Fermat's Library

@fermatslibrary

A platform for illuminating academic papers. We publish an annotated paper every week. Our chrome extension for arXiv:

Joined September 2015

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  1. Pinned Tweet

    We launched Margins A free online repository where you can 📝 Save and annotate your papers 🗣 Share papers and collaborate with anyone 💻 Annotate using LaTeX, Code, Markdown and more

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  2. Here's a visual proof that (2a+1)²=8Tₐ+1, where Tₐ is a triangle number Tₐ = 1+2+...+a ⚫️🔴🔴🔴🔴⚫️⚫️⚫️⚫️ ⚫️⚫️🔴🔴🔴⚫️⚫️⚫️🔴 ⚫️⚫️⚫️🔴🔴⚫️⚫️🔴🔴 ⚫️⚫️⚫️⚫️🔴⚫️🔴🔴🔴 🔴🔴🔴🔴🔵🔴🔴🔴🔴 🔴🔴🔴⚫️🔴⚫️⚫️⚫️⚫️ 🔴🔴⚫️⚫️🔴🔴⚫️⚫️⚫️ 🔴⚫️⚫️⚫️🔴🔴🔴⚫️⚫️ ⚫️⚫️⚫️⚫️🔴🔴🔴🔴⚫️

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  3. Feb 1

    The Global Seed Vault located in Svalbard, Norway is a storage facility that holds more than 980,000 samples of crops, from almost every country in the world. Its purpose is to safeguard the world’s unique crop genetic material. 2.5 billion seeds may be stored in the Vault.

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  4. Jan 31

    The battery symbol was inspired by the looks of voltaic batteries from the early 19th century.

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  5. Jan 30

    In the 18th century, it was fashionable for men of an intellectual bent to have their portraits painted while wearing banyans and turban-like caps. They believed "loose dresses contribute to the easy and vigorous exercise of the faculties of the mind". Here's Euler's portrait.

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  6. Jan 29

    In 1823, Niels Hendrik Abel managed to prove that there is no algebraic formula to solve equations of degree 5

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  7. Jan 28

    The distribution of women and men across academic disciplines seems to be affected by perceptions of intellectual brilliance. Today's paper presents 4 studies performed to assess the perception of brilliance by young children aged 5 to 7. Insightful 🧐:

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  8. Jan 27

    A visual proof A square inscribed in a semicircle has 2/5 the area of a square inscribed in the circle of the same radius. 🧐

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  9. Jan 26

    An integral for the Golden Ratio 𝜙

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  10. Jan 25

    Here's the remarkable coincidence that allows us to see total solar eclipses: the diameter of the Moon is 400 times smaller than the diameter of the Sun, but it is also 400 times closer to us.

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  11. Jan 24

    Richard Feynman found trigonometry notation to be ambiguous and confusing. "If I had sin f, it looked like s×i×n×f" So he decided to create his own notation. See below. 🧐 What do you think?

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  12. Jan 23

    When John Bardeen won the 1956 Nobel Prize in Physics, the Swedish king criticized him for not bringing his kids to the ceremony. He promised he would bring them the next time he won - and in 1972, he did when he became the first person to win 2 prizes in the same field.

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  13. Jan 22

    It took us 255 years to go from Galilean transformations for falling bodies to Lorentz transformations that are in accordance with Einstein's special relativity.

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  14. Jan 21

    This week's paper is a viewpoint article titled “World Scientists' Warning of a Climate Emergency” by William J. Ripple and 11.258 Scientists Signatories. Here's the paper:

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  15. Jan 20

    Fermat dies in 1665 - his last theorem is unsolved ↓ ⏳88 y ↓ Euler proves it for n=3 ↓ ⏳72 y ↓ Legendre & Dirichlet prove it for n=5 ↓ ⏳14 y ↓ Lamé proves it for n=7 ↓ ⏳69 y ↓ Wolfskehl offers prize for solution in the next 100 years ↓ ⏳86 y ↓ Wiles proves it 🎉

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  16. Jan 19

    The Williams-Kilburn tube introduced in 1947 was the first entirely electronic memory used in early computers. It used a cathode tube to store bits as dots on the screen's surface. Each tube could store about 1024 bits of data.

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  17. Jan 18

    377 years ago Pierre Hérigone wrote a six-volume algebra text almost entirely in symbols, in which he first proposed the use of ⊥ (perpendicular) and ∠ (angle).

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  18. Jan 17

    Tree Mountain is an artificial mountain near Ylöjärvi in Finland. Over a period of 4 years 11,000 people planted 11,000 trees in a specifically designed mathematical pattern based on the golden section. The project was conceived by the artist Agnes Denes in 1984.

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  19. Jan 16

    This is the largest known Fibonacci number that's also prime, which is 21925 digits long and was proved prime by Mathew Steine and Bouk de Water in 2015.

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  20. Jan 15

    Gustav Dirichlet (1805–1859) was a prodigy who at the age of 20 proved that Fermat’s Last Theorem has no solution when n=5

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  21. Jan 14

    "Truth... is much too complicated to allow for anything but approximations" - John von Neumann

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