Ken Ono feared AI. Now he trains it

Physics Today recently published an interesting and thought-provoking Q&A with eminent mathematician Ken Ono, who recently took a leave of absence from his tenure-track position at the University of Virgina to join Axiom Math, an company developing AI tools to verify mathematical proofs. From the article’s opening paragraphs:

“Am I doing a better service to science by writing 20 more papers that only people in my field will read or by participating in this movement?” Ken Ono asked himself last year. At the time, Ono was an endowed chair at the University of Virginia. In the following months, he’d take a leave of absence from the university, move to Silicon Valley, and become the founding mathematician at an AI startup, Axiom Math.

Axiom is one of several companies focused on developing AI tools to verify mathematical proofs. In the future, similar tools could be applied to check AI-generated computer code, a potentially lucrative service now that AI tools can write lines of code faster than any human can debug them. Startups Harmonic and Math Inc as well as Google’s DeepMind are targeting similar AI-powered verification tools.

Axiom has attracted investor attention, reaching a valuation of $1.6 billion earlier this year. (Ono says that he has shares in the company and that he receives a salary that is similar to his former compensation at Virginia.) His interests, he says, are in helping researchers use AI to think in more-creative ways and across more disciplines.

This Musical’s Secret Weapon Is A Math Major

The Wall Street Journal recently published an interesting article (well, I found it interesting) about how “applied mathematics [is being] used to move around six different audiences in a new version of The Phantom of the Opera.” From the article’s opening paragraphs:

Simon Broucke didn’t expect to use his mathematics degree for his music assistant job at “Masquerade,” the new interactive revival of “The Phantom of the Opera” in New York.

But when “Masquerade” producers were struggling to figure out how to make it so the actors and the audience moved through the show on schedule, Broucke, 26, volunteered his background. He has dual degrees from Columbia University in music and mathematics, which uses spreadsheets and modeling to solve real-world problems. 

“Masquerade” follows the point of view of the Phantom, a disfigured musical genius who lives below the Paris Opera House and is obsessed with singer Christine Daaé. Producer Randy Weiner and his wife, the director Diane Paulus, needed to get the audience in lockstep from the start to the finish of the show in just under two hours. They also needed to get all 42 actors to their spots to perform at the right time throughout the space.

This would be simple if there was only one audience. Instead there are six. 

I thought this was a fun application of mathematics in an utterly unexpected context.

News flash: ChatGPT sometimes asserts false statements are true (Part 2)

I feel like I’ve done my good deed for the day by uncovering another instance when ChatGPT claimed a “fact” from the secondary mathematics curriculum that is simply incorrect. This one’s a doozy: it claimed that the binomial coefficent \displaystyle {23 \choose 6} = 100,947 is equal to \displaystyle {22 \choose 5} = 26,334. (The first identity in the first line below is correct; the second one is not.)

Lesson: ChatGPT is a nice tool but you get what you pay for.

Predicate Logic and Popular Culture (Part 297): Megamind

Let p be the statement “This is an Easter Bunny,” let q be the statement “There is a tooth fairy,” and let r be the statement “There is a Queen of England.” Translate the logical statement

\sim p \land \sim q \land \sim r.

This matches a line from the movie “Megamind.”

green line

Context: This semester, I taught discrete mathematics for the first time. Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

Predicate Logic and Popular Culture (Part 296): Kanye West

Let H be the set of all things, K(x) be the proposition “x kills you,” and let S(x) be the proposition “x makes you stronger.” Translate the logical statement

\forall x \in H( \sim K(x) Rightarrow S(x) ).

This matches the first line of “Stronger” by Kanye West.

green line

Context: This semester, I taught discrete mathematics for the first time. Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

Predicate Logic and Popular Culture (Part 295): Radiohead

Let p be the statement “I am king” and let q be the statement “You will be first against the wall.” Translate the logical statement

p \Longrightarrow q

This matches a line by from “Paranoid Android” by Radiohead.

Context: Part of a discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

Predicate Logic and Popular Culture (Part 294): Aerosmith

Let P be the set of all people, and let D(x) be the statement “x has dues in life to pay.” Translate the logical statement

\forall x \in P (D(x))

This matches a line by from “Dream On” by Aerosmith.

Context: Part of a discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

Predicate Logic and Popular Culture (Part 293): The Dark Knight

Let p be the statement “You die a hero” and let q be the statement “You live long enough to see yourself become the villian.” Translate the logical statement

(p \land \sim q) \lor (\sim p \land q)

This matches a line by Harvey Dent/Two-Face in “The Dark Knight.”

Context: Part of a discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.