Can anyone be good at math?

Miscellaneous General
1

I’ve recently considered pursuing a degree in one of the math, science, or engineering fields. I have a degree in economics, but I have never been strong in math. Although I do enjoy math, but I never had that “natural” talent. When speaking about my plans everyone keeps brining up “are you good at math?” As if math can’t be learned without some herculean effort.

What are your thoughts on this idea? I feel like it goes into the whole left brain vs right brain idea, which I have heard is erroneous.

2

I think that almost anyone can learn the math required to be an engineer (speaking as an engineer). It’s just like any other skill that must be learned. The reason that I feel many people state that they are “bad at math” is they simply don’t enjoy solving those types of problems.

If you don’t enjoy doing something, you’re certainly not going to spend much time learning that skill. Just like repairing cars, cooking, making music, or any number of other things, people tend to persue math if they enjoy it.

That’s not to say that people don’t have natural talent; they do. However, I think that most people have the ability to learn how to use the calculus, differential equations, and physics skills requried to be an engineer. If you like technology, tinkering, and figuring things out, I think it’s a great career.

3

I agree, I studied math at the end of my degree, best decision ever.

Personally, i think people just suck at teaching math and it discourages people from ever trying.

4

Have you observed it in others? Did you have math competitions at school?

5

Simply put like the other posters have said, if you enjoy it there’s no reason you won’t develop all the skills necessary. Practice has always been the secret to mastery in nearly any field- plus with all the resources splattered all over the internet to help you learn this kind of stuff, you have nothing but good luck on your side.

Natural “talent” in something like math is simply a bit of better intuition some people may have had while being involved in math that you haven’t yet. But throw yourself into solving enough problems, and it’ll all come to you naturally till everyone will start asking you how long you’ve had this “natural talent” in math.

6

I agree with the above poster who pointed out about enjoying learning and doing something as an important motivation. I don’t know if i’m a good example since I had a bit of a natural talent for maths as a kid, but this might have equally well been due to early exposure from my dad for both me and my sister(he typically taught us what we were to later learn at school 1-2 years in advance). My real interest in the subject came later though as a motivation to understand physics, and this allowed me to enjoy learning it at a higher level.

That being said, mathematical economics sometimes almost bores me to tears. I don’t think I would have liked maths as much if I had to learn it originally to do economics so I think I can sympathise with you on that. I wouldn’t say a lack of a formal background should necessarily be a barrier either. One of the econ Phds at my current university who most impressed me with his mathematical abillity had a history degree as his bachelors.

With tenacity and enthusiasm you can be unstoppable.

7

In high school I hated economics. Now, I love economics. I was considering doing a math minor, but decided it would add too much time to my undergrad studies and I’ve already wasted too much time as an undergrad (super super senior status). It’s a question of opening your mind and enjoying learning something new.

8

I agree, I studied math at the end of my degree, best decision ever.

Personally, i think people just suck at teaching math and it discourages people from ever trying.

I agree with this. I learned more math from studying the history and philosophy of math than I did in any of my math classes.

9

lol ditto, not that it is still anywhere near my radar of most thought about things. I think my aversion of all things math in school was that it wasbeing taught as a contextless abstraction.

Your better off learning music theory/ an insnturment, a second language, or logic.

10

"lol ditto, not that it is still anywhere near my radar of most thought about things. I think my aversion of all things math in school was that it wasbeing taught as a contextless abstraction.

Your better off learning music theory/ an insnturment, a second language, or logic. "

Interesting…i’ve played trumpet and guitar since i was 12, i speak french fluently, and love debate; makes sense.

11

I know for me, speaking as a college student majoring in Mechanical engineering, just finished my first year, that there is a vast difference in mathematical “skill/ability” among my classmates.

I was lucky and was able to take Calc I and II in high school, so I just finished Linear Algebra/Differential Equations this semester. But even at my school, people majoring in math- same degree as the math professors, are far and few between- my roommate is one of about 10 undergrads in the entire school of ~5000.

This does vary though as the actual math courses seem to be more involved of the why it is- although my LADE teacher just said it is what it is because it works for maintaining independence in the terms(by multiplying by ln(x) or x, based on the case. In my physics courses it seems more important that you can get from point A to the answer- the in between is up to you, especially as you can use a calculator there and in the math courses no calculator or formula sheets allowed- even with Laplace transforms.

This affects the students are there are some who seem to get the basic principles and fail to succeed in math, but succeed in the science side- I’ve been lucky/taught/self-taught just to power through the stuff.

12

im not a natural when it comes to math but find that solving something previously out of my reach to be greatly satisfying. my career in the field of laser and plasma tech i do a bit more math than im suited for. that being said… repetition works. repetition works. kahn academy on youtube helps.

