe 10 will be keen to further the field. Without the focus that Math receives, it will be dead under the weight of $'s that young people make solving simple linear algebra through python functions (not easy I admit).
And for the pure progress of the field, let's keep solving.
So I don't disagree that math can be very hard, and that it's useful to keep pushing the boundaries of the field. But my question would be, if you're not someone who's interested in pushing to the edge of field, and do just want a job that pays you some money, is there that much point in learning all of it? Some pieces, sure, but even for data jobs that are ostensibly math jobs, I'm skeptical that any college level math is that applicable. Sure, they "teach you how to think" and they make you more quantitatively comfortable. But it feels like we value the hard math for reasons that go a lot beyond that.
To put it another way, I don't disagree that math is useful and good. My question is entirely around how valuable it is relative to how valuable we act like it is.
Love this post Benn! Like Dave I have a son in college - he loves sports statistics, showing his analysis in Tableau, and is learning R. But he has HATED the fact that the stats curriculum is so math-heavy - he would rather learn data-science tasks like data cleansing, statistical summaries, and how to communicate his analysis to others.
Thanks Josh! And I've obviously got a bias here, but I think doing something like writing a blog, even if very rarely, in which you do analysis on some subject you're interested in is a huge help. By finding a data question you actually want to answer, rather than one that you're answering for the sake of doing the work, people typically push much further than they would with a toy problem. It's in that phase, where you say "wait, that's weird, what about this?," that I think people learn the most. Plus, if it's something you're interested in, you're also trying to interpret the results, and figure out what they mean qualitatively. And that's a much richer version of the job than working with dummy datasets to solve dummy math problems.
Hah! Agree so much. You reminded me of when I did this once, many years ago: https://tanzu.vmware.com/content/blog/pharts-a-proposed-metric-for-measuring-basketball-player-value
Reminiscent of a classic: https://www.reddit.com/r/baseball/comments/6vbg4z/we_need_to_talk_about_fartslams/
Great post Benn, thanks !
Funny because I wrote an article recently on why do we study maths (🖇️ https://medium.com/@benoit.pimpaud/why-do-we-study-mathematics-52d75d7fd049).
Being highly numerate doesn't serve that much daily data practitioners - we all agree. But maths help a lot to comfortably think in guesstimates and understand a problem/solution space.
Imo, that's where maths really shine.
Moreover, there is something full-filling to understand the common underlying concepts between all problems and systems (which maths bring 99% of the time).
Thanks!
I think that's fair, ish. On one hand, I agree from my own experience - reasoning through math problems definitely provides a lot of indirect training for reasoning through other problems, and in a way that's surely useful. On the other hand, I'd imagine a lot of other fields (philosophy, history, the law, etc) would say the same thing. So I'd think math "provides a way to think," but I'm not convinced that it's necessarily a better way than other disciplines.
Good point on other disciplines - probably confirmation bias here, but I tend to think math as a less anthropological field than philosophy, history, litterature, etc. Explaining why it's so powerful to step back on problems.
Anyway, it's not about comparing fields with each other (as you said other fields bring so much thoughts and mental models) and being curious and learning widely is neither about math nor a consequence of it.
On your first point, one other thing that someone said is, unlike other fields, math arrives at the same answer. So, while everything teaches you "how to think" or whatever, only in math (and the sciences, I guess) do those different ways of thinking arrive at the same conclusion.
I'm not really sure what to make of that, but seems like an interesting point.
As usual, Seth Godin says it best:
https://seths.blog/2023/01/build-a-new-one/
"Nothing much changes until someone cares enough to build an alternative."
And this is probably why nothing will ever really change here - at this point, the hierarchy has become self-reinforcing that nothing will ever emerge as an alternative.
“ever” is a long time :-) From my perspective, the hierarchy had a great run, but is starting to collapse under its own weight. It’s a matter of when, not if. Which means the real challenge is creating new tools that embody the right values BEFORE that happens...
If you figure out how to time that one, I got a check for you.
Sure: 2040+-5 years. Alas, not sure if a check will help, since that will also coincide with the collapse of money as we know it. :-) [FWIW, I came to that date independent of MIT https://medium.com/predict/2040-the-world-will-collapse-this-mit-computer-has-confirmed-it-5b038bec32db]
A can of beans and a space blanket, then.
I agree that if we did have good data visualisation courses that built skills over a number of years, then those people would likely be well suited for roles as analysts. Maths is a long term learned skill, like music, art, and writing. Most buzzword courses are weeks or months long at most. They are not long term, difficult, or challenging…and I suspect knowledge is not always well retained. I know people who are good musicians who are very capable analysts, but I’ve seen many more fail, for their inability to understand and grow in the field.
I hire people into data roles, from many backgrounds, but I find those with a maths/science/eng background pick things up faster, and grow in the role quicker. Those without are still capable but they find it much more challenging.
Is that because they know math though? (That's a real question.) Someone else messaged me about this post and said they disagreed because math teaches you logic and how to reason. Which I think is a fair criticism - you probably do get more comfortable in thinking in certain ways by studying math. I don't think other fields don't teach that too, but everything has their own bent. So it's not math per se that's all that valuable, but the way of thinking it encourages.
I think that’s right! I deleted a whole paragraph around how maths helps you understand functions, logic and fitting things together creatively. Things like nesting functions in excel come much easier to those that have covered similar concepts in maths.
I often joke that most advanced maths I used as an analyst was revenue growth…but even this simple equation needs rearranging- and we see students starting science degrees not even knowing how to rearrange equations (let alone economics or commerce)!