Borislava Grkovic > Borislava's Quotes

“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

“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

“It's not wrong to say Hilbert was a genius. But it's more right to say that what Hilbert accomplished was genius. Genius is a thing that happens, not a kind of person.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“who spends himself in a worthy cause; who at the best knows in the end the triumph of high achievement, and who at the worst, if he fails, at least fails while daring greatly, so that his place shall never be with those cold and timid souls who neither know victory nor defeat.”
― Jordan Ellenberg, How Not To Be Wrong: The Hidden Maths of Everyday

“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

“If you’ve ever run an experiment, you know scientific truth doesn’t pop out of the clouds blowing a flaming trumpet at you. Data is messy, and inference is hard.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“Excellence doesn’t persist; time passes, and mediocrity asserts itself.*”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“Mark Twain is good on this: “It takes a thousand men to invent a telegraph, or a steam engine, or a phonograph, or a telephone or any other important thing—and the last man gets the credit and we forget the others.”
― Jordan Ellenberg, How Not To Be Wrong: The Hidden Maths of Everyday

“It’s not always wrong to be wrong.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“What can I say? Mathematics is a way not to be wrong, but it isn't a way not to be wrong about everything. (Sorry, no refunds!) Wrongness is like original sin; we are born to it and it remains always with us, and constant vigilance is necessary if we mean to restrict its sphere of influence over our actions. 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. 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.

I'll do my best to resist the temptation. But watch me carefully.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“Don’t talk about percentages of numbers when the numbers might be negative.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“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

“0.33333. . . . .= 1/3. Multiply both sides by 3 and you’ll see 0.99999. . . .= 3/3= 1.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“You can't write a sonnet if you have to look up the spelling of each word as you go.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“To do mathematics is to be, at once, touched by fire and bound by reason.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“torturing the data until it confesses,”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“That’s how the Law of Large Numbers works: not by balancing out what’s already happened, but by diluting what’s already happened with new data, until the past is so proportionally negligible that it can safely be forgotten.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking

“If something is true and you try to disprove it, you will fail. We are trained to to think of failure as bad, but it's not all bad. You can learn from failure. You try to disprove the statement one way, and you hit a wall. You try another way, and you hit another wall. Each night you try, each night you fail, each night a new wall, and if you are lucky, those walls start to come together into a structure, and that structure is the structure of the proof of the theorem. For if you have really understood what's keeping you from disproving the theorem, you very likely understand, in a way inaccessible to you before, why the theorem is true. This is what happened to Bolyai, who bucked his father's well-meaning advice and tried, like so many before him, to prove that the parallel postulate followed from Euclid's other axioms. Like all the others, he failed. But unlike the others, he was able to understand the shape of his failure. What was blocking all his attempts to prove that there was no geometry without the parallel postulate was the existence of just such a geometry! And with each failed attempt he learned more about the features of the thing he didn't think existed, getting to know it more and more intimately, until the moment when he realized it was really there.”
― Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking