[Null Donut]

@Doughnought

fresh(wo)man in Mathematics / unique up to isomorphism

Vrijeme pridruživanja: rujan 2019.
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  1. proslijedio/la je Tweet
    29. sij

    As a binary operation, exponentiation is kinda weird (let's take positive numbers as the domain). It fails all kinds of familiar axioms: 1/

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  2. proslijedio/la je Tweet
    20. sij

    Very simple ct fact: If you regard the poset category of naturals ordered by n <= m if n | m, then limits and colimits are just gcd and lcm, respectively.

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  3. proslijedio/la je Tweet
    20. sij

    Totally missed this awesome fact on my first pass through group theory!

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  4. proslijedio/la je Tweet
    30. pro 2019.

    1/ So what's an operad? The basic idea is that it's a blueprint for certain kinds of algebraic structure. Other ways to control algebraic structure are monads, algebraic and Lawvere theories, and just collections of commutative diagrams. But operads are distinct from these.

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  5. proslijedio/la je Tweet
    11. stu 2019.

    So I guess I will start with explaining operads. In order to do so I will first explain multicategories and then probably conflate their definitions later on. A multicategory is a sort of generalization of a category. (1/12)

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  6. proslijedio/la je Tweet
    16. sij

    Mathematician Emily Riehl receives President's Frontier Award | Hub

    3 proslijeđena tweeta 14 korisnika označava da im se sviđa
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  7. proslijedio/la je Tweet
    14. sij

    Formalized by logicians in the 19th century, the law of excluded middle legalized centuries of tacit discrimination against middles everywhere.

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  8. proslijedio/la je Tweet
    8. sij

    When I took number theory in undergrad, I was thinking if Z/n is a ring and sometimes even a field, what sorts of things that we do with R can we do with Z/n? How would you graph a function Z/n -> Z/m? You would cross them and then color some points in this discrete torus.

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  9. proslijedio/la je Tweet
    8. sij

    Tim Hosgood, Ryan Keleti and others have now translated Grothendieck's "EGA1" into English! You can nab a free copy here: EGA is Éléments de Géométrie Algébrique, where Grothendieck reformulated algebraic geometry using "schemes". (1/n)

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  10. proslijedio/la je Tweet
    5. sij
    Odgovor korisnicima

    Source B, Linsky: “The Evolution of Principia Mathematica”

    1 reply 10 proslijeđenih tweetova 42 korisnika označavaju da im se sviđa
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  11. proslijedio/la je Tweet
    3. sij

    Q'n: How did mathematicians notate the empty set before ∅?

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  12. proslijedio/la je Tweet
    29. pro 2019.

    ...group theory really studies something else from sets. And so does topology, and analysis and so on. Their *ideas* are not grounded in set theory, they live on their own

    1 reply 1 proslijeđeni tweet 8 korisnika označava da im se sviđa
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  13. proslijedio/la je Tweet
    29. pro 2019.

    This is a major shift in perspective in my mind: we *do* study structures independently of set theory! E.g. groups do not appeal to the ontology of sets, thus you can happily bring about much of group theory in any topos you like, or, equivalently...

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  14. proslijedio/la je Tweet
    29. pro 2019.

    All proofs of uncountability of reals known to me prove uncountability in strong form: given a sequence of reals there is a real not in the sequence. Are there any proofs that directly establish the weaker statement that there is no surjection from N to R?

    6 replies 8 proslijeđenih tweetova 39 korisnika označava da im se sviđa
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  15. proslijedio/la je Tweet
    26. pro 2019.

    Zalamea describing what makes mathematics contemporary

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  16. proslijedio/la je Tweet
    24. pro 2019.

    Initial objects and final objects

    3 proslijeđena tweeta 12 korisnika označava da im se sviđa
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  17. proslijedio/la je Tweet
    19. pro 2019.

    Is there a set with 2.5 elements? No! But here's a "groupoid" with 2.5 elements. To get it, just take a set with 5 elements and fold it in half. The point in the middle gets folded over, and becomes half a point. Sounds wacky, but you can make this into rigorous math! (1/n)

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  18. proslijedio/la je Tweet
    19. pro 2019.

    Galois Representations: An Oversimplified Thread 1/n

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  19. proslijedio/la je Tweet
    15. pro 2019.

    Category theory unifies and clarifies our concepts. For example, in any category we can define the concepts of "product" and "coproduct". Let's see how they work in examples! (1/n)

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  20. proslijedio/la je Tweet
    14. pro 2019.

    Trying our best

    6 replies 38 proslijeđenih tweetova 225 korisnika označava da im se sviđa
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