Is it common for scientists to forget basic math?

[Simfish]

Basic math, such as...

Deriving the quadratic equation, taking the derivative of a logarithm in a base other than e, taking integrals of trigonometric substitutions, remembering what a subspace actually means, not remembering how to derive the general solution for a first order differential equation, etc..?

Of course, it's much quicker to do those things when you look back at them again (and you don't have to struggle to understand anything anymore). But still, sometimes I worry about my memory problems or something.

Is it even common for them to sometimes forget them multiple times? Like, forgetting to do it once, then forgetting to do it 4 years later?

 

[arunma]

I don't know about the average scientist, since I have no data on this. But despite having done none of these things. But I feel pretty confident that I could do any of the things you listed above either immediately or after reviewing for ten minutes or so. Actually on my field theory final last year, I got a differential scattering cross section which had a bunch of trigonometric terms, and I decided to integrate it by hand just for fun (it was a takehome, so time wasn't an issue). Didn't seem to have any problems there. But then, I was also a math major, so I spent a bit more time doing this stuff than your average physicist.

 

[bignum]

Yes, lol, just the other day I forgot it is okay to square both sides of an equation to solve. lol.

Derivatives and integrals are usually derived on top of their head probably. I do not htink everyone will remember all of them.

 

[winowmak3r]

I think it's natural to forget things you don't use very often or to have the occasional slip-up. I forget negative signs all the time. I'm not sure how often you're using what you mentioned but if it's not very often then I wouldn't worry about it. It's pretty human to have to dust off the cobwebs every once and a while and we all make mistakes, sometimes pretty silly ones.

 

[Pinu7]

My dad says that every math grad student forgets a big chunk of calculus sometime while working towards his PhD.

You could have forgotten some stuff due to stress. In this case, review some math a little bit using an old textbook/internet and take a little vacation.

 

[Landau]

Basic math, such as...

Deriving the quadratic equation, taking the derivative of a logarithm in a base other than e, taking integrals of trigonometric substitutions, remembering what a subspace actually means, not remembering how to derive the general solution for a first order differential equation, etc..?
Is it even common for them to sometimes forget them multiple times? Like, forgetting to do it once, then forgetting to do it 4 years later?

Yes, lol, just the other day I forgot it is okay to square both sides of an equation to solve. lol.

Well, yes: if you only remember the facts, and don't understand where they come from or why they are true, then you keep forgetting them. If you don't understand WHY you can square both sides of an equation, and are comfortable with some authority telling you "yes it is valid" without question, then in a year or so you'll have no idea again. If you don't understand why a subspace is defined as it is (or why it has the properties it has), you'll forget it again. Etc.
That's why you should alway ask "why", and derive every result yourself to the last detail. It takes a lot of time, but once you fully understand something, you will probably never forget it again.

Of course, details like the sum formulae for trigonometric functions are things you will forget if you don't use them regularly. That's ok, as long as you know how to derive them, e.g. using complex exponentials.

But as a math student, I may be biased.

a bunch of trigonometric terms, and I decided to integrate it by hand just for fun (it was a takehome, so time wasn't an issue). Didn't seem to have any problems there. But then, I was also a math major, so I spent a bit more time doing this stuff than your average physicist.

I'm pretty sure the average physics student spends more time integrating trigonometric function by hand than the avarage math student.

 

[bignum]

Well, yes: if you only remember the facts, and don't understand where they come from or why they are true, then you keep forgetting them. If you don't understand WHY you can square both sides of an equation, and are comfortable with some authority telling you "yes it is valid" without question, then in a year or so you'll have no idea again. If you don't understand why a subspace is defined as it is (or why it has the properties it has), you'll forget it again. Etc.
That's why you should alway ask "why", and derive every result yourself to the last detail. It takes a lot of time, but once you fully understand something, you will probably never forget it again.

Of course, details like the sum formulae for trigonometric functions are things you will forget if you don't use them regularly. That's ok, as long as you know how to derive them, e.g. using complex exponentials.