13

That is so fascinating! Which book did you like the most? Your experience agrees with this article:

Final exams were coming, but I still could not afford the textbook for Botany 100…With nothing to cram from, I made my way to the library. But finding no botany texts in the stacks, I checked out the autobiography of Gregor Mendel, the “father” of genetics, whose field had been the major emphasis of Dr. Baker, my instructor.

So while my classmates were poring over the graphs and study questions in the textbook, I lay on my bed, reading about Mendel’s childhood illnesses, his interest in plants, and his stream of consciousness musings.

When I finally got to Mendel’s experiments growing green peas, I was pretty into it, having accompanied him on his “journey” since Day 1.

“You received a perfect score on the genetics section,” said Dr. Baker. “That’s never happened.”

I was no science genius. The D earned later in zoology confirmed that fact.

But acing the test made me wonder: Were textbooks necessary? Could students succeed while saving money, using free resources from the library, or from life?

14

Most math instruction and math books are obfuscatory. I have no idea why except, perhaps, that the teachers and authors themselves were subjected to obfuscatory mathematical instruction and never really grasped the subjects themselves and so they are just aping whatever they know for sure isn’t wrong.

My recommendation is that, in addition to your regular studies, you pick up a particular field of mathematics which has a strong foundation in intuition (say, Euclidean geometry or number theory or complex analysis, etc.) and then read old, out-of-print books on the subject form your university library, do the book problems and just generally tinker with the subject on your own until you feel you really have a grasp on it. Just don’t ever let it go, keep tinkering. I play with integer sequences, for example. They’re loads of fun and you can learn (maybe even discover) interesting things along the way. For example, I found an interesting fact about a certain kind of generalized Fibonacci sequences (turns out, it’s already been discovered but it’s a recent discovery!). The Fibonacci sequence is generated by beginning with 1, 1 and then adding the last two numbers to generate the next:

1, 1, 2, 3, 5, 8, 13, 21, …

If you wanted, you could also start with 1, 1, 1 and add the first and third of the last three numbers, like so:

1, 1, 1, 2, 3, 4, 6, 9, 13, 19, …

This is not a Fibonacci sequence but it looks a lot like one. I’ll call it the Fraggle sequence. One of the amazing facts about the Fibonacci sequence is that you can take the ratio of any two numbers and plot them and they tend toward a limit:

1/1, 2/1, 3/2, 5/3, 8/5, 13/8, 21/13, …

These fractions tend toward a number and the number to which they tend is… brace yourself… the Golden Mean!

1.61803

This number is often called phi (the Greek letter). One of the remarkable facts about phi is the following:

phin-1 + phin = phin+1

But this isn’t even the best part. The formal definition of the Fibonacci sequence is the following:

an-1 + an = an+1

Do you see the formal similarity between the Fibonacci sequence definition and the relation between powers of phi?

If you take the ratios of the Fraggle sequence, you will find that these ratios also tend to a number, slightly smaller than phi. I’ll call it frag. I haven’t formally proved this but I worked out numerically that the following is true of frag (it has been proven by someone else):

fragn-2 + fragn = fragn+1

Now here’s the coup de grace… look at the formal definition of the Fraggle sequence:

an-2 + an = an+1

And there are a whole class of numbers which conform to this pattern. In other words, for each sequence of the form:

an-k + an = an+1

… there is a real number x such that the following relation holds:

xn-k + xn = xn+1

This is a very remarkable fact to me since you are getting a real number from the ratios of an integer sequence with formal properties that mimic the formal definition of the original integer sequence! How cool is that!

Refs:

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/phi.html

http://oeis.org/A000045

Clayton -

15

My practical suggestions:

  1. Avoid using calculators as much as possible so you are forced to learn about prime numbers and calculating techniques

  2. Use common sense and substitute tiny numbers to help figure out limits and derivatives; don’t worry about logic or rigorousness. Accept Leibniz’s infinitesimal numbers, e.g. (x+dx)^2, where dx is an infinitesimal number, is equal to x^2+2xdx+dx^2. Since the latter term dx^2 is infintely smaller than the former terms, it can be discarded, leaving x^2+2xdx. Thus, if x increases by dx to become x+dx, then x^2 increases by 2x dx; the derivative is then 2x. Infinitesimals caused endless pointless quibbling until Robinson’s non-standard analysis put them on a firm footing anyway.

