Can You Succeed in Mathematics? Common Concerns Answered
Table of Contents
Introduction
We often see threads from new members asking whether they are cut out for mathematics, physics, engineering, or other technical fields. For some reason they become discouraged in high school and conclude they cannot succeed. I offer the following answers to common concerns.
1. My IQ Is Too Low
Understanding IQ concerns
This is a very common concern. High school students take an IQ test, dislike the result, and then argue that a score of only 110 (or similar) means they cannot succeed in mathematics.
Testing and limitations
First, IQ tests were originally devised to identify intellectual disability. A score around 60 or 70 may indicate the need for professional support, but IQ scores are not reliable measures at the high end.
Assessment advice
Avoid online IQ tests; they are unreliable. Only an assessment by a qualified professional should be treated as meaningful. Even then, the IQ number alone does not determine academic success. For example, I have been relatively successful in academia despite obtaining a score of 96 on an IQ test. If I can succeed, so can you.
Practice and persistence
Mathematics requires some natural aptitude, but above all it requires consistent, deliberate practice. If you can achieve decent results on math tests without excessive study, you are likely able to do well in university-level mathematics. Be prepared to work hard and to work smart.
2. I Struggle with Math Competitions
Competitions versus research
I struggled with competitions as well. I have always performed poorly in mathematics competitions and, somewhat ironically, did better in physics competitions despite understanding physics less well than mathematics. Your performance in timed contests is not a meaningful indicator of research or long-term mathematical ability.
Different skills required
Research mathematics rewards the ability to digest a problem slowly, examine it from multiple angles, and peel away layers carefully. This requires patience, sustained effort, broad knowledge, careful planning, and some luck. In contrast, competitions require solving several problems under strict time constraints. The two activities emphasize very different skills.
3. My High-School Results Were Low
Implications of low grades
Low high-school grades are a disadvantage because university places heavier and more frequent evaluation on students. If you were not strong in math tests in school, you will likely face greater challenges in a university setting.
Ways to improve readiness
However, low high-school results do not necessarily mean you are not cut out for university. Reflect carefully on what went wrong and which factors affected your results. You may need time to build readiness: re-taking foundational courses, pursuing targeted tutoring, or starting at a community college can all be sensible options.
Final Word
How to respond to obstacles
Throughout your career you will meet obstacles—everyone does. Some people encounter them earlier than others; some face more obstacles. What determines your development as a scientist is how you respond. Do you give up? That would be an understandable response. Not being willing to put in the effort to overcome an obstacle does not make you unintelligent, but it does mean you are not following the path scientists take.
Closing metaphor and resources
Scientists are those who repeatedly address obstacles. Like a river encountering a stone: the river yields, and slowly the stone is eroded until the river regains its path. Be the river.
Read my next article on dealing with doubt as a student.
Advanced education and experience with mathematics
I am not particularly intelligent, I don’t have any gifts for maths or physics and I am left bewildered at some of the discussions here. I have little understanding of what the formula mean or the terms used, but I enjoy my time here very much, and little by little I am learning. I am teaching myself as I have no other way of doing it, and the experience I have here is very positive.
I am driven by a crazy curiosity, physics fascinates me it’s like an endless rabbit hole, the further you fall, the more it delights and frustrates you. I’ll never come up with a theory or a breakthrough, never work in a lab but I will keep trying and keep learning.
This insight is very motivational, thank you.
“This is a pet peeve of mine, as well, especially when two occurrences of “it” in one sentence have different antecedents. For example, if a student says, “It converges because its limit is zero,” with the first it being “the series” and “its” referring to the general term of the series.
I’ve often advised students that they should use the word “it” in a math class only when what it refers to is crystal clear.”
Yes. This is the right kind of thinking. I came to the same understanding many years ago.
“If this is about post #15, he is just trying to be realistic based on the people he has met. Some people or students resist trying to learn, for whatever reason – they actively resist to learn. You find reactions like, “that was not the way I was taught”, or “this is too complicated”, or someone will refuse to draw a diagram or picture. Others…”
I was talking about the original post :smile:.
