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The Math Myth

econlog.econlib.org

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Re: The Math Myth

#171

Post by sarchertech »

Ologn wrote: post #142
analog31 wrote: post #25

At my workplace, we have about 60 scientists and engineers. The author's observation is accurate, that most people never use math beyond Excel and 8th grade math. They also never use most of the theory that they learned in their science (including CS) and engineering educations. The typical career arc is to get through college, then sit down at a CAD workstation, or programming terminal, and forget all of your math a…

> When a math or theory problem arises, they take it to the resident "math person." When an obvious math or theory problem arises. I'm sure they run across problems that more advanced math can solve, or stumble into problems due to not knowing more advanced math, yet their lack of knowledge prevents them from even understanding they confront a math problem. Sometimes the problem is not what they know they don't know,…

This happens constantly to people who think they don't need CS to program. Something that should have been a 2 hour implementation of an algorithm invented in the 60s turns into a 2 week exercise in frustration.

Re: The Math Myth

#172

Post by JoeAltmaier »

morgante wrote: post #161
mamcx wrote: post #158

I think that in the pursuit of higher levels of understanding, some people miss what is even more important to know. Is better to have strong basic skills, than high-level skills. I was (supposedly) of the bests student of my college. However, terrible at math? Of course. My grandmother was able to do arithmetic in his head like nothing , yet I even have trouble with sum and rest. She only have 3 years of education a…

> They need to have strong, fluent understanding of the very basic (imagine if a developer can't perform without look basic list manipulations). Why? Basic arithmetic is almost entirely useless as a skill. Why should I spend my time learning something which computers will always be able to do more reliably and faster than me?

...so that you understand what it does. Else it will remain magic, and you may entertain other magical thinking as well. Like Astrology or Numerology or even that maybe you could win the lottery. Its important to have a good understanding at a very basic level of what math, statistics and physics are about.

Re: The Math Myth

#173

Post by superuser2 »

treehau5 wrote: post #157
Bahamut wrote: post #132

Earlier quoted context omitted.

There is more to math than just calculations, algebra, geometry, etc. Logic, and reasoning through choices & the effects of those choices are vital math skills as well, and for many people in math, they don't manifest until one takes a few rigorous proof-based classes, where one often sees new approaches to arriving at concepts they know, and how to properly get to a conclusion from a particular point. I wish these s…

For software engineers specifically -- every time you are coding formalized programmatic logic, you are using math. If you took a logics and proofs course, it would help you formalize logic better. Every time you write a "for" loop you are essentially using summations. There is a book called Concrete Mathematics and one of the primary authors is Donald Knuth, basically it's "Programmers math" and in my opinion, would…

>every time you are coding formalized programmatic logic, you are using math

Almost no one (outside of those who were friends with math majors) are actually familiar with the nature of proof-based mathematics. When you hold out "programming is math" the general public, policymakers, admissions offices, kids who might want to be programmers, etc. don't make the association to Analysis and Abstract Algebra, they make it to high school Algebra, Geometry, Algebra II/Trig, Precalculus, and (maybe, for the better kids at richer high schools) Calculus.

This has the effect of selecting programmers for their skill, patience, and diligence in executing the algorithms they're given. This is exactly backwards!

In my opinion, if you're looking for an analogy to a high school class, programming is chemistry. You're given a reasonable number of facts about the world, some lab and algorithmic procedures, and a problem. How to string together your intuitions, information, and procedures to arrive at an answer is entirely up to you.

Re: The Math Myth

#174

Post by morgante »

JoeAltmaier wrote: post #172
morgante wrote: post #161

Earlier quoted context omitted.

> They need to have strong, fluent understanding of the very basic (imagine if a developer can't perform without look basic list manipulations). Why? Basic arithmetic is almost entirely useless as a skill. Why should I spend my time learning something which computers will always be able to do more reliably and faster than me?

