Thales: Ancient Greeks built the cosmos with right triangles

The ancient Greeks were obsessed with geometry, which may have formed the basis of their philosophical cosmology.

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  • Every triangle inscribed inside a circle on its diameter is a right triangle.
  • Upon this discovery, Thales is said to have performed a great ritual sacrifice.
  • Might Thales have believed that the entire cosmos was constructed of right triangles?
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Will AI replace mathematicians?

If computers can beat us at chess, maybe they could beat us at math, too.

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  • Most everyone fears that they will be replaced by robots or AI someday.
  • A field like mathematics, which is governed solely by rules that computers thrive on, seems to be ripe for a robot revolution.
  • AI may not replace mathematicians but will instead help us ask better questions.
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Hidden philosophy of the Pythagorean theorem

Pythagoras may have believed that the entire cosmos was constructed out of right triangles.

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  • Ancient Greeks believed that fire, air, water, and earth were the four elements of the universe.
  • Plato associated these four elements with 3D geometrical solids.
  • Pythagoras may have believed that the right triangle formed the basis of all reality.
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The foundations of mathematics are unproven

Philosopher and logician Kurt Gödel upended our understanding of mathematics and truth.

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  • In 1900, mathematician David Hilbert laid down 23 problems for the mathematics world to solve, the biggest of which was how to prove mathematics itself.
  • Far from solving the issue, Kurt Gödel showed just how groundless the axioms of mathematics are.
  • Gödel's theorem does not devalue mathematics but reveals that some truths are unprovable.
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There is no dark matter. Instead, information has mass, physicist says

Is information the fifth form of matter?

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  • Researchers have been trying for over 60 years to detect dark matter.
  • There are many theories about it, but none are supported by evidence.
  • The mass-energy-information equivalence principle combines several theories to offer an alternative to dark matter.
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