How Not to Be Wrong Quotes

“I think we need more math majors who don't become mathematicians. More math major doctors, more math major high school teachers, more math major CEOs, more math major senators. But we won't get there unless we dump the stereotype that math is only worthwhile for kid geniuses.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“A basic rule of mathematical life: if the universe hands you a hard problem, try to solve an easier one instead, and hope the simple version is close enough to the original problem that the universe doesn’t object.”
― Jordan Ellenberg, How Not To Be Wrong: The Hidden Maths of Everyday

“Knowing mathematics is like wearing a pair of X-ray specs that reveal hidden structures underneath the messy and chaotic surface of the world.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“Improbable things happen a lot.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“Working an integral or performing a linear regression is something a computer can do quite effectively. Understanding whether the result makes sense—or deciding whether the method is the right one to use in the first place—requires a guiding human hand. When we teach mathematics we are supposed to be explaining how to be that guide. A math course that fails to do so is essentially training the student to be a very slow, buggy version of Microsoft Excel.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“Dividing one number by another is mere computation ; knowing what to divide by what is mathematics.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“A mathematician is always asking, “What assumptions are you making? And are they justified?”
― Jordan Ellenberg, How Not To Be Wrong: The Hidden Maths of Everyday

“One of the most painful parts of teaching mathematics is seeing students damaged by the cult of the genius. The genius cult tells students it’s not worth doing mathematics unless you’re the best at mathematics, because those special few are the only ones whose contributions matter. We don’t treat any other subject that way! I’ve never heard a student say, “I like Hamlet, but I don’t really belong in AP English—that kid who sits in the front row knows all the plays, and he started reading Shakespeare when he was nine!” Athletes don’t quit their sport just because one of their teammates outshines them. And yet I see promising young mathematicians quit every year, even though they love mathematics, because someone in their range of vision was “ahead” of them.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“if gambling is exciting, you’re doing it wrong.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“Genius is a thing that happens, not a kind of person.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“Mathematics is the extension of common sense by other means.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“Nonlinear thinking means which way you should go depends on where you already are.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“Math, like meditation, puts you in direct contact with the universe, which is bigger than you, was here before you, and will be here after you.”
― Jordan Ellenberg, How Not To Be Wrong: The Hidden Maths of Everyday

“One of the great joys of mathematics is the incontrovertible feeling that you've understood something the right way, all the way down to the bottom; it's a feeling I haven't experienced in any other sphere of mental life. And when you know how to do something the right way, it's hard-for some stubborn people, impossible-to make yourself explain it the wrong way.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“It is an old maxim of mine that when you have excluded the impossible, whatever remains, however improbable, must be the truth, unless the truth is a hypothesis it didn’t occur to you to consider.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“A math teacher’s least favorite thing to hear from a student is “I get the concept, but I couldn’t do the problems.” Though the student doesn’t know it, this is shorthand for “I don’t get the concept.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“The Pythagoreans, you have to remember, were extremely weird. Their philosophy was a chunky stew of things we’d now call mathematics, things we’d now call religion, and things we’d now call mental illness.”
― Jordan Ellenberg, How Not To Be Wrong: The Hidden Maths of Everyday

“In the Bayesian framework, how much you believe something after you see the evidence depends not just on what the evidence shows, but on how much you believed it to begin with.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“A reasonable person believes, in short, that each of his beliefs is true and that some of them are false.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“Mathematicians can be persnickety about logical niceties. We're the kind of people who think it's funny, when asked, "Do you want soup or salad with that?" to reply, "Yes.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“When you reason correctly, as Silver does, you find that you always think you’re right, but you don’t think you’re always right.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“Before the work of Georg Cantor in the nineteenth century, the study of the infinite was as much theology as science; now, we understand Cantor’s theory of multiple infinities, each one infinitely larger than the last, well enough to teach it to first-year math majors. (To be fair, it does kind of blow their minds.)”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“Safety warning: never divide by zero unless a licensed mathematician is present.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“It's not like that, as we've seen. Mathematicians aren't crazy, and we aren't aliens, and we aren't mystics.

What's true is that the sensation of mathematical understanding-of suddenly knowing what's going on, with total certainty, all the way to the bottom-is a special thing, attainable in few if any other places in life. You feel you've reached into the universe's guts and put your hand on the wire. It's hard to describe to people who haven't experienced it.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“But real-world questions aren't like word problems. A real-world problem is something like "Has the recession and its aftermath been especially bad for women in the workforce, and if so, to what extent is this the result of Obama administration policies?" Your calculator doesn't have a button for this. Because in order to give a sensible answer, you need to know more than just numbers. What shape do the job-loss curves for men and women have in a typical recession? Was this recession notably different in that respect? What kind of jobs are disproportionately held by women, and what decisions has Obama made that affect that sector of the economy? It's only after you've started to formulate these questions that you take out the calculator. But at that point the real mental work is already finished. Dividing one number by another is mere computation; figuring out what you should divide by what is mathematics.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“you never miss the plane, you’re spending too much time in airports.”
― Jordan Ellenberg, How Not To Be Wrong: The Hidden Maths of Everyday

“There are two moments in the course of education where a lot of kids fall off the math train. The first comes in the elementary grades, when fractions are introduced. Until that moment, a number is a natural number, one of the figures 0, 1, 2, 3 . . . It is the answer to a question of the form “how many.”* To go from this notion, so primitive that many animals are said to understand it, to the radically broader idea that a number can mean “what portion of,” is a drastic philosophical shift. (“God made the natural numbers,” the nineteenth-century algebraist Leopold Kronecker famously said, “and all the rest is the work of man.”) The second dangerous twist in the track is algebra. Why is it so hard? Because, until algebra shows up, you’re doing numerical computations in a straightforwardly algorithmic way. You dump some numbers into the addition box, or the multiplication box, or even, in traditionally minded schools, the long-division box, you turn the crank, and you report what comes out the other side. Algebra is different. It’s computation backward. When you’re asked to solve”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“Maybe individual people seem irrational because they aren’t really individuals! Each one of us is a little nation-state, doing our best to settle disputes and broker compromises between the squabbling voices that drive us.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“Outsiders sometimes have an impression that mathematics consists of applying more and more powerful tools to dig deeper and deeper into the unknown, like tunnelers blasting through the rock with ever more powerful explosives. And that's one way to do it. But Grothendieck, who remade much of pure mathematics in his own image in the 1960's and 70's, had a different view: "The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration...the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it...yet it finally surrounds the resistant substance."

The unknown is a stone in the sea, which obstructs our progress. We can try to pack dynamite in the crevices of rock, detonate it, and repeat until the rock breaks apart, as Buffon did with his complicated computations in calculus. Or you can take a more contemplative approach, allowing your level of understanding gradually and gently to rise, until after a time what appeared as an obstacle is overtopped by the calm water, and is gone. Mathematics as currently practiced is a delicate interplay between monastic contemplation and blowing stuff up with dynamite.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“Math gives us a way of being unsure in a principled way: not just throwing up our hands and saying "huh", but rather making a firm assertion: "I'm not sure, this is why I'm not sure, and this is roughly how not sure I am." Or even more: "I'm unsure, and you should be too.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking