foundations of mathematics

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Achilles paradox

Contrasting triangles in Euclidean, elliptic, and hyperbolic spaces.

For Students

foundations of mathematics summary

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bunch of numbers

Unusual Counting Systems

number zero, 0 balloon

Is Zero an Even or an Odd Number?

Aristotle (384-322 BC), Ancient Greek philosopher and scientist. One of the most influential philosophers in the history of Western thought, Aristotle established the foundations for the modern scientific method of enquiry. Statue

Philosophers to Know, Part I

Discover

Orange basketball on black background and with low key lighting. Homepage 2010, arts and entertainment, history and society

The 10 Greatest Basketball Players of All Time

American bison (Bison bison) also known as buffalo or plains buffalo on the prairie, western U.S.

What’s the Difference Between Bison and Buffalo?

Poker game. Card game. Royal Flush in poker. Hearts suit gambling

Poker Hands Ranked

The impeachment trial of Pres. Andrew Johnson, illustration from Frank Leslie's Illustrated Newspaper, March 28, 1868.

What If the President Is Impeached?

Small, white rat (genus Rattus) on a glass table. (rodent, laboratory, experiment)

Cruel and Unusual Punishments: 15 Types of Torture

Estimated battle casualties, Normandy invasion, World War II. WWII, D-Day

Estimated Battle Casualties During the Normandy Invasion and Campaign to Liberate Paris (June–August 1944)

Normandy Invasion: Omaha Beach. World War II. D-Day. Infographic. SPOTLIGHT VERSION

Facts and Figures About the Landings on Omaha Beach During the Normandy Invasion on June 6, 1944

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Photos

Achilles paradox

Contrasting triangles in Euclidean, elliptic, and hyperbolic spaces.

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Topics

incompleteness theorem Gödel’s second incompleteness theorem Gödel’s first incompleteness theorem philosophy of mathematics mathematics probability and statistics numerals and numeral systems matrix function fractal graph derivative algorithm vector error

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mathematics: Foundations of geometry

Key People

Stanisław Leśniewski

Polish logician and mathematician

David Hilbert

David Hilbert

German mathematician

Peano, Giuseppe

Giuseppe Peano

Italian mathematician

Paul Isaak Bernays

Swiss logician and mathematician

Quiz

Equations written on blackboard

Numbers and Mathematics