Home > Author > Jordan Ellenberg

1 " 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

2 " 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

3 " 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. "

4 " The more chances you give yourself to be surprised, the higher your threshold for surprise had better be. If a random Internet stranger who eliminated all North American grains from his food intake reports that he dropped fifteen pounds and his eczema went away, you shouldn’t take that as powerful evidence in favor of the maize-free plan. Somebody’s selling a book about that plan, and thousands of people bought that book and tried it, and the odds are very good that, by chance alone, one among them will experience some weight loss and clear skin the next week. And that’s the guy who’s going to log in as saygoodbye2corn452 and post his excited testimonial, while the people for whom the diet failed stay silent. "

5 " Dividing one number by another is mere computation ; knowing what to divide by what is mathematics. "

6 " A statistically significant finding gives you a clue, suggesting a promising place to focus your research energy. The significance test is the detective, not the judge. <...> If a result is novel and important, other scientists in other laboratories ought to test and retest the phenomenon and its variants, trying to figure out whether the result was a one-time fluke or whether it truly meets the Fisherian standard of “rarely fails.” That’s what scientists call replication; if an effect can’t be replicated, despite repeated trials, science backs apologetically away. The replication process is supposed to be science’s immune system, swarming over newly introduced objects and killing the ones that don’t belong. "

7 " You can't write a sonnet if you have to look up the spelling of each word as you go. "

8 " Improbability, as described here, is a relative notion, not an absolute one; when we say an outcome is improbable, we are always saying, explicitly or not, that it is improbable under some set of hypotheses we've made about the underling mechanisms of the world. "

9 " The ultimate reason for teaching kids to write a proof is not that the world is full of proofs. It's that the world is full of non-proofs, and grown-ups need to know the difference. It's hard to settle for a non-proof once you've really familiarized yourself with the genuine article. "

― Jordan Ellenberg , Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else

10 " Недостатньо того, щоб дані узгоджувалися з вашою теорією; вони мусять не узгоджуватися із запереченням вашої теорії "

11 " Often people think of developments in computation as arising when we make our computers more blazingly fast, so they can compute more stuff, bigger data. It's actually just as important to prune away big parts of the data that aren't relevant to the problem at hand! The fastest computation is the one you don't do. "

12 " 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. "

13 " Knowing mathematics is like wearing a pair of X-ray specs that reveal hidden structures underneath the messy and chaotic surface of the world. "

14 " Improbable things happen a lot. "

15 " 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. "

16 " if gambling is exciting, you’re doing it wrong. "

17 " A mathematician is always asking, “What assumptions are you making? And are they justified? "

18 " 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. "

19 " Genius is a thing that happens, not a kind of person. "

20 " 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. "