Puzzle: Let A^1 : CAlg(R) -> Set be the forgetful functor from commutative algebras over the real numbers to Set. Show that there is no natural transformation A^1 -> A^1 such that A^1(R) -> A^1(R) is the exponential function. Can you do it without using that A^1 is representable?
Jakob
@jdw@mathstodon.xyz
mastodon
4.5.8
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible.
I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields.
I try to be friendly towards my fellow creatures, which of course has political implications.
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Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
@jdw@mathstodon.xyz
·
2d ago
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Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
@jdw@mathstodon.xyz
·
2d ago
The last couple of days I've been wrapping my head around Gröbner bases over arbitrary (strongly discrete for the constructivists) ground rings and damn, that theory is elegant. Somehow being forced to take care of ideals in the ground ring rather than just zero/non-zero elements forces a more elegant treatment 😅 I'm writing it up in my own words right now…
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Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
@jdw@mathstodon.xyz
·
3d ago
Can someone explain to me which developments of the recent months justify the MSCI world index being rated 5% higher than at the beginning of the year?
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Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
@jdw@mathstodon.xyz
·
4d ago
I really wish the Fediverse was more diverse… Do you have any ideas what could be done about this on an individual and on a structural level?
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Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
@jdw@mathstodon.xyz
·
Apr 09, 2026
Consider the complete lattice of substructures of an algebraic structure, or just submodules of a module, or even just ideals in a commutative ring. Every element of this lattice is a join of »principal« substructures (generated by one element). Is there anything else that is special about the set of principal substructures (or its individual elements) from an order-theoretic point of view?
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Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
@jdw@mathstodon.xyz
·
Apr 09, 2026
@soaproot @antoinechambertloir @dwarn It appears that my question has a positive answer as per Proposition 3.13 in this paper: https://www.sciencedirect.com/science/article/pii/S074771710880154X?via%3Dihub
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Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
@jdw@mathstodon.xyz
·
Apr 08, 2026
@jonmsterling Internally, that is :)
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Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
@jdw@mathstodon.xyz
·
Apr 08, 2026
I was trying to explain to my (non-mathematical) girlfriend why it might be interesting to see what could be proved using constructive logic/why constructive proofs are stronger than classical ones. I came up with an analogy to a court situation where you can't be sentenced even if it can be proved that last night you either commited crime A or crime B but it is not clear which one. You can only be sentenced if there is a proof that you committed crime A or there is a proof that you committed crime B. (Does anyone know if such a scenario ever occurred in reality?)
Anyway, the talk didn't exactly go as I had anticipated, because the law of excluded middle didn't seem intuitive to her at all. »Wait, claiming that everything always has to be either this way or the other, isn't this a very right wing thing to say? It's like saying that there can only be two genders, that doesn't make sense to me at all!« So in the end I was trying to make plausible why some people would be convinced that either there is at least one unicorn or there are no unicorns at all, but I don't think she was convinced.
So I guess I have a constructive girlfriend.
Anyway, the talk didn't exactly go as I had anticipated, because the law of excluded middle didn't seem intuitive to her at all. »Wait, claiming that everything always has to be either this way or the other, isn't this a very right wing thing to say? It's like saying that there can only be two genders, that doesn't make sense to me at all!« So in the end I was trying to make plausible why some people would be convinced that either there is at least one unicorn or there are no unicorns at all, but I don't think she was convinced.
So I guess I have a constructive girlfriend.
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Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
@jdw@mathstodon.xyz
·
Mar 24, 2026
@soaproot No, it's the same thing. Wikipedia just uses multiplicative notation and talks about (X_1)^(m_r) * … * (X_m)^(m_r) where X_1, …, X_r are formal symbols and (m_1, …, m_r) ∈ ℕ^r, instead of (m_1, …, m_r) directly. I just decided to strip away the multiplicative notation to make the post more widely accessible.
At first they leave the conditions »total order« and »the neutral element is minimal« from my original post away, but they add them in »Definition, details and variants« and mention the relation with well-ordering.
At first they leave the conditions »total order« and »the neutral element is minimal« from my original post away, but they add them in »Definition, details and variants« and mention the relation with well-ordering.
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Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
@jdw@mathstodon.xyz
·
Mar 23, 2026
@antoinechambertloir Yes, all the standard examples of monomial orders are *weight orders* for some concrete rational weight vectors. For these it is easy to see that they are well-founded. (I'm not 100% sure everything works fine with non-rational weights because of the constructive difficulties with real numbers.)
Appearantly https://link.springer.com/chapter/10.1007/3-540-15984-3_321 contains a proof that every ordering is a weight ordering, but unfortunately I can't access the paper. I doubt the proof will be constructive.
Appearantly https://link.springer.com/chapter/10.1007/3-540-15984-3_321 contains a proof that every ordering is a weight ordering, but unfortunately I can't access the paper. I doubt the proof will be constructive.
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Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
@jdw@mathstodon.xyz
·
Mar 23, 2026
@dwarn Thanks! I couldn't yet connect everything, but using your keyword Dickson's lemma I found it interesting that Cox, Little, O'Shea in their very nice book Ideals, Varieties and Algorithms call Dickson's lemma the statement that every ideal generated by monomials in a polynomial ring over a field is finitely generated. They give a direct proof (not referring to Hilbert's basis theorem), but at first sight it doesn't seem to be fully constructive.
(Btw, there is a recent 5th edition from 2025 of their book, as I just found out.)
(Btw, there is a recent 5th edition from 2025 of their book, as I just found out.)
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Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
@jdw@mathstodon.xyz
·
Mar 23, 2026
A monomial ordering is a total order on ℕ^r making ℕ^r into an ordered monoid, i.e. 0 <= m for all m and m <= m' implies m + n <= m' + n for all m, m', n.
Classically, every monomial ordering is a well-ordering (algebra people like to deduce this from Hilbert's basis theorem).
Is it true constructively that every monomial ordering is well-founded, i.e. allows well-founded induction?
Feel free to boost if you have constructive people in your bubble 😅
Classically, every monomial ordering is a well-ordering (algebra people like to deduce this from Hilbert's basis theorem).
Is it true constructively that every monomial ordering is well-founded, i.e. allows well-founded induction?
Feel free to boost if you have constructive people in your bubble 😅
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Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
@jdw@mathstodon.xyz
·
Mar 14, 2026
@pojntfx Which icon is missing on the laptop?
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Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
@jdw@mathstodon.xyz
·
Mar 11, 2026
@siosm @nobody_2454 Oh that would be great!
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Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
@jdw@mathstodon.xyz
·
Mar 10, 2026
@tomkalei You just have to hope that the machine doesn't find a proof of False and is using that as a lemma. @tao
https://mathstodon.xyz/@highergeometer/116196176162277025
https://mathstodon.xyz/@highergeometer/116196176162277025
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Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
Jakob
@jdw@mathstodon.xyz
I’m a mathematician working as a #Rust programmer, based in #Regensburg, Germany. I enjoy fun and easy math questions, mostly within algebraic geometry. I like constructive mathematics, mainly for aesthetical reasons, and try to think and write constructively when possible. I’m also interested in literature, history, sociology, economics and philosophy and I enjoy reading books from these fields. I try to be friendly towards my fellow creatures, which of course has political implications.
mathstodon.xyz
@jdw@mathstodon.xyz
·
Feb 21, 2026
@mei I wish this had happened to me when I learned category theory 🙃
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