“I think there are people who innately lack the ability to use precise language. For example, there are people who seem to be infested with pronouns.”This is a pet peeve of mine, as well, especially when two occurrences of “it” in one sentence have different antecedents. For example, if a student says, “It converges because its limit is zero,” with the first it being “the series” and “its” referring to the general term of the series.
I’ve often advised students that they should use the word “it” in a math class only when what it refers to is crystal clear.
“That was motivating.”
If this is about post #15, he is just trying to be realistic based on the people he has met. Some people or students resist trying to learn, for whatever reason – they actively resist to learn. You find reactions like, “that was not the way I was taught”, or “this is too complicated”, or someone will refuse to draw a diagram or picture. Others…
That was motivating.
“Good suggestion. But is it something you have to have, or is it something you gain during your education?”
I think there are people who innately lack the ability to use precise language. For example, there are people who seem to be infested with pronouns. They say things like “I’ll get it done when they find it and he brings me the one that fits onto its other thing.”
As another example, I know a small number of people who are very capable at practical matters, but simply cannot write. I don’t mean that they write badly. I mean that when they need to write something, they face a “mental block”. They can’t start the process of writing.
There are people who reject formal presentations. For example, one encounters forum posters who take the view that they know what a certain mathematical object “really is” and reject formal mathematical definitions. I think such a person can be educated in mathematical formality if they can retain their enthusiasm for mathematics after they realize their limitations. However, I think the statistically most frequent result of a collision between education and a person who thinks they know how mathematical things “really” are is that the person either rejects the education or he understands the education and loses his enthusiasm for the subject because the subject is disappointingly different that what he expected.
“Not really. Most cashiers jobs you don’t need to work very hard or very smart. You can get by with a mediocre work ethic as long as you are honest and don’t steal any of the cash passing through your hands.
I worked a bit of retail in high school and college. I got mad when I figured out they kept putting me as a cashier because I wasn’t stealing from them. I liked the other jobs better. The most important lesson was to aim for a career where one had to offer a bit more than simply not stealing.”
“As a consumer, I see good cashiers who are honest (with me) and not-so-good cashiers that are honest. If we are discussing the standard as “getting by” then what would that mean when referring to science and math ?
All I’m suggesting is that there could be some explicit insights of the form “You need Y” to balance out those of the form “You don’t need X”. – Or perhaps the conclusion is that you don’t absolutely need any particular thing to succeed specifically in science or math ?”
Some or at least a few people in scientific careers who are not handling money are also dishonest. Usually a matter of social and personal deception for the purposes of gaining power and position.
“As a consumer, I see good cashiers who are honest (with me) and not-so-good cashiers that are honest. If we are discussing the standard as “getting by” then what would that mean when referring to science and math ?
All I’m suggesting is that there could be some explicit insights of the form “You need Y” to balance out those of the form “You don’t need X”. – Or perhaps the conclusion is that you don’t absolutely need any particular thing to succeed specifically in science or math ?”
You probably need at least an average intelligence to go along with a work ethic.
You’d be surprised how a good work ethic can make you smarter and smarter if you keep working hard in the educational process.
If you are interesting in “just getting by” pick another major.
“With the caveat that I’m not a guidance counselor, I think that to understand pure mathematics, one must have a tolerance for “legalism” – i.e. interpreting things exactly as they are written, splitting hairs, tolerating less ambiguity in statements that is normal in common speech etc.
”
Good suggestion. But is it something you have to have, or is it something you gain during your education?
“So what would be some of the things you need according to you?”
With the caveat that I’m not a guidance counselor, I think that to understand pure mathematics, one must have a tolerance for “legalism” – i.e. interpreting things exactly as they are written, splitting hairs, tolerating less ambiguity in statements that is normal in common speech etc.
I’ve encountered people who expect devices like cars, dishwashers and voltmeters to “just work” by themselves and become impatient and indignant when it’s necessary to fiddle with them. Can such a personality succeed in experimental science?
“As a consumer, I see good cashiers who are honest (with me) and not-so-good cashiers that are honest. If we are discussing the standard as “getting by” then what would that mean when referring to science and math ?
