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How much math you need for programming (2014)

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Re: How much math you need for programming (2014)

#61

Post by wott »

enriquto wrote: post #48
mattbit wrote: post #28

> Now what does does a mathematician do? He tries to understand nature and uses mathematics as a language to do that. I would argue that this is wrong. That's what physicists do, not mathematicians. Mathematics is about abstract ideas, which can live regardless of nature or application. Physics instead is about understanding nature. Most physicists use mathematics to do that, but that's just for practical reasons. Th…

> I would argue that this is wrong. That's what physicists do, not mathematicians. Notice that many mathematicians would not agree with you, here (but probably, a majority would). As the mathematician V.I.Arnold famously said, "mathematics is a branch of physics where experiments are cheap". So, yes, in the minds of lots of mathematicians, what they do is precisely to study and understand nature.

I see mathematics as completely opposite to studying nature.

Mathematicians work on extremely simple objects as a basis. For example (since we're here), give them a 0 and 1, and they will spend 200 years building a whole theoretical world from that, an artificial system they will describe through thousands and thousands of pages of theorems, getting more and more complex as time goes.

Nature is an extremely complex system from the start. Trying to understand and describe it is not at all the same approach. You take a complex system (the complexity of the system is given, fixed externally by the nature) and try to simplify it.

You can see this difference in the software world too.

Mathematicians (CS) will build and favour the use languages which are based on a single simplistic axiom: "everything is a list" for the most famous example, "everything is a function" for others, and then you are supposed to build all the rest on those simplistic bases, and in practice that will mean twisting, bending, squeezing the problem world (i.e. the nature) to make it fit in your model.

On the other side, you have programmers, which will more often favour practical, pragmatical languages, which do not exhibit the clean regular, symmetrical simplicity of the former ones, but which are more adapted to describe a complex, irregular world.

Re: How much math you need for programming (2014)

#62

Post by MeinBlutIstBlau »

alkonaut wrote: post #24

You need all the math for the domain. If you are in engineering, games, DSP, ML, then that can be a lot . At the same time some developers can go a whole career without ever (knowingly) using a floating point number. They work with web sites/services/databases/apis etc. But developers should at least know basic calculus, logic, and what what you need to grok basic algorithms and data structures. That part of math isn…

I still fail to see how calculus relates to programming for what most people do. Web or not.

Re: How much math you need for programming (2014)

#63

Post by MeinBlutIstBlau »

throw6537 wrote: post #59
alkonaut wrote: post #24

You need all the math for the domain. If you are in engineering, games, DSP, ML, then that can be a lot . At the same time some developers can go a whole career without ever (knowingly) using a floating point number. They work with web sites/services/databases/apis etc. But developers should at least know basic calculus, logic, and what what you need to grok basic algorithms and data structures. That part of math isn…

Meh, disagree. A bunch of developers I know don't know the Pythagorean theorem but they are crazy good (developers). It completely depends on what your job requires you to do. For some developers to be great, they don't need even middle school math.

I agree with this 100%. Hard math rarely has a use outside of it's scope. How often are you really trying to simplify the cotangent multiplied by an arcsin? Sure people who deal with trigonometry do often. But that subset of people is even smaller than people who do geometry. I'd wager carpenters do more math on a daily basis than the average programmer.

Re: How much math you need for programming (2014)

#64

Post by _void »

mattbit wrote: post #28

> Now what does does a mathematician do? He tries to understand nature and uses mathematics as a language to do that. I would argue that this is wrong. That's what physicists do, not mathematicians. Mathematics is about abstract ideas, which can live regardless of nature or application. Physics instead is about understanding nature. Most physicists use mathematics to do that, but that's just for practical reasons. Th…

Sometimes I feel like software developers don't actually know the fundamentals of how the programs run, not taking into account all the math behind the algorithms, etc. Being good developer IMO is first understanding the system from ground up, second - understanding the domain and if it requires math, yes, you need to know that as well. Otherwise you can go on your whole career copy/pasting and using APIs/language features you have no idea how it's working.

