Doing Math

What is Math? | Myths | Careers


What is Math?

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Myths about Mathematics

Below you will find a list of commonly held beliefs about mathematics and mathematicians which are false. Some are specific to the Harvard Math Department, and some are more general.

You need to be a "math person" to be good at math.
Mathematical thinking is a skill like any other; all that it takes to be good at it is practice. The more you do math, the deeper your understanding of the ideas will be. The idea that you can increase your understanding in any kind of learning is called having a "growth mindset," and having a growth mindset has been shown to increase achievement in math learning environments. To learn more about how to have a growth mindset, visit our Inclusive Classrooms webpage.
You need to be a "genius" to be REALLY good at math.
This is simply a more extreme version of our first myth. Similarly, the only thing it takes to be REALLY good at math is the willingness to devote lots of time and energy to understanding it. The more time you spend with mathematics, the more it will feel like a good friend who you know very well, but who can still surprise you.
There are fewer black and/or women mathematicians because they're not as good at it.
There are many ways to refute this myth. First and foremost you can find information about talented Black mathematicians on the websites Mathematically Gifted and Black, and Mathematicians of the African Diaspora. Looking through the biographies of these Black mathematicians, as well as biographies of many other women mathematicians of other races you start to see a trend of resistance to their presence in academia. Most of Black and/or women mathematicians throughout history, and still today, have experienced racism and sexism in the mathematical community, including protests at their hiring, being denied positions, denied pay, objectified, harassed, excluded, and being explicitly told that they don't belong. This doesn't even include the way systemic racism and sexism in our society pushes Black people and women away from STEM careers. This is also related to the previous two myths listed above. Rachel Bernstein published an article in Science explaining how the idea that "genius" is required to succeed in mathematics keeps women and Black people from pursuing a career in mathematics.
Regardless of ability level, white men were the major contributors to mathematics throughout history.
Mathematics has been created all over the world, and many times multiple civilizations and people were discovering the same ideas completely independently from each other. Even an idea as accepted as the number 0 was something which had to be thought of, and was done so all over the world, from the Babylonians to the Mayans. There are also ideas which are attributed to white men which have been shown to exist before they used it. There is evidence that Pythagoras' Theorem was in use by ancient civilizations in Mesopotamia, Egypt, India, and China well before the time of Pythagoras. There is no one type of person who has claim on the ideas in mathematics. It is a universal study and is open to contributions from everyone.
To be good at math means never making mistakes.
Mistakes are an essential part of learning and doing mathematics. Making, finding, and analyzing mistakes provides a deeper understanding in any kind of learning, than if you simply got it right initially. Mistakes prompt you to think about ideas for longer, more carefully, and from different perspectives. The goal should not be to avoid mistakes, but to dive into them.
In order to be a math concentrator at Harvard, you need to start in Math 25 or Math 55.
We have concentrators in the math department who began their mathematical career at Harvard in every class we offer, from Math M, to graduate classes. There is no one way to be a concentrator, and the department and concentration is open to any student who wants to participate.
In order to pursue math as a career, you need to start in Math 25 or Math 55.
Again, we have concentrators who have gone onto mathematical careers, including attending grad school for math or math education, who began at any level in our mathematical sequence.
Only people who have PhDs in mathematics are mathematicians.
Mathematics and mathematicians have existed as long as there have been humans. Only recently in human history have we even introduced the idea of a doctorate, and even then there have been plenty of important contributions to mathematics that have happened outside of that context. Pierre de Fermat made huge contributions to the fields of number theory and analytic geometry despite not having a a degree in mathematics. Srinivasa Ramanujan is another extremely influential mathematician without a PhD. However, one doesn't need to be influential to be a mathematician. Much like anyone who plays a musical instrument can claim the title musician, anyone who consistently engages in mathematical thinking is a mathematician.
Math requires only memorization, and no creativity.
Essentially the opposite is true! Tackling hard problems, doing research, and understanding concepts at a deep level requires a huge amount of creativity, curiosity, and persistence. Memorization comes in handy when learning the language of mathematics, inasmuch as memorization plays a part in learning any language. Even here, rote memorization is less useful than immersion and consistent usage for the purposes of gaining fluency.
You must be able to learn and do math quickly in order to succeed at it.
Most difficult problems, both in research and applications, are simply not solvable overnight. Many mathematicians work on problems for years, or even lifetimes! Perseverance and sustained attention are usually more relevant than speed. This is not to say that speed is bad or has no benefits, just that there are many paths to success.

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