Name: A Mathematician's Lament
ISBN: 9781934137178

A Mathematician's Lament

"One of the best critiques of current mathematics education I have ever seen."--Keith Devlin, math columnist on NPR's Morning Edition A brilliant research mathematician who has devoted his career to teaching kids reveals math to be creative and beautiful and rejects standard anxiety-producing teaching methods. Witty and accessible, Paul Lockhart's controversial approach will provoke spirited debate among educators and parents alike and it will alter the way we think about math forever. Paul Lockhart, has taught mathematics at Brown University and UC Santa Cruz. Since 2000, he has dedicated himself to K-12 level students at St. Ann's School in Brooklyn, New York.

What Hacker News says

Fr0styMatt88Sep 2026

I remember hating math from late primary school to all through high school. I never learned my times tables properly. They were just absolutely boring AF. What I didn't realize at the time though was that I basically set myself up for failure. When the basic building blocks are hard, everything else on top gets unnecessarily hard.

I remember reading Lockhart's Mathematician's Lament and loving it. I discovered that I actually liked math when I was able to let go of the "there is only one way to do things" and realize that math, in a sense, is 'made up but logically consistent' (notwithstanding the arguments about whether math is innate to the universe or invented by man, which I err more on the innate side -- I'm thinking of a slightly different concept here).

When I learn something, I always need to know the why. We were never taught that in school. "Just because" has never been a good enough answer for me in anything I want to learn. Learning about the history of the problems, why certain solutions came up as solutions and why they were needed in the first place made everything much more concrete for me.

I've been using ChatGPT over the last month or so to re-learn my times tables and basic arithmetic from the ground up. I had no idea what 'automaticity' was (I never developed it; I still would manually count simple multiplications in my head or on my fingers). I had never made the connection between algebra and arithmetic -- at least not deeply. In that you can manipulate arithmetic expressions just the same as algebraic ones if you want (72 - 37, you mean I can subtract 2 from both sides first to make the calculation easier?!?!).

Now I'm motivated though, because I know why I'm learning it. I can look at it with my adult brain. I guess it's a bit like the difference between a kid being forced to take piano lessons and an adult that's really motivated to learn and practice because they suddenly discover they want to play.

Oh and 3Blue1Brown is amazing!

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goku12Mar 2026

Agreed on all counts.

> They shouldn't teach calculus like they taught it to me and my peers. Basically we just one day started "differentiating" equations. We learnt a completely mechanical process.

I had a similar experience and it did ruin the fun in Calculus for me. It took me a long time to derive a bare-minimum mental model that I was satisfied with. It was at this point that I could 'feel' (imagine) how the general second-order linear differential equation (of two variables) works, without the need to 'calculate' or derive anything. This equation is the fundamental model for countless phenomena in the universe. It's such a shame, because that equation is easy to explain in words, without doing a single step of derivation.

Don't get me wrong. Formalism and rigor do have very important roles in Mathematics. But ignoring intuition and emphasizing formalism doesn't get you anywhere. Intuition isn't always right, but it shows you the 1000ft view of the problem when it does get it right. Formalizing the solution gets easier from there.

I have noticed that even professionals are taken by surprise when I convey the descriptive explanation. It shows how badly these things are taught. (I don't know if this is the situation everywhere.)

> The sooner this intuition is there the better. Then teach the maths.

Yes, that is exactly what I was suggesting. However, that 'intuition' is also part of Mathematics. Many practitioners call it the 'Mathematical sense', as opposed to common sense. You might have seen a rare few gifted individuals who find the correct answers to unintuitive and confusing problems (like the infamous Monty Hall problem) in their first try. They're employing this mathematical sense while the others revert to common sense. Who knows? Even you may be using it and surprising others without realizing it.

Unfortunately, our educational systems have reinforced this misconception that Mathematics is all about manipulating numbers and symbols (for many, even the idea about symbols are missing). This is a very sad situation that just sucks the life out of mathematics. A long essay (book) by Paul Lockhart, named 'A Mathematician's Lament' explains this problem splendidly.