Re: How much math you need for programming (2014)

#65

Post by coldtea »

mattbit wrote: post #28

> Now what does does a mathematician do? He tries to understand nature and uses mathematics as a language to do that. I would argue that this is wrong. That's what physicists do, not mathematicians. Mathematics is about abstract ideas, which can live regardless of nature or application. Physics instead is about understanding nature. Most physicists use mathematics to do that, but that's just for practical reasons. Th…

>I would argue that this is wrong. That's what physicists do, not mathematicians. Mathematics is about abstract ideas, which can live regardless of nature or application.

Regardless of nature of application, yes, but not so abstract otherwise.

Many mathematicians consider math to be more like physics, where you discover things, there is experiments, etc., than a mere axiomatic system where you invent things.

That was an increasingly popular idea about math in the 20th century (and haven't heard otherwise in the 21st).

Re: How much math you need for programming (2014)

#66

Post by alkonaut »

MeinBlutIstBlau wrote: post #62
alkonaut wrote: post #24

You need all the math for the domain. If you are in engineering, games, DSP, ML, then that can be a lot . At the same time some developers can go a whole career without ever (knowingly) using a floating point number. They work with web sites/services/databases/apis etc. But developers should at least know basic calculus, logic, and what what you need to grok basic algorithms and data structures. That part of math isn…

I still fail to see how calculus relates to programming for what most people do. Web or not.

I mean things like knowing simple polynomials, which ties into things like asymptotic complexity. Which has the word “asymptotic” in it. That basic.

Re: How much math you need for programming (2014)

#67

Post by coldtea »

mkl wrote: post #60
enriquto wrote: post #48

Earlier quoted context omitted.

> I would argue that this is wrong. That's what physicists do, not mathematicians. Notice that many mathematicians would not agree with you, here (but probably, a majority would). As the mathematician V.I.Arnold famously said, "mathematics is a branch of physics where experiments are cheap". So, yes, in the minds of lots of mathematicians, what they do is precisely to study and understand nature.

I am a mathematician. Nature is of no consideration whatsoever in some fields of maths. But nature or applications to it are the primary focus in many other fields of maths. In still others, nature would be a source of analogies, or applications of a few special cases, etc. Muddying the waters, some mathematicians would expand the definition of "nature" to include completely abstract ideas - anything that feels "disc…

>I am a mathematician. Nature is of no consideration whatsoever in some fields of maths.

It's not about actual nature (the universe etc) being into consideration.

It's about many mathematicians coming to see maths as exploration (physics-style) of a mathematical universe, so to speak, rather than a simple constructive process.

So, they come to see mathematics as a kind of physics in this regard, no in the sense that they concern themselves with the outside nature. But in that math work appears to them as exploring a natural landscape (just one made of patterns and numbers).

Re: How much math you need for programming (2014)

#68

Post by User23 »

st1x7 wrote: post #49
Traubenfuchs wrote: post #39

As a CRUD or frontend dev you should be able to know the numbers from -100 to +100. Modulo is a bonus. Anything else is not required for the majority of programming jobs/tasks. Yet beginners getting hazed and outsiders getting scared with CS/algodat and math is essential for keeping wages up and „normies“ away.

- there is a lot more to programming than CRUD and frontend - you're putting algorithms and data structures in the same basket as mathematics - algorithms and data strucutures are useful in pretty much any programming job including CRUD and frontend

Algorithms and data structures are mathematics.

Re: How much math you need for programming (2014)

#69

Post by alkonaut »

throw6537 wrote: post #59
alkonaut wrote: post #24

You need all the math for the domain. If you are in engineering, games, DSP, ML, then that can be a lot . At the same time some developers can go a whole career without ever (knowingly) using a floating point number. They work with web sites/services/databases/apis etc. But developers should at least know basic calculus, logic, and what what you need to grok basic algorithms and data structures. That part of math isn…

Meh, disagree. A bunch of developers I know don't know the Pythagorean theorem but they are crazy good (developers). It completely depends on what your job requires you to do. For some developers to be great, they don't need even middle school math.

I doubt Pythagoras would show up very often outside of domain problems, but basic logic and polynomials, logarithms etc shows up everywhere where you do algorithms and data structures.

Math is a language and a developer will get a code review explaining something using that language (complexity etc).

You can do without it but that doesn’t mean it’s a good idea not to simply know those things. It’s not years and years of math, it’s a tiny bit.

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