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

    37 replies 610 retweets 2,379 likes
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  2. 15 hours ago

    Here's an interesting surprise: if you write down the digits of e you quickly find a 649 digit prime!

    BERJAYA
    47 replies 366 retweets 3,521 likes
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  3. Nov 22

    "Do not imagine that mathematics is hard and crabbed and repulsive to common sense. It is merely the etherealization of common sense" - Lord Kelvin

    BERJAYA
    21 replies 411 retweets 2,475 likes
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  4. Nov 21

    Dirac's Equation (1928) Paul Dirac described the electron in terms of both its wave function - the quantum probability of its position - and its mass times the speed of light - a relativistic interpretation of its energy. This equation implied the existence of antimatter.

    BERJAYA
    22 replies 375 retweets 2,525 likes
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  5. Nov 20

    The Martian dichotomy is a curious feature of Mars - cratered southern highlands and relatively smooth plains of the northern lowlands. The origin of the dichotomy, which likely set the course for the geologic evolution of Mars, remains a mystery.

    BERJAYA
    10 replies 111 retweets 732 likes
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  6. Nov 19

    Heisenberg's Uncertainty Principle (1927) The position (x) and the velocity (p) of an object cannot both be measured exactly at the same time. When we know the position of an object with high certainty (Δx is small) then we have a large uncertainty on its momentum (Δp large).

    BERJAYA
    92 replies 683 retweets 5,240 likes
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  7. Nov 18

    Every odd integer is the difference of 2 squares Proof: 1) Pick an odd number ░░ ░░ ░░ ░░ ░░ 2) Bend it in half ░░ ░░ ░░ ░░ ░░ 3) Fill in the rest ░░ ░░ ░░ ░░ ▓▓ ▓▓ ░░ ▓▓ ▓▓ The odd nbr is the area difference of the big and small squares

    40 replies 655 retweets 3,628 likes
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  8. Nov 17

    Uranium is actually a fairly common element. We could extract 70 tons of uranium from every cubic mile of sea water. Learn more about uranium mining in this week's paper:

    BERJAYA
    20 replies 169 retweets 1,048 likes
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  9. Nov 16

    Here are some of the notations used for the cube root: ℞³ - Chuquet 🇫🇷 (1484) ℞3ᵃ - Pacioli 🇮🇹 (1494) ℞ cub. - Cardan 🇮🇹 (1545) w√ - Rudolff 🇩🇪 (1525) ∛ - Girard 🇫🇷 (1629) √3.) - Harriot 🇬🇧 (1631) √C - Descartes 🇫🇷 (1637) √³ - Wallis 🇬🇧 (1655)

    18 replies 165 retweets 1,129 likes
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  10. Nov 15

    The plus sign comes from the abbreviation of the Latin word "et" meaning "and". There were recorded more than 100 abbreviations for "et" before Johann Widman put + in print for the first time in 1489.

    19 replies 353 retweets 1,779 likes
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  11. Nov 14

    2nd Law of Thermodynamics The entropy, also known disorder, of a system will increase over time. The Universe is full of irreversible processes that continuously increase its total entropy thus tending to disorder rather than order.

    BERJAYA
    181 replies 1,326 retweets 8,822 likes
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  12. Nov 13

    Erdős published more than 1500 papers • The most number of publications in one year was in 1978 at 65 when he published 49 papers • He published 118 papers after 80

    BERJAYA
    17 replies 196 retweets 1,341 likes
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  13. Nov 12

    In 1775, Lagrange introduced these compact forms to describe the area of the triangle or the volume of the tetrahedron.

    BERJAYA
    26 replies 481 retweets 2,922 likes
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  14. Nov 11

    Giuseppe Luigi Lagrangia was born in Turin 🇮🇹 in 1736. He later moved to France 🇫🇷 naturalized french and adapted his name to Joseph-Louis Lagrange.

    BERJAYA
    19 replies 223 retweets 1,704 likes
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  15. Nov 10

    You can read the annotated paper by David's Krakauer et al here:

    22 retweets 134 likes
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  16. Nov 10

    This week's paper is a novel approach to describe an "individual" in Biology without relying on features like cell membrane, but instead on a mathematical formulation that takes into account the information propagated in time.

    BERJAYA
    20 replies 292 retweets 1,561 likes
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  17. Nov 9

    "The advancement and perfection of mathematics are intimately connected with the prosperity of the State" - Napoleon

    BERJAYA
    32 replies 451 retweets 2,796 likes
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  18. Nov 8

    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 116 retweets 1,841 likes
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  19. Nov 8

    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.

    BERJAYA
    41 replies 555 retweets 3,159 likes
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  20. Nov 7

    FUN FACT: The planet Venus has a rotation period of 243 Earth days and it orbits the Sun every 225 Earth days. Venus takes longer to rotate about its axis than any other planet in the Solar System. One day on planet Venus is longer than one year.

    BERJAYA
    154 replies 1,873 retweets 9,548 likes
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  21. Nov 6

    In 1659, Johann Heinrich Rahn published Teutsche Algebra. This was the first time the division symbol ÷ appeared in print.

    BERJAYA
    31 replies 723 retweets 3,932 likes
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