Quotes About Mathematics

Arguably their greatest intellectual feat was the invention of zero. In his classic account Number: The Language of Science, the mathematician Tobias Dantzig called the discovery of zero "one of the greatest single accomplishments of the human race," a "turning point" in mathematics, science, and technology.

Meanwhile, the first recorded zero in the Americas occurred in a Maya carving from 357 A.D., possibly before the Sanskrit

The Olmec, Maya, and other Mesoamerican societies were world pioneers in mathematics and astronomy—but they did not use the wheel. Amazingly, they had invented the wheel but did not employ it for any purpose other than children's toys. Those looking for a tale of cultural superiority can find it in zero; those looking for failure can find it in the wheel.

Tentatively, therefore, archaeologists assign the invention of zero to sometime before 32 B.C., centuries ahead of its invention in India.

I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics, for men thus endowed seem to have an extra sense.

Zero was the solution to the problem. By around 300 BC the Babylonians had started using two slanted wedges, , to represent an empty space, an empty column on the abacus. This placeholder mark made it easy to tell which position a symbol was in.

presented in an honest and straightforward manner. A little mathematical sophistication—and a little practice—allows you to recognize errors of randumbness, causuistry, and regression to the moon; once you get used to spotting phony patterns and false connections, you'll begin to see them everywhere.

Pythagoras concluded that ratios govern not only music but also all other types of beauty. To the Pythagoreans, ratios and proportions controlled musical beauty, physical beauty, and mathematical beauty. Understanding nature was as simple as understanding the mathematics of proportions.

In other words, the diagonal of that square is irrational—and nowadays we recognize that number as the square root of two.

The number-shape duality in Greek numbers made it easy; after all, zero didn't

In string theory, zero has been banished from the universe; there is no such thing as zero distance or zero time. This solves all the infinity problems of quantum mechanics.

In Cantor's mind there were an infinite number of infinities-the transfinite numbers-each nested in the other. Aleph 0 is smaller than Aleph 1, which is smaller than Aleph 2, which is smaller than Aleph 3, and so forth. At the top of the chain sits the ultimate infinity that engulfs all other infinities: God, the infinity that defies all comprehension.

a mathematician could show how a triangle's angles sum to 180 degrees, or any other geometric fact. On the other hand, calculus was based on faith.

Today most mathematicians accept the continuum hypothesis as true, though some study non-Cantorian transfinite numbers where the continuum hypothesis is taken to be false.)

All polynomials of degree n-those that have a leading term of x^n- split into n distinct terms. This is the fundamental theorem of algebra.

Non-euclidian sofa

The central limit theorem tells us that in repeated samples, the difference between the two means will be distributed roughly as a normal distribution.

Regression analysis enables us to go one step further and "fit a line" that best describes a linear relationship between the two variables.

Although the field of statistics is rooted in mathematics, and mathematics is exact, the use of statistics to describe complex phenomena is not exact.

The t-distribution is actually a series, or "family," of probability density functions that vary according to the size of our sample.

For large samples, we can assume that the standard deviation of the sample is reasonably close to the standard deviation of the population.*

Time speeds up as it goes by. Someone explained to me that there is a mathematical reason for this: as you age, each year becomes a smaller percentage of the life you have already lived.

But when you want to mark a number on an abacus, what do you do if there are no stones in a column? The number 60 is one wedge in the sixties column and no wedges in the ones column. How do you write "no wedges"? The Babylonians needed a placeholder that represented nothing. They had to, in effect, invent zero. And so they created a new character, with no value, to signify an empty column. They denoted it with two slanted wedges.

The Greeks, meanwhile, explicitly rejected zero. Since their mathematical system was based on geometry, numbers had to represent space of one sort or another—length, angles, area, etc. Zero space didn't make sense.