Fermat's Library

@fermatslibrary

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

fermatslibrary.com
Joined September 2015
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  1. Pinned Tweet
    28 Sep 2018

    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

    33 replies 434 retweets 1,548 likes
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  2. 4 hours ago

    The largest prime below 1,000,000,000 is 999,999,937

    20 replies 237 retweets 1,832 likes
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  3. Nov 23

    Universe ↑ ↑ 10²⁴ ↑ ↑ 🌌 Milky Way ↑ ↑ 10¹⁸ ↑ ↑ 10¹⁵ ↑ ↑ 💫 Solar System ↑ ↑ ☀️ Sun ↑ 🌍 Earth 10⁶ ↑ ↑ 🏔 Mountains ↑ 🐋 Whales 👫 Humans ↓ 🐞 Ladybug 10⁻³ ↓ ↓ 10⁻⁶ 🦠 Virus ↓ 🧬 DNA ⚛️ Atoms ↓ 10⁻¹² ↓ ↓ 10⁻¹⁵ ↓ ⚡️ Electrons ⚫️ Quarks

    95 replies 4,480 retweets 14,742 likes
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  4. Nov 22

    Floor function is missing, it should be ⌊A^{3^{n}}⌋

    9 replies 37 retweets 511 likes
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  5. Nov 22

    In 1947 W. H. Mills proved that there is a number A, such that the following number is prime for all integer values of n.

    51 replies 330 retweets 1,826 likes
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  6. Nov 21

    The chemical element Berkelium was originally named after the University of California Berkeley ➡️ which is named after the city of Berkeley ➡️ which is named after the philosopher George Berkeley, who didn't believe in the existence of a physical world!

    21 replies 490 retweets 2,603 likes
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  7. Nov 20

    Start with 82 and go backwards to 1 8281807978777675747372717069686 7666564636261605958575655545352 5150494847464544434241403938373 6353433323130292827262524232221 2019181716151413121110987654321 ...this number is prime!

    254 replies 5,394 retweets 37,467 likes
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  8. Nov 19

    The Internet came to life 50 years ago during the Cold War, when government agencies were worried about maintaining communication in the event of a nuclear attack. As a result, survivability became a core design goal. Read about it in this week’s paper:

    11 replies 316 retweets 1,071 likes
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  9. Nov 18

    In 1920, it took Lewis Richardson, the English physicist who pioneered modern mathematical techniques of weather forecasting, 6 weeks to predict the weather 6 hours in advance.

    10 replies 201 retweets 1,244 likes
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  10. Nov 17

    We've got an idea for a podcast A discussion around the annotated papers we publish - we might also have featured guests (authors, other scientists) join the discussion. Would you listen? like or retweet to let us know

    102 replies 389 retweets 3,450 likes
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  11. Nov 16

    Here's one of the first methods used by Hipparchus to determine the distance to the Moon in 129 BC

    42 replies 1,403 retweets 5,734 likes
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  12. Nov 15

    Googol = 10¹⁰⁰ A Googol is a 1 followed by 100 zeroes. Other names for googol include ten duotrigintillion on the short scale, ten thousand sexdecillion on the long scale, or ten sexdecilliard on the Peletier long scale. 🧐

    37 replies 569 retweets 2,444 likes
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  13. Nov 14

    Liouville proved the following property of the divisors of the divisors of a number: 1) Start with a number (e.g. 10) 2) Write down its divisors (1,2,5,10) 3) Write down the number of divisors of each divisor (1,2,2,4) 4) (1+2+2+4)²=81=1³+2³+2³+4³

    45 replies 913 retweets 4,468 likes
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  14. Nov 13

    John Moffat 1) Started as a painter 2) Learned relativity borrowing books from the local library (even exchanged letters with Einstein) 3) 1st person to be admitted to Cambridge PhD program without an undergraduate degree 4) Currently Prof. emeritus in physics at the U.of Toronto

    37 replies 1,326 retweets 6,768 likes
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  15. Nov 12

    How do airplanes fly? The popular explanation for lift is based on Bernoulli's principle. This explanation fails to explain inverted flight or flat wings. So how do planes really fly? 🤔 Find the answer here:

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    31 replies 588 retweets 2,281 likes
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  16. Nov 11

    If the fraction is irreducible it means the denominator and numerator have no common divisors. Assuming k divides 21n+4 and 14n+3, then k also divides 2(21n+4)=42n+8 and 3(14n+3)=42n+9 as well as the difference (42n+9)-(42n+8)=1 - we conclude that the only common divisor is 1!

    16 replies 131 retweets 1,235 likes
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  17. Nov 11

    Here's an example of a problem from the first International Mathematics Olympiad (IMO) whose solution is accessible to anyone with basic understanding of math. The solution fits in a single tweet.

    35 replies 487 retweets 2,086 likes
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  18. Nov 10

    This is the largest left-truncatable prime: you always get a prime regardless of how many leading digits are omitted.

    41 replies 851 retweets 3,999 likes
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  19. Nov 9

    A demonstration of the conservation of angular momentum using a Hoberman sphere. Angular momentum depends on the rotational velocity of an object, and on its rotational inertia. When an object changes its shape, its angular velocity will also change.

    239 replies 8,300 retweets 44,809 likes
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  20. Nov 8

    Here's an interesting approximation for the number 8

    225 replies 3,696 retweets 28,557 likes
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  21. Nov 7

    There are infinitely many primes of the form n²+m²

    34 replies 315 retweets 1,766 likes
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