As a mathamatician, I’m glad to see folks like Andrew Lih at Edge.org agreeing with me that calculus isn’t that important.
It’s easily the least applicable technical prereq distracting people from mastering the most in-demand branch of STEM: Computer Science. And although calculus obviously has some transferability to other fields, I’d argue that the transferability of calculus is lower than almost any other branch of mathematics you could name.
Sure, it’s an easy enough subject to teach. High school and college instructors know the curriculum well. And for a tiny minority of students, it’s an interesting abstract course to consume. But it’s mostly a weeder course… in a world where we could weed students with so much more generally valuable courses, like discrete math or computability.
I hope Computer Science programs start dropping calculus as a requirement and that high schools start focusing on more valuable higher math skills like discrete math, statistics, and linear algebra.
26 Responses to “All Math Isn’t Equally Worthwhile”
May 26
Maxim Kesinhttp://siags.siam.org/siagla/articles/Strang2001.pdf
May 26
Teresa GonczyYes! Statistics and discrete math would be much more relevant for most students.
May 26
Daniel BurfootI agree with this sentiment, but I wouldn’t want to use any software that was written by someone who couldn’t learn calculus. The “more is better” philosophy applied to software is going to lead us to a dark and terrible place.
May 26
Robert GrossI’m curious to know why you wouldn’t post Richard Loosemore’s comment. I would hate to think that your affiliation with the Machine Intelligence Research Institute has prejudiced you against what Dr. Loosemore has to say. I think he said something to the effect that your cheerleading of the dropping of calculus from school curricula is idiocy. I’d also hate to think that your blog is censorious in nature and that you simply shove any disagreements down the memory hole in an act of craven weakness and intellectual disingenuousness.
May 26
Maxim KesinDaniel, the problem is mostly with the imbalance on the path to learning, IMO. We’ll make get more math proficient people (including in calculus) if we do some calc+some other cool math vs. shoving 3 helpings of calculus down everyone’s throat.
May 26
tmosleyI never once found use for calculus in my career as a chemist (chemists only need to know how to count to 8), but I have found some of the concepts useful in trading. Really all you need to know is the relationships between first and second derivatives, and that integration gives you the area beneath a line. That gives a sort of fundamental understanding of the relationships between different indicators. But it is pretty worthless for the vast majority of people, I will agree.
May 26
Steven GrimmI have thought for a long time that the public interest would be far, far better served by statistics than by calculus or geometry as a mandatory high-school subject. Obviously some aspects of statistics require calculus but there’s a lot you can usefully cover without it. Basic knowledge of statistics is a critical bullshit-mitigation skill in a democracy. Politicians and pundits rarely abuse the Pythagorean Theorem to try to manipulate public opinion.
May 26
Ankur PandeyTotally agree! Most High school & Freshman university systems in India follow a rather stringent Calculus curriculum. And minimal statistics. This has puzzled me for years.
May 26
Tony ZamoraIs outsourcing arithmetic to a calulator overall beneficial? Would outsourcing calculus to comp sci software be overall beneficial?
May 26
Artem LamninDifferential equations are pretty important to understand as a prerequisite for working in the engineering field (non-CS). Same for linear algebra. Integrals, probably less so, but there are plenty of formulas that cant really be taught without students knowing what an integral is.
May 26
Alex KawasClassical mechanics and microeconomics don’t make any sense without calculus.
May 26
Oliver MayorIn my adventures in school, I ended up sitting through an intro stats course several times. Each time, the major takeaways from the course were memorizing simplistic formulae and plugging them into calculators or Excel. They usually skimmed probability.
May 26
Artem LamninI took AP Stats in high school, and out of all math based subjects, it was easily the most uninteresting. Still, it is fairly applicable to non-CS engineering. Stuff like bell curves and correlation coefficients is pretty important to understand. Probability isnt IMO, unless you’re doing “design of experiments” or “game theory” type work.