  3. Learn Taylor series as they are extremely useful.

  4. Learn the geometric series, 1/(1-x)=1+x+x^2+x^3+…

  5. Accept Euler’s divergent series, e.g.

1/(1-x)=1+x+x^2+x^3+…

Differentiating:

1/(1-x)^2=1+2x+3x^2+4x^3+…

Substituting x=-1 yields

1/4 = 1 - 2 + 3 - 4 + …

Another example; it was either Goldbach or Euler (I can’t remember) who computed the sum of the reciprocals of each number one less than a power

1/3+1/7+1/8+1/15+1/24+1/26+… = 1

and it can be proven easily using the divergent Harmonic series s=1+1/2+1/3+1/4+…

Mathematicians hate divergent series despite the best mathematicians ever (IMO) Euler using them like crazy. They are also used all the time in quantum field theory.

  1. Learn the Zeta function / Bernoulli numbers and the Euler-Maclaurin formula as it’s very useful for calculating
16

Math is not hard.

Everything else is ridiculously easy.

17

When people ask whether you’re good at math, 9 times out of 10 they really mean are you good at fractions, division and multiplication.

A lot of kids, and girls especially, totally lose interest in mathematics based on the way it’s taught in elementary education. By 3rd or 4th grade, being “good at math” is more of an insult than a compliment.

Anyone can learn even the most complex, established mathematics subjects. Formulating advanced theories is quite a bit more difficult, and takes real talent. The most important qualities for any student of mathematics are patience and persistence.

My impression of the mathematics as it’s taught and used in physics, engineering and especially economics is that it tends to be less rigorous in the proofs, and often skips over many steps in the process. But then my concentration was in mathematical theory where you were heavily penalized for skipping over such details. I can definitely see, however, how a student can get lost when their instructor doesn’t cover the complete proof. It left me with the impression than these physicists, engineering and economics students were getting short changed.

18

Scroge - Honestly, get a book called How to Prove it,

Read it, then decide

19

I find it to be an issue of context and usage. If you learn a foreign language then never speak it, your skills dimish and/or vanish. Likewise, if you speak to someone with a bizarre dialect, you may not understand them despite speaking the same language.

I studied BioChemistry. You use a great deal of algebreic manipulations and a fair amount of Calculus within that subject. I did very well in all of those classes, but when placed into my required maths, I barely passed and even failed a few times. Considering that my major required maths all the way up to Calculus III, I struggled for quite some time.

I found this product line at www.mathtutordvd.com and it literally changed the entire game for me. For $130 USD I purchased lessons all the way from advanced college algebra to Calculus III. The few months of self study with these exams has even me a superior education to what would have taken me 6 semesters in a university setting to aquire. I simply CLEP’ed through everything. I tried highly regarded books, private tutors, everything. These DVDs were like magic. I couldn’t more highly recommend them.

20

Good point. The greatest mathematicians of all time have been very comfortable using “non-standard” methods to arrive at conclusions that have taken years for the more “conservative” mathematicians to ground on the orthodox system (ZFC). There is this huge Aristotelean hang-up over working with “actual” infinities versus “potential” infinities which is precisely why Leibniz’s infinitesimals are considered “un-rigorous” even though there is nothing un-rigorous about them, which is essentially what Robinson’s non-standard analysis shows… if you rigorously define the concept of an infinitesimal and then manipulate it according to its algebraic rules, guess what, you get sensible answers that correspond to mainstream calculus with 1/10th the labor of taking the limit of everything and applying epsilon-delta arguments. There is a field of mathematics (large cardinal theory) that takes actual infinities as proper objects of discussion and manipulates them like any other mathematical object.

Another big hang up is on the concept of incompleteness. Mathematicians are still running around nearly a century after Godel proved the limits of formal systems acting like all we need is the “right set of axioms” and everything will just become clear. The reality is that no set of axioms will exhaust mathematical truth since there are always true mathematical statements which are not provable from a given set of axioms. Contemporary mathematician Gregory Chaitin has significantly extended Godel’s results to show that almost all true mathematical statements are not provable from a given set of axioms. A whole new field of mathematics (algorithmic information theory) has grown up around these results. But despite these well-established results, mainstream mathematicians (the analysis/group theory/topology types) continue to act as if the goal of mathematics is the search for the perfect set of axioms and, once these are found, mathematics will be “finished”, that is, it will be solved like the game of checkers. Godel, Turing, Chaitin and others have conclusively proved this is not true.

@baxter: If you’re not already familiar with them, take a look at p-adic numbers… divergent series are the norm there but the metric works out such that what would be divergent series in a standard metric converge… for example, 2^1+2^2+2^3+…+2^n = -1 (sum as n->oo) in 2-adic. I’m not finding enough online resources for p-adics so I’m going to have to buy a book. My interest in p-adics comes from my profession as a computer engineer… it turns out that truncated 2-adic numbers are precisely how we represent integers in the machine (also known as “2’s complement” in computer lingo) and there is something so compellingly elegant about these numbers that I just have to understand more about them.

Clayton -