All I’m suggesting is that there could be some explicit insights of the form “You need Y” to balance out those of the form “You don’t need X”. – Or perhaps the conclusion is that you don’t absolutely need any particular thing to succeed specifically in science or math ?”
So what would be some of the things you need according to you?
“Not really. Most cashiers jobs you don’t need to work very hard or very smart. You can get by with a mediocre work ethic as long as you are honest and don’t steal any of the cash passing through your hands.
”
As a consumer, I see good cashiers who are honest (with me) and not-so-good cashiers that are honest. If we are discussing the standard as “getting by” then what would that mean when referring to science and math ?
All I’m suggesting is that there could be some explicit insights of the form “You need Y” to balance out those of the form “You don’t need X”. – Or perhaps the conclusion is that you don’t absolutely need any particular thing to succeed specifically in science or math ?
“Doesn’t that describe what you need to succeed in anything ?
”
Not really. Most cashiers jobs you don’t need to work very hard or very smart. You can get by with a mediocre work ethic as long as you are honest and don’t steal any of the cash passing through your hands.
I worked a bit of retail in high school and college. I got mad when I figured out they kept putting me as a cashier because I wasn’t stealing from them. I liked the other jobs better. The most important lesson was to aim for a career where one had to offer a bit more than simply not stealing.
” hard work, smart work, a little bit of talent, seeking the possible opportunities and taking advantage of them instead of letting them pass, good mental health, etc.”
Doesn’t that describe what you need to succeed in anything ?
Your insight encourages people who have studied science or math to some extent to persevere. That’s probably good advice for most people who frequent physicsforums. But if you imagine yourself in the role of a guidance counselor to a more general population, surely there are cases where you’d advise a person differently – or warn them that they need to change some mental traits if they want to continue.
Of course, “negative” advice is not always correct. One can cite cases like “X’s teachers told him he would never suceed in science, but he became a great ….”. However, there are also cases like “Y’s teachers told him he would never succeed in science career and he didn’t”. Perhaps the latter case is statistically more frequent – so frequent that it examples of it don’t become prominent.
“The insights focus on giving answers of the form: “Don’t worry about X, you can do well in (advanced) mathematics or science without having it”. What about some insights of the form “Worry about Y, you’ll have trouble in advanced mathematics or science if you don’t have it.” (?)”
I do believe I covered that implicitely. I didn’t want to put the focus on it though. But I’ve been very clear what you need to make it in the sciences: hard work, smart work, a little bit of talent, seeking the possible opportunities and taking advantage of them instead of letting them pass, good mental health, etc.
Excellent insight! As a high school student aspiring to be a physicist – there are often moments where I feel like giving up – it’s too hard for me , maybe I’m not smart enough! This post underlines most of what goes through our minds. Thanks :smile:
Good Insight. Majoring in math or science is more of a test of one’s perseverance and work ethic than anything else.
Are you a quitter when the going gets tough? Don’t bother. No matter how smart you are, the going will get tough.
The insights focus on giving answers of the form: “Don’t worry about X, you can do well in (advanced) mathematics or science without having it”. What about some insights of the form “Worry about Y, you’ll have trouble in advanced mathematics or science if you don’t have it.” (?)
A really good insight. Times are tough, competition is very high, through all fields and levels in science, so this justifies up to a point an easy discouragement; on the other hand the only viable way to succeed, is covered very well in the insight. And yes, it is very hard – if at all, to find a reliable IQ test on the net. The real IQ test, is done through high efforts and time spent to overcome the obstacles.
I am not particularly intelligent, I don't have any gifts for maths or physics and I am left bewildered at some of the discussions here. I have little understanding of what the formula mean or the terms used, but I enjoy my time here very much, and little by little I am learning. I am teaching myself as I have no other way of doing it, and the experience I have here is very positive.I am driven by a crazy curiosity, physics fascinates me it's like an endless rabbit hole, the further you fall, the more it delights and frustrates you. I'll never come up with a theory or a breakthrough, never work in a lab but I will keep trying and keep learning.This insight is very motivational, thank you.
That was motivating.