PS: Funnily enough, I always struggled in and hated mathematics! Others were so good at applying long sequences of operations to get to the answer, while it was Chinese to me! (No offense intended here). But I was good at science. I relied on countless diagrams, tables, concept graphs, signal flow graphs, etc in place of equations and formulae to achieve this. I just converted them to equations and formulae whenever I needed to reproduce those. I thought, "Who needs mathematics when you can reason your way to the answer?"

It was close to the end of my formal education that I realized that every reasoning that I had done in my life was proper Mathematics! I had strong autistic traits and following numerous steps in sequence and in parallel was near impossible for me. But where I made up for that was in spatial intelligence. I had created book after book of Mathematics described in a visual language that I could digest. I didn't really hate mathematics. What I hated was the way in which it was taught and represented.

Learning Mathematics has become a whole lot easier and enjoyable after realizing it and embracing the fact that I needed my own ways of doing it. But honestly, I wish that so much time wasn't wasted in needless frustration.

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suranyamiDec 2024

“Measurement” by Paul Lockhart, of “A Mathematician’s Lament” fame.

This was recommended by the delightful and talented Tibees YouTuber.

A few pages in and I was absolutely hooked and ready to start proving geometric conjectures…

A truly amazing communicator and educator.

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sethpurcellNov 2024

Given the sentiment in these comments, I figure this crowd might be interested in the book "Measurement" by Paul Lockhart (the guy who wrote "A Mathematician's Lament")

He's of the opinion that math should be taught not as jumping through hoops for "reasons", but as an art, enjoyable for its own sake, and that this would actually produce more confident and capable thinkers than the current approach. (I think the argument applies to almost all education but his focus is just on math.)

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pbrowne011Sep 2024

Paul Lockhart's "A Mathematician's Lament" [1] is the work that inspired his book, "Measurement" [2], which this video covers. I've always enjoyed it as a portrayal of the yin and yang of mathematics, calculating equations vs. proving them. The American education system overindexes on calculations, which, as Lockhart points out, tend to drown out the deeper joy that comes with mathematics. It's fascinating to see the battle between rote calculation and discovery play out at all levels, from students who feel that they "don't get math", to former olympiad medalists who struggle in graduate school.

[1] https://www.ams.org/notices/201304/rnoti-p461.pdf

[2] A preview: https://www.hup.harvard.edu/file/feeds/PDF/9780674067349_sam...

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graemepAug 2024

I home educated my kids, from about eight or nine to 16. In the UK where 16 is an important point of change (end of compulsory school age, and its when children in schools a critical set of exams).

A few things from my experience.

To a large extent the early years of home education are an extension of the teaching parents do anyway.

As they get older it takes less of your time. Children need to learn, but you need to facilitate rather than teach and/or pay for tutors.

You will need a lot of books, obviously different books at different ages. There are good books on every subject and its far too early to start thinking about exactly what books you need to use.

I have found its best to focus on doing things that are enjoyable and create a love of learning rather than thinking about syllabus. A Mathematician's Lament by Paul Lockhart and How Children Fail by John Holt are well worth reading. Things like memorising times tables and long division do not matter. No one uses handwwriting much in adult life (although it does still need to be legible for exams).

Part time supplementing is very different from home education. IMO that is also just an extension of parentings.

Home education is incredibly flexible. My kids have done GCSEs/IGCSEs (those UK exams we take at 16 in schools) in a variety of subjects with a choice no one school can offer, and many that few schools offer at all: Latin, astronomy and classical civilisation.

You can also do a lot of non-academic stuff. Both my daughters could solder by the time they were six or seven because I built circuits with them. My older daughter is now doing a degree apprenticeship (she has a job and a salary and her tuition fees paid while studying - very good for daddy's wallet!) in electrical engineering. We both credit HE with developing her interest in a subject very few girls do - she was the only girl in her A level (UK exams done at 18 - roughly equivalent to US APs) electronics class.

Finally, I am very glad I decided to home educate, and it has worked out extremely well for my kids. I think they could have achieved the same in terms of grades at school, but not the love of learning nor the self-discipline that they got from HE.

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