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Quotes from Geometry in 2, 3 and 4 Dimensions — Michael Atiyah

1929–2019 England

← All quotes by Michael Atiyah

9 quotes

4 dimensions is... very important, even if you don't believe in it.

Geometry in 2, 3 and 4 Dimensions (2011)

The 19th century finished with a very very deep theory of 2 dimensional surfaces, in all aspects: geometrical, analytical, complex, real.

Geometry in 2, 3 and 4 Dimensions (2011)

In the 20th century we moved... from 2 dimensions to 3...

Geometry in 2, 3 and 4 Dimensions (2011)

In 3 dimensions the curvature is more complicated... It's determined not by by a single number r, but by a number R that depends on 2 directions i and j, called the Ricci curvature...

Geometry in 2, 3 and 4 Dimensions (2011)

In dimension one, along a straight line or on the edge of a circle there is no real geometry. All you can do is to measure how far along the path you are.

Geometry in 2, 3 and 4 Dimensions (2011)

The 20th century... was devoted to ideas of 3 dimensional geometry, and this is the culmination... today...

Geometry in 2, 3 and 4 Dimensions (2011)

The genus is the number of holes. The sphere [surface] has no hole... The torus is a sphere with a hole bored through...

Geometry in 2, 3 and 4 Dimensions (2011)

A cylinder looks curved, but it's... flat from the point of view of Gaussian curvature. It curves in one direction, but not in the other, and it's important that... both change.

Geometry in 2, 3 and 4 Dimensions (2011)

[J]ust as the past is important, so the future is important, although the future is a little harder to predict.

Geometry in 2, 3 and 4 Dimensions (2011)

Attribution

Quotes and notes from Wikiquote: Michael Atiyah (page history), available under CC BY-SA 4.0.