But as a math student, I may be biased.

I never mentioned anything about role-learning. I understand the concepts, but drawing them out takes a bit of effort. Besides, in school you just have to accept what they tell you unfortunately, if you spend too much time on the theories, you are going to lag behind and then get poor grades and you won't get into any university. You don't really have a choice (at least in my school)

 

[Landau]

You mentioned 'scientists', so I assumed you were talking about university. But ayway, my reply stays the same: if you understand the concepts (well), then you should have no trouble deriving the results, altough it may take some time to fill in the details.

If you do have trouble deriving the results, repeat: after a month, test yourself again. Also, focus on the main idea. For example, in deriving the solution to the quadratic equation, there's only one word you have to remember: completing the square. The algebraic details are not important, you only need to know this 'trick' works.

\\edit: I now realize bignum is not the same person as OP :)

 

[Shackleford]

I never mentioned anything about role-learning. I understand the concepts, but drawing them out takes a bit of effort. Besides, in school you just have to accept what they tell you unfortunately, if you spend too much time on the theories, you are going to lag behind and then get poor grades and you won't get into any university. You don't really have a choice (at least in my school)

That's true in physics and probably even more so in engineering. We just have to accept things mathematicians discover and apply them, for the most part. However, if you work on a math minor, as I am, you kind of get to see somewhat the world of mathematicians, which is largely not a computational world. My vector analysis professor liked to just start deriving formulas from first principles in class when he couldn't recall something off the top of his head.

 

[Acut]

I usually forget.
That's why it's always more interesting remembering how to derive things instead of the equations itself.

 

[bignum]

You mentioned 'scientists', so I assumed you were talking about university. But ayway, my reply stays the same: if you understand the concepts (well), then you should have no trouble deriving the results, altough it may take some time to fill in the details.

If you do have trouble deriving the results, repeat: after a month, test yourself again. Also, focus on the main idea. For example, in deriving the solution to the quadratic equation, there's only one word you have to remember: completing the square. The algebraic details are not important, you only need to know this 'trick' works.

Actually I am going for a double major math and physics, so I know where you are coming from when you say people just accept what they learn. It happens all the time, but the build up from high school forces people to do so, it is not really our choice. Look at me for instance, my grades suck because I spend all my time building intuitions (going beyond the curriculum) instead of following what the curriculum sets for us and I lag behind (I know this is very difficult to understand). For quadratics, I am a very lazy person, I just plug it into my graphic calculator and solve, lol.

 

[Hurkyl]

Yes, lol, just the other day I forgot it is okay to square both sides of an equation to solve. lol.

Just to emphasize what everyone has been saying about learning the "why"... did you remember that squaring both sides can introduce new solutions that aren't solutions to the original equation?

 

[bignum]

Just to emphasize what everyone has been saying about learning the "why"... did you remember that squaring both sides can introduce new solutions that aren't solutions to the original equation?

Not sure what you meant, but when i thought about it, I went back to the definition of squaring. Multiplying the number by itself to both sides, but obviously I am introducing two new numbers which aren't equal on both sides. I ended up multiplying it by its conjugate.

Is that you meant?

 

[Hurkyl]

A lot of algebraic manipulations to equations are "reversible" -- for example, adding equations:

Theorem: if "a=b", then the two equations "c=d" and "c+a=d+b" have the same solution set​

Other operations aren't reversible -- squaring is one of them. We have the following theorem:

Theorem: Any solution to "a=b" is a solution to "a²=b²"​

but not the following:

NotATheorem: Any solution to "a²=b²" is a solution to "a=b"​

For example, x=1 has only one solution for x, but x²=1 has two solutions for x.


Most operations you can do to an equation are not reversible, but most the most useful one are -- e.g. adding a constant, or multiplying by a non-zero constant. The operations of multiplying by a variable or squaring are notorious, because they aren't reversible, and beginners tend to forget. e.g. many 1=0 "proofs" involve trying to reverse one of those operations.

