Mathematics is...

“Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.” -- Bertrand Russell

“Mathematics is made of 50 percent formulas, 50 percent proofs, and 50 percent imagination.”

“Mathematics is the art of giving the same name to different things.” -- J. H. Poincare

“Philosophy is a game with objectives and no rules. Mathematics is a game with rules and no objectives.”

"Mathematics is a game played according to certain simple rules with meaningless marks on paper." -- David Hilbert

"Mathematics consists in proving the most obvious thing in the least obvious way." -- George Polya

"In mathematics, you don't understand things. You just get used to them." -- Johann von Neumann

"A tragedy of mathematics is a beautiful conjecture ruined by an ugly fact.”

“Mathematics is like love; a simple idea, but it can get complicated.”

"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."

“Mathematics is like checkers in being suitable for the young, not too difficult, amusing, and without peril to the state.” -- Plato

"The essence of mathematics is not to make simple things complicated, but to make complicated things simple." -- S. Gudder

"There are two ways to do great mathematics. The first is to be smarter than everybody else. The second way is to be stupider than everybody else -- but persistent." -- Raoul Bott

"Obvious is the most dangerous word in mathematics." -- E.T. Bell

"Arithmetic is being able to count up to twenty without taking off your shoes." -- Mickey Mouse

"The greatest unsolved theorem in mathematics is why some people are better at it than others." -- Adrian Mathesis

"Mathematics is not a deductive science – that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork." -- Paul Halmos

“The different branches of Arithmetic are Ambition, Distraction, Uglification, and Derision.” – Lewis Caroll

"Mathematics is written for mathematicians." – Copernicus

"Mathematics should be fun." -- Peter J. Hilton

"Small minds discuss persons. Average minds discuss events. Great minds discuss ideas. Really great minds discuss mathematics."

"But in the new (math) approach, the important thing is to understand what you're doing, rather than to get the right answer." -- Tom Lehrer

Zeno's Paradox

Zeno, a Greek man around the time of 500 B.C., decided to take a runner

This runner is racing a turtle and for every 10 ft the turtle goes the runner goes 100 ft. but Zeno gives the turtle a 300 ft head start. So now for the as the race starts the runner has to go 300 ft to catch up, but by the time this happens the turtle goes 30 ft. Then the runner goes 30 ft and the turtle goes 3ft this continues for infinity.
So who wins?

The Turtle! (after an infinite amount of years)

It's all about Pi

Historians estimate that by 2000 B.C. humans had noticed that the ratio of circumference to diameter was the same for all circles. This discovery hinged on the idea of proportion - in this case humans noticed that if you double the distance "across" a circle, then you double the distance "around" it. As of today this is the formula:

where Pi was constant. (It wasn't until 1706 that this notation, using the Greek letter seen in the above equation - often written Pi and pronounced like the English 'pie' - was introduced by William Jones). But one problem remained - what is the numerical value of Pi?

let's take a look! Person/People Year Value Babylonians ~2000 B.C. 3 1/8 Egyptians ~2000 B.C. (16/9)^2= 3.1605 Chinese ~1200 B.C. 3 Old Testament ~550 B.C. 3 Archimedes ~300 B.C. proves 3 10/71uses 211875/67441=3.14163 Ptolemy ~200 A.D. 377/120=3.14166... Chung Huing ~300 A.D. sqrt(10)=3.16... Wang Fau 263 A.D. 157/50=3.14 Tsu Chung-Chi ~500 A.D. proves 3.1415926 Aryabhatta ~500 3.1416 Brahmagupta ~600 sqrt(10) Fibonacci 1220 3.141818 Ludolph van Ceulen 1596 Calculates Pi to 35 decimal places Machin 1706 100 decimal places Lambert 1766 Proves Pi is irrational Richter 1855 500 decimal places Lindeman 1882 Proves Pi is transcendental Ferguson 1947 808 decimal places Pegasus Computer 1957 7,840 decimal places IBM 7090 1961 100,000 decimal places CDC 6600 1967 500,000 decimal places

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