...so that you understand what it does. Else it will remain magic, and you may entertain other magical thinking as well. Like Astrology or Numerology or even that maybe you could win the lottery. Its important to have a good understanding at a very basic level of what math, statistics and physics are about.

I never said you shouldn't understand what it does. It's just that I think it's useless to drill on arithmetic.

I know very well what a computer is doing when I tell it to divide 188416 by 20148. That doesn't mean it's useful for me to be able to mentally do it.

Mental arithmetic is incredibly overvalued and useless as a skill, especially since it's largely uncorrelated with actual depth of mathematical understanding.

Re: The Math Myth

#175

Post by klunger »

Hmm, I agree that much of the higher level math is not required for engineering work that has extended math requirements for the engineering degree. However, at least for aerospace, it goes a bit beyond 8th grade algebra and excel.

I used to work as an aerospace engineer, doing trajectory analysis. We used high school trig and algebra, as well as first semester calculus pretty much all the time. But, I don't think any of the other required math classes for my aerospace degree were ever used (3 semesters calc, 2 semesters linear algebra, diff. eq, IIRC). I did end up using a fair amount of stats, which was not required for my degree, but really should have been.

Re: The Math Myth

#177

Post by jostmey »

Few people have to use calculus or advanced probability or number theory, but everyone relies on it. The article missed this point.

Need some examples? Public key cryptography, machine learning, physics simulations of the aerodynamic properties of an airplane. I could go on and on. Just because a vast majority of the population never has to think about how this stuff works does not imply that it is somehow useless. We would not be where we are today without all this mathematics.

Re: The Math Myth

#178

Post by kazinator »

lisper wrote: post #134
kazinator wrote: post #113

Earlier quoted context omitted.

> find a decimal representation of a number 0.99999999...1 This denotes the abstract idea that we take 0.999... (infinite number of 9's) and add another digit. This is no more or less abstract than 0.999... to begin with. 0.999... is a unicorn, and 0.999...9 is a unicorn with a pink ribbon on the tip of its horn.

> add another digit But you can't. All of the places where you might want to add a digit are already occupied by 9's.

So you're saying a countable infinity can be occupied, so that there is no room for one more.

You must then disbelieve concepts such as that the even integers can be put in 1:1 correspondence with all integers; i.e. that there are exactly as many even integers as there are integers.

Re: The Math Myth

#179

Post by tmptmp »

>>The second argument is the one I always hear around the mathematics department: mathematics helps you to think clearly. I have a very low opinion of this self-serving nonsense. In sports there is the concept of the specificity of skills: if you want to improve your racquetball game, don't practice squash!

The analogy with sports fails miserably and the author seems to not understand this. Math is a brain skill and we do need to apply brain to understand a given situation in a better manner, to abstract away some things and focus on some other things. So, if you expect someone to better understand complex situations, then you need them to have some knowledge of higher math.

One may ask where do you encounter such situations? Insurance, debates of fiscal policies, debates about racial biases and social structures, anything to do with modern finance, language structures, medical decisions. Take your pick.

So, if you have to do anything complicated in such social areas too, you need to have some knowledge of higher math.

Skills in sports are not of such versatile nature, hence the analogy fails.

Re: The Math Myth

#180

Post by analog31 »

mmmBacon wrote: post #149
analog31 wrote: post #25

At my workplace, we have about 60 scientists and engineers. The author's observation is accurate, that most people never use math beyond Excel and 8th grade math. They also never use most of the theory that they learned in their science (including CS) and engineering educations. The typical career arc is to get through college, then sit down at a CAD workstation, or programming terminal, and forget all of your math a…

Worked in HW design for 16 years and I've never seen a design that was done by trial and error. Usually lots and lots of simulation and calculation up front followed by a DOE (design of experiment) to provide insight in areas which are difficult or impossible to simulate well. It's most certainly not trial and error.

Thanks for mentioning that. My experience could be unique to the industry that I'm in, or even just to the places where I've worked.
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