Is Math Real?
Eugenia Cheng
Basic Books, $30
Every mathematician has a story that goes something like this. You’re at a party, and someone asks what you do for a living. “I’m a mathematician,” you say. “You must be a genius!” they reply. Or perhaps you end up being an impromptu therapist to someone who needs to vent about traumatic experiences they had in math class decades ago.
Mathematics is treated with both reverence and fear: People often see math as an objective, apolitical tool that can buttress or refute arguments, but they also feel intimidated and anxious when they think they might have to use it.
Mathematician Eugenia Cheng has spent much of her career working to alleviate those anxieties. As scientist in residence at the School of the Art Institute of Chicago, she teaches mathematics to artists, many of whom have never seen themselves as “math people.” She has also written several books, for both adults and children, that seek to cultivate mathematical curiosity and illustrate some of the ways mathematical thinking can enrich our lives. Her latest, Is Math Real?: How Simple Questions Lead Us to Mathematics’ Deepest Truths, demonstrates the ways that seemingly naïve questions can unlock fascinating journeys to understanding math for math’s sake, rather than purely in service of real-world applications.
Math has a reputation for supplying concise, black-or-white answers to questions. Getting straightforward math questions right or wrong is often presented as the litmus test of whether someone has mathematical ability. But that view of math is simplistic, Cheng explains. Rather than a tool for obtaining objective right answers, math is a method for asking questions and exploring the possibilities those questions raise.
Students are naturally curious about numbers and patterns, but math classes often teach them that math facts should be accepted without question. For instance, a student might learn that a prime number is defined as a whole number — a positive number without a fractional or decimal part — that is only divisible by itself and 1. The number 1, however, is not considered a prime number. If a student asks why not, they will likely be told it just isn’t; deal with it.
But in fact, there is a good reason to exclude 1 from the prime numbers. As Cheng describes, the prime numbers are the multiplicative building blocks of the whole numbers; every whole number greater than 1 can be broken down as a product of prime numbers. Because multiplying by 1 doesn’t do anything to a number, 1 isn’t needed to build the other whole numbers, at least when multiplication is considered. (For addition, it’s a whole different story.) Excluding 1 from the primes allows us to break every whole number greater than 1 down into a product of primes in only one way — 12 is the product of two copies of 2 and one copy of 3, for example, and cannot be broken down into any different set of primes. If 1 were a prime number, those products would no longer be unique. You could toss any number of 1s into the mix and still get the same product.
Mathematicians have found the uniqueness of these products useful for exploring properties of numbers, so they came to the consensus not to include 1 in the primes about a century ago. Considering the reasons mathematicians define primes precisely the way they do is more interesting than simply accepting the definition so you can get an A on a math test.
The prime number example is just one of many simple questions that Cheng poses in the book to motivate deep dives into the logical foundations of Western mathematics: Why does 1+1 = 2? Why does −(−1) = 1? Why does 2+4 = 4+2? And, yes, is math real? Cheng’s answers to those questions touch not only on our understanding of mathematics itself, but also on her personal experiences with math education as both student and teacher.
She also examines how mathematical thinking intersects with life within and outside of the classroom, from the subtle imperialism of the commonly used Mercator map projection, which inflates the perceived size of countries that were colonialist powers, to the parallels between open-mindedness to new mathematical ideas and open-mindedness to the experiences of marginalized groups in society.
Is Math Real? will help readers understand the questions that drive mathematicians and encourage people to see the value of math in their own lives.
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FAQs
Her latest, Is Math Real?: How Simple Questions Lead Us to Mathematics' Deepest Truths, demonstrates the ways that seemingly naïve questions can unlock fascinating journeys to understanding math for math's sake, rather than purely in service of real-world applications.
Is math real Dr. Eugenia Cheng? ›
Is Math Real? is a much-needed repudiation of the rigid ways we're taught to do math, and a celebration of the true, curious spirit of the discipline. Written with intelligence and passion, Is Math Real?
Is math a fact or truth? ›
However in these statements maths doesnt make any definite statements of truth. It simply extrapolates what must be true on the condition of things that cant be proven to be true or false. Thus math cant ever truly claim anything to be true absolutely.
Are mathematical truths absolute? ›
Absolutetrue statements do exist. We find them, for example, in mathematics. Althoughthere are mathematical theorems, which are not absolute true, nonetheless somemathematical theorems depend neither on the time nor on the place or culture. Therefore, there are the absolute, invariable, objective truths in mathematics.
What degrees did Eugenia Cheng have? ›
BA, 1997, University of Cambridge; MMath, 1998, University of Cambridge; PhD, 2002, University of Cambridge. Books: How to Bake Pi, Basic, 2015; Beyond Infinity, Basic, 2017; The Art of Logic in an Illogical World, Basic, 2018.
Who is the smartest math guy? ›
Carl Gauss (1777-1855)
Isaac Newton is a hard act to follow, but if anyone can pull it off, it's Carl Gauss. If Newton is considered the greatest scientist of all time, Gauss could easily be called the greatest mathematician ever.
Why is 3x 1 unsolvable? ›
In the 3x+1 problem, no matter what number you start with, you will always eventually reach 1. problem has been shown to be a computationally unsolvable problem.
What's the hardest math to learn? ›
The most difficult math type is typically abstract mathematics. Abstract mathematics is a branch of mathematics that deals with abstract concepts, such as sets, groups, and rings. Abstract mathematics is very challenging because it requires students to think abstractly and reason logically.
How do we know maths is real? ›
We don't know if mathematics is true. But we're sure that the mathematical facts we know are consistent and therefore provides an infallible yardstick against which theories and observations in other sciences can be compared.
What is math dyslexia called? ›
Dyscalculia is a learning disorder that affects a person's ability to do math. Much like dyslexia disrupts areas of the brain related to reading, dyscalculia affects brain areas that handle math- and number-related skills and understanding.
Maths is innate
Shapes that can be seen repeatedly in themselves (never-ending patterns) are called Fractals. They exist in nature ranging from macroscopic to microscopic observations as rivers, coastlines, mountains, clouds, plants, snowflakes, lightning strikes, seashells and even blood vessels.
Is maths a universal truth? ›
Others argue that mathematics is a universal and exists independently of human consciousness and that we merely discover and uncover its truths. There is no one “correct” answer to this question, and different people may have different perspectives on it depending on their beliefs and experiences.
What is a mathematical truth that can be proven? ›
In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems.
What are mathematical truths that are accepted without proof? ›
Axioms and postulates are essentially the same thing: mathematical truths that are accepted without proof. Their role is very similar to that of undefined terms: they lay a foundation for the study of more complicated geometry.
Is math even a real book? ›
All that abstraction prompts some to wonder: Is math even real? Mathematician Dr. Eugenia Cheng has heard this question many times over her career. The quandary is the basis of her latest book, Is Math Real?: How Simple Questions Lead Us to Mathematics' Deepest Truths.
What is math lady real name? ›
The meme is known as “Math Lady” or also known as “Confused Lady”. The “lady” is, in fact, Renata Sorrah who is playing a character from the telenovela “Senhora do Destino”, a popular show in Brazil.
Is everyday math evidence based? ›
Everyday Mathematics is the most research-grounded and field-tested elementary mathematics program available today.
Who is the worlds best math teacher? ›
Anil Khare stands head and shoulders above the rest as the best mathematics tutor in the world. His extensive knowledge, exceptional teaching methodology, and dedication to his students have positively impacted the mathematical journeys of over 5000 individuals worldwide.
