Jordan Ellenberg Quotes & Sayings

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

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

Public opinion doesn't exist. More precisely, it exists sometimes, concerning matters about which there's a clear majority view. — Jordan Ellenberg

Genius is a thing that happens, not a kind of person. — Jordan Ellenberg

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

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

Nobody ever looks in the mirror and says, "Let's face it, I'm smarter than Gauss." And yet, in the last hundred years, the joined effort of all these dummies-compared-to-Gauss has produced the greatest flowering of mathematical knowledge the world has ever seen. — Jordan Ellenberg

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

In 1931, Kurt Godel proved in his famous second incompleteness theorem that there could be no finitary proof of the consistency of arithmetic. He had killed Hilbert's program with a single stroke.

So should you be worried that all of mathematics might collapse tomorrow afternoon? For what it's worth, I'm not. I do believe in infinite sets, and I find the proofs of consistency that use infinite sets to be convincing enough to let me sleep at night. — Jordan Ellenberg

We become like those pious people who, over time, accumulate a sense of their own virtuousness so powerful as to make them believe the bad things they do are virtuous too. — Jordan Ellenberg

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

Mathematics, mostly, is a communal enterprise, each advance the product of a huge network of minds working toward a common purpose, even if we accord special honor to the person who places the last stone in the arch. — Jordan Ellenberg

A reasonable person believes, in short, that each of his beliefs is true and that some of them are false. — Jordan Ellenberg

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

One thing the American defense establishment has traditionally understood very well is that countries don't win wars just by being braver than the other side, or freer, or slightly preferred by God. The winners are usually the guys who get 5% fewer of their planes shot down, or use 5% less fuel, or get 5% more nutrition into their infantry at 95% of the cost. — Jordan Ellenberg

you never miss the plane, you're spending too much time in airports. — Jordan Ellenberg

Mathematics is the extension of common sense by other means. — Jordan Ellenberg

We tend to teach mathematics as a long list of rules.You learn them in order and you have to obey them, because if you don't obey them you get a C-.This is not mathematics. Mathematics is the study if things that come out a certain way because there is no other way they could possibly be. — Jordan Ellenberg

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

Suppose you have a group of fifty experimental subjects, who you hypothesize (H) are human beings. You observe (O) that one of them is an albino. Now, albinism is extremely rare, affecting no more than one in twenty thousand people. So given that H is correct, the chance you'd find an albino among your fifty subjects is quite small, less than 1 in 400,* or 0.0025. So the p-value, the probability of observing O given H, is much lower than .05. We are inexorably led to conclude, with a high degree of statistical confidence, that H is incorrect: the subjects in the sample are not human beings. — Jordan Ellenberg

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

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

Nowadays, the Abrahamic argument - just look at everything, how could it all be so awesome if there weren't a designer behind it? - has been judged wanting, at least in most scientific circles. But then again, now we have microscopes and telescopes and computers. We are not restricted to gaping at the moon from our cribs. We have data, lots of data, and we have the tools to mess with it. — Jordan Ellenberg

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

My reading practice is one reason I mostly don't read electronically. Different books are in different rooms of my house, and one is in my backpack. Physical location tells me what book to read. — Jordan Ellenberg

Big Data isn't magic, and it doesn't tell the feds who's a terrorist and who's not. But it doesn't have to be magic to generate long lists of people who are in some ways red-flagged, elevated-risk, "people of interest." Most of the people on those lists will have nothing to do with terrorism. How confident are you that you're not one of them? — Jordan Ellenberg

Safety warning: never divide by zero unless a licensed mathematician is present. — Jordan Ellenberg

we're not actually people at all, but simulations running on an ultracomputer built by other people. — Jordan Ellenberg

A mathematician is always asking, "What assumptions are you making? And are they justified? — Jordan Ellenberg

Improbable things happen a lot. — Jordan Ellenberg

Dividing one number by another is mere computation ; knowing what to divide by what is mathematics. — Jordan Ellenberg

He was unsweaty, undusty, and unbloody, but he was right. He was a critic who counted. — Jordan Ellenberg

if gambling is exciting, you're doing it wrong. — Jordan Ellenberg

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

Yes, the existence of human life is evidence for the existence of God; but it's much better evidence that our world was programmed by people much smarter than us. — Jordan Ellenberg

Cauchy was not interested in the needs of engineers. Cauchy was interested in the truth. — Jordan Ellenberg

Every time you observe that more of a good thing is not always better; or you remember that improbable things happen a lot, given enough chances, and resist the lure of the Baltimore stockbroker; or you make a decision based not just on the most likely future, but on the cloud of all possible futures, with attention to which ones are likely and which ones are not; or you let go of the idea that the beliefs of groups should be subject to the same rules as beliefs of individuals; or, simply, you find that cognitive sweet spot where you can let your intuition run wild on the network of tracks formal reasoning makes for it; without writing down an equation or drawing a graph, you are doing mathematics, the extension of common sense by other means. When are you going to use it? You've been using mathematics since you were born and you'll probably never stop. Use it well. — Jordan Ellenberg

There is real danger that, by strengthening our abilities to analyze some questions mathematically, we acquire a general confidence in our beliefs, which extends unjustifiably to those things we're still wrong about. — Jordan Ellenberg

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

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

This is a collaboration between a complex analyst, a dynamical system expert, and an arithmetical algebraic geometer. It sounds like a joke, a complex analyst, a dynamical system expert, and an arithmetical algebraic geometer walk into a bar ... — Jordan Ellenberg

What Secrist's findings really show is that businesses are much more like the cities in Wisconsin. Superior management and business insight play a role, but so does plain luck, in equal measure. — Jordan Ellenberg

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