 

[Shackleford]

A lot of algebraic manipulations to equations are "reversible" -- for example, adding equations:

Theorem: if "a=b", then the two equations "c=d" and "c+a=d+b" have the same solution set​

Other operations aren't reversible -- squaring is one of them. We have the following theorem:

Theorem: Any solution to "a=b" is a solution to "a²=b²"​

but not the following:

NotATheorem: Any solution to "a²=b²" is a solution to "a=b"​

For example, x=1 has only one solution for x, but x²=1 has two solutions for x.


Most operations you can do to an equation are not reversible, but most the most useful one are -- e.g. adding a constant, or multiplying by a non-zero constant. The operations of multiplying by a variable or squaring are notorious, because they aren't reversible, and beginners tend to forget. e.g. many 1=0 "proofs" involve trying to reverse one of those operations.

In the second theorem couldn't you view the additional a and b on their respective sides as an "instantaneous constant"? And so that's why it's reversible? I hope that makes sense.

 

[mal4mac]

Well, yes: if you only remember the facts, and don't understand where they come from or why they are true, then you keep forgetting them. If you don't understand WHY you can square both sides of an equation, and are comfortable with some authority telling you "yes it is valid" without question, then in a year or so you'll have no idea again. If you don't understand why a subspace is defined as it is (or why it has the properties it has), you'll forget it again. Etc.
That's why you should alway ask "why", and derive every result yourself to the last detail. It takes a lot of time, but once you fully understand something, you will probably never forget it again.

Of course, details like the sum formulae for trigonometric functions are things you will forget if you don't use them regularly. That's ok, as long as you know how to derive them, e.g. using complex exponentials.

But as a math student, I may be biased.

I'm pretty sure the average physics student spends more time integrating trigonometric function by hand than the avarage math student.

When do you ever fully understand something? Russell spent a hundred pages of his Principia proving that 1+1=2, and people very much question his proofs. So even if you went as far as deriving everything as far down as far as Russell for every part of mathematics, you would still never fully understand the mathematics you use. Rememeber Socrates - we know *nothing* (not exactly, not fully). Physics students need only go through "Maths for Physicists" not read a book case full of equivalent Pure Maths books. They don't have to prove everything, what are Mathematicians for?! You forget things you fulkly understand anyway. You fully unsderstand simple French sentences, like "The sun is setting over the library". One timne you could perhaps translate this, but you can't now (I bet!) Or history dates. Knowing the date *is* understanding it, but I bet you forgot a whole pile of them.

 

[Klockan3]

Every baby understands 1+1=2, not being able to prove it from a given set of axioms do not mean that you do not understand why it is true.

Btw, you don't understand what understanding means...

You fully unsderstand simple French sentences, like "The sun is setting over the library".

That is not what you mean by understanding in maths. Understanding a language means that you memorized the words, understanding maths is very different from memorizing formulas. You understand parts of maths once everything becomes so clear that it you intuitively feel that it can't possibly be in any other way.

And when you learn a language well enough so that you think in it rather than translating to yourself you will never forget it.

 

[MathematicalPhysicist]

Every baby understands 1+1=2, not being able to prove it from a given set of axioms do not mean that you do not understand why it is true.

Btw, you don't understand what understanding means...

That is not what you mean by understanding in maths. Understanding a language means that you memorized the words, understanding maths is very different from memorizing formulas. You understand parts of maths once everything becomes so clear that it you intuitively feel that it can't possibly be in any other way.

And when you learn a language well enough so that you think in it rather than translating to yourself you will never forget it.

It's true by definition, so what there is to understand in 1+1=2?
For me I+I=II is more intuitive than 1+1=2.

 

[Klockan3]

It's true by definition, so what there is to understand in 1+1=2?
For me I+I=II is more intuitive than 1+1=2.

II=2 by definition...

And the reason mathematicians try to prove it in elaborate ways is because they want an as slim axiom system as possible.

 

[MathematicalPhysicist]

Didn't say otherwise, though I don't see anyway that proves it, even in the notion of set theory you don't prove it, I mean you define the natural numbers from adding to the empty set itself and a set that contains the empty set and such etc, just another way to look at it, it doesn't prove it thought.
How can you prove a definition?

 

[Shackleford]

Didn't say otherwise, though I don't see anyway that proves it, even in the notion of set theory you don't prove it, I mean you define the natural numbers from adding to the empty set itself and a set that contains the empty set and such etc, just another way to look at it, it doesn't prove it thought.
How can you prove a definition?

Good point. You can't prove a definition. A definition is an abstract set of parameters and conditions. Mathematics works within definitions and seeks to also describe something in any different number of ways. That's something that my recent vector analysis professor could do - explain or prove things in several different ways right off the top of his head.

 

[twofish-quant]

When do you ever fully understand something? Russell spent a hundred pages of his Principia proving that 1+1=2, and people very much question his proofs.

The trouble with this sort of intuitive understanding is that it's a wonderful way of doing physics, but a rotten way of doing certain types of maths.

It turns out that the hard part of Russell's proof that took several hundred pages was to proof that addition was well defined. That given the definition of addition, that you would always be able to add two numbers and get an answer and you could add two numbers in different ways that give you two different answers.

If you just write the set theory definition of addition and the set theory definition of natural numbers, then showing that 1+1 *can* equal 2, is something that will take you three lines. What will take you several hundred pages is to prove that 1+1 can *only* equal 2.

 

[twofish-quant]

II=2 by definition...

And the reason mathematicians try to prove it in elaborate ways is because they want an as slim axiom system as possible.

And they also want a consistent axiom system. Yes you *can* define things, but it's not obvious whether or not your definitions conflict with each other.

 

[arunma]

I'm pretty sure the average physics student spends more time integrating trigonometric function by hand than the avarage math student.

Well I was a wimpy math major. I got away with taking the calculus sequence, some advanced calculus and linear algebra, numerical methods, and a course that was called "algebra" but contained no algebra. My math advisor, unaware that I had no plans of going to graduate school in math, actually commented that my high grades would do me no good because I was taking all weak classes.

But now that you mention it, I'd say that most of the math I know, I learned in physics. Granted I don't use it too often in grad school, but whatever.

 

[Hurkyl]

Also, AFAIK, Russell, more or less, proved that 1+1=2 was a consequence of formal logic, which is a radically different statement than 1+1=2 is a consequence of arithmetic. (The latter being nearly trivial -- many settings take that as the definition of 2)

 

[Jerbearrrrrr]

(@arunma) That isn't even an option in some universities.

I still don't know my times tables. I was always on the slower side of my class with them too, actually. 4*8 still gets me...well, 4*8 is okay but not 8*4, god forbid.
Going off on a tangent now (it's okay guys, I checked that this topic was on a differentiable curve...well at least differentiable at this point here) I kind of think long division is a good personality test for kids haha (just remembering my time back in year 4 when no one could apply the algorithm). It's not hard, but it certainly sorts out the...patient from the rest.

 

[Girlygeek]

This is why I have been keeping my old math and science textbooks, as well as some very handy sparkcharts as quick references when doing homework. I fully intend for them to be available to me when I get a job, too, though I would also probably be able to find the answer on the internet. The human mind can become cluttered and if you aren't using something on a regular basis it will certainly fade!

 

[Abraham]

@ Jerbearrrrrr

Wow, I thought I was the only one afflicted with that. Odd. I routinely screw up on 4*8 or 8*4 too (and write anything from 24, 36, 21...)

 

[Shackleford]

Yeah, that damn commutativity of scalar multiplication is quite befuddling! lol.

 

[mal4mac]

1 + 1 = 2 doesn't work in cloud algebra...

 

[Shackleford]

1 + 1 = 2 doesn't work in cloud algebra...

What's cloud algebra? lol.

 

[dmatador]

Yeah, that damn commutativity of scalar multiplication is quite befuddling! lol.

Nobody said those numbers are from a field! Maybe they are just from plain old Z. What a horrible joke! Jokes.