Roger Joseph Witte

@CburgesCliff R

FORTRAN baby 💪

@mouse_math This mirrors the historical development; abstract algebra is surprisingly modern!

in school we first encounter vectors as a directed arrow, consisting of a pair of numbers representing length and direction. but by the time we take abstract algebra, we learn that "vectors" can be a far broader class of things, which obey the axioms of a vector space.

@JDHamkins @ThosVarley The counter example was a new proof of a theorem by Charles Resc that HOTT researchers found.

@JDHamkins @ThosVarley I think that having a Lean or Coq formalization proves just shunts the checking from checking the logic into checking that the formal statements really do express the intended ideas. Joel's second point is only majoritatively true (but I can only think of one counter-example)

I am seeing the doomed future of AI math: just received another set theory paper by a set theory amateur with an AI workflow and an interest in the continuum hypothesis. At first glance, the paper looks polished and advanced. It is beautifully typeset and contains many correct definitions and theorems, many of which I recognize from my own published work and in work by people I know to be expert. Between those correct bits, however, are sprinkled whole passages of claims and results with new technical jargon. One can't really tell at first, but upon looking into it, it seems to be meaningless nonsense. The author has evidently hoodwinked himself. We are all going to be suffering under this kind of garbage, which is not easily recognizable for the slop it is without effort. It is our regrettable fate.

@mouse_math @lady_valor_07 Safety pins and elastic bands also

@lady_valor_07 pieces of string, wire, and twine. also a pair of used shoelaces, a few mismatched buttons, some nails and/or screws, a bolt to something, a ticket to a concert or ball game or movie, and paper clips.

starting a junk drawer. What else do I need?

@JoanneMOrmesher You look very pretty but slightly bored in this picture.

@miniapeur Is this the difference homomorphism and isomorphism.

@JoanneMOrmesher You are dressed up very feminine and girly in that photo, but I bet you prefer your sooty overalls when you are bashing orms.

After losing my old nicknames and usernames after the name change, today I gained a new nickname. Someone referred to me me as Joanne Ormbasher in an email today and I haven't laughed so much at an email..gave me some amusement in a very trying day! That ones stuck.😅

@emilyriehl Minor dad joke - talking about k and suck!

In a talk called "A reintroduction to proofs" emilyriehl.github.io/files/reintrod… I've speculated about teaching an undergraduate level introduction to proofs course but using dependent type theory as the implicit formal system in place of set theory and first order logic.

@mouse_math One of the disadvantages of car-centric (zoned) planning is that it makes it more difficult to give up driving. You are almost under house arrest. When my Dad, in London England, decided he was no longer safe at the wheel, he was still able to walk to the local shops.

i see the dementia and confusion on the faces of elderly drivers as they try to navigate the busy parking lot of the supermarket. often it is combined with frustration and impatience. it is, by far, the most dangerous part of my daily ride.

@mouse_math Is the lower one the fano plane? There's a lecture on you tube at the Royal Institution by Jordan Ellenberg on beating a lottery with a fano plane.

point/line duality in finite geometry.

@TaliaRinger Wishing you both speedy recovery! And let's hope that, for once, your husband doesn't get to share in the family experience.

I'm sick in like 3 different ways today, and home with a sick baby, wish me luck

@JoanneMOrmesher Is this proof that you can look great and feel s**t at the same time?

Friday has been rough, software failures, repeated work, awkward paperwork and a lack of chocolate hobnobs in the house. Thank F*ck its the weekend.

@wylfcen It's almost extinct - you can still find enclaves in Essex - but MLE is probably the main London dialects.

@littmath Having carefully watched the ludicrous conclusions of efforts to mathematically analyse love by both Eugenia Cheng and Hannah Fry (seperately), I would urge caution.

Planning to discuss this in week 4 of my upcoming algebraic geometry class.

@mouse_math That only gets you a RNG (no multiplicative identity).

fun fact: you can make a ring out of any abelian group 𝐺 by taking the group operation to be addition, and defining the operation of multiplication for all 𝑎,𝑏∈𝐺 by 𝑎𝑏=0.

@Jose_A_Alonso Short and obvious - as all the best mathematical writing appears once read and understood (of course, it's a clif prior to that)

Mathematics is hard for mathematicians to understand too. ~ Emily Riehl. science.org/doi/10.1126/sc… #Math

@Ganeshuor My favourite pi approximation is square root 10. It's especially convenient when you need pi squared

Archimedes used polygons to pin π between 3.1408 and 3.1429. Zu Chongzhi gave the legendary π approximation 355/113. Aryabhata used the remarkably accurate value π ≈ 3.1416. Madhava discovered the infinite series that pushed π into modern precision. Ludolph van Ceulen calculated π to 35 digits by hand. John Wallis introduced the infinite product now known as the Wallis formula for π. Isaac Newton computed 15 digits of π using his own power series. Leonhard Euler revealed deep π identities through analysis and infinite products. Ramanujan created ultra-fast π formulas still used in algorithms today. Gauss advanced π computation through elliptic integrals and the AGM method.

@littmath @BlakeDemarest12 @jasondeanlee I like Andre Baur's idea that with formal proofs the computer verifies the string of symbols. But the human has to verify that the string symbols means what is intended.

@BlakeDemarest12 @jasondeanlee Like in practice, in any English language proof there are various things taken as given, left to the reader, etc. What is allowable when one does this is some kind of social contract.

What to do when my students and I can no longer verify gpt output. Can't tell if it's right or wrong...

@littmath @AcerFur Depending on how similar the two proofs are, it still might be important and influential. We should remember that maths is about the proofs as well as the things being proven.

@AcerFur This kind of thing happens all the time. Coming up with a proof independently is absolutely a W and a very bullish sign for future work.

Sigh Erdős problem 481 apparently already had a proof… why does life refuse to give me a lasting W