May 26
Alex KawasCurriculum for stats is terrible. I love stats as a tool. I hated every class I took.
May 26
Steven GrimmI’m less interested in people learning specific equations and more interested in people learning the concepts of statistics, which can often be explained at a high level with little or no math. For example: knowing why it is that, if they don’t disclose the sample size, the results are likely worthless. Knowing that “average” is an imprecise word and that the person quoting an “average” statistic to you can choose either of two valid meanings with possibly very different results. Knowing how sample bias can affect the results.
There have been good, non-math-heavy books on statistics written for decades, e.g., “How to Lie with Statistics” (though that one in particular could use a new revision with less outdated examples). http://www.amazon.com/How-Lie-Statistics-Darrell-Huff/dp/0393310728
May 26
Louie HelmI agree that linear algebra would be better than statistics if you could wave a wand and get more of one than the other. Statistics is easier though and more applicable to more peoples’ lives. Maybe teach that in high school and then move on to linear algebra in college.
May 26
James Anderson MerrittSteven Grimm: I love “How to Lie With Statistics!” I agree that it needs some updating, especially to suit it to a high school math class, but that shouldn’t be too hard. I actually think that this should be taught in association with a Civics class, especially as our politics seems so driven by polls these days.
May 26
Miles ThomasAre you plugging linear algebra because it’s useful for machine learning? In terms of the end applications for which I could guess you think these things might be useful (FAI research, Bay tech job type thing), I could understand, say, logic, stats, probability, programming, comp. sci, etc. as directly useful. But while I could guess, I can’t think of a definite end application for which linear algebra is directly useful.
May 26
Kelly Hoverocerous MacNeillanecdote: I learned calculus in college because I was an engineering guy. I never used calculus once at any of my engineering jobs. I’m now a programmer and I find that my lack of intuitive understanding of higher level calculus concepts like PDEs and vector calculus is where I struggle the most when trying to implement techniques out of the research papers that I’m reading.
edit: though I do use linear algebra all the time.
May 26
richardstarrActually, Calculus as well as other maths that are possibly going to be utilized at some point by the computer scientist should, in my opinion, continue to be taught. It’s the stuff after that like matrix theory that should go in the crapper.
Perhaps it was just my teacher, but when I asked for a real world application so I could better wrap my mind around the concepts, they were not able to provide it to me. So, for me, it ended up being mostly a complicated “game” instead.
The reason why they teach higher maths is that in theory we might need to understand them to implement the data models some client (scientist/engineer) wants. I admit this likely made more sense back when computer scientists were a rarer breed, but I still think the exposure has value.
May 26
Carol JohnsonCalculus was necessary and important to Albert Einstein being the man who invented it. Nearly every piece of modern high tech equipment we strategically depend upon today was made possible due to all the gifted mathematics and physics he left us.
May 27
guywhodoesnotgetsarcasmEinstein did NOT “invent” calculus, functions of modern calculus have been around since the 17th Century and it was the British physicist and mathematician, Isaac Newton who developed the framework and formalized calculus, followed by Gottfried Liebniz who was first to publish. Einstein discovered the energy equivalence formula, which is really about mass and energy equivalence.
May 26
Joshua Daniel SchulterMiles, linear algebra provides a lot of useful tools for dealing with multidimensional arrays of data, and it comes up pretty frequently in data analysis, image processing, and a bunch of other places. It also helps to develop certain modes of thought which come in quite handy.
May 26
Louie HelmLinear algebra is directly useful for understanding quantum physics / quantum algorithms. Probably not important for FAI. But from a theoretical POV, quantum algorithm design is sorta the more fundamental form of algorithm design in a world made of quantum particles. So being able to understand it is the only way in principle to know what can and can’t be calculated at different efficiencies.
May 26
Richard BartonLinear algebra is great for graphics and visualizations.
May 27
Maxim KesinVladimir, “If you see a field of science relying heavily on statistics” – pharmacology?