ARTi
What does the mathematical field of topology study?

The million dollar map of invisible shapes

Chapter 1

Mapping the invisible shapes

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Chapter 2

The bridge builder from Edinburgh

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Chapter 3

The million dollar hunt

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YOUR GOAL

Master of The million dollar map of invisible shapes

Ch 1 · Mapping the invisible shapes
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diego The Hodge Conjecture

Can we map a complex space? (Yes we can!) By gluing simple shapes in place! (Piece by piece!)

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diego The mystery of higher dimensions

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The mystery of higher dimensions

diego Mathematicians study shapes in four, five, or infinite dimensions.

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Equations that draw complex pictures

diego Algebraic geometry turns algebraic equations into geometric shapes.

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The Hodge Podge
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diego The Hodge Podge

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Fun Fact

The doughnut mug: In topology, a doughnut and a coffee cup are considered completely identical because both have exactly one hole.

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Glossary
cohomology (noun)
A mathematical method in topology that associates algebraic invariants with a geometric space to analyze its structural properties. In 1950, William Hodge proposed his landmark conjecture utilizing these algebraic tools to study complex geometric spaces.

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Gossip

Which dimension would you visit?

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Quiz

How many spatial dimensions do humans physically perceive in daily life?

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diego Equations that draw complex pictures

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Quiz

In algebraic geometry, what is used to define geometric curves and surfaces?

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diego Doughnuts and coffee cups as twins

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Quiz

What does the mathematical field of topology study?

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diego Slicing up complex curved spaces

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Quiz

Who is credited with founding the field of topology in 1895?

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Quiz

Why are a doughnut and a coffee mug considered identical in topology?

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Quiz

Which mathematician introduced the concept of manifolds in 1854?

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Quiz

What is a 'manifold' in mathematics?

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Quiz

Who introduced the coordinate system in 1637 that links algebra and geometry?

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