28 July 2024 | 12:23 pm

In response to my blog post about how its easier to FIND novelty songs (and other things) than it used to be (see here) Lance showed how easy it is to CREATE a novelty song using AI. He had an AI write lyrics and music for THE BILL, see here.

The song is pretty good and pretty accurate (except that I don't drink coffee or burn toast and I would not say that in math I'm *quite the star*), but this post is NOT about the song.

There have been songs about

The Mandelbrot set (see here),

Lobachevsky (see here),

Gauss's Law (see here),

Galois (see here),

The Bolzano-Weierstrass Theorem (see here),

William Rowan Hamilton (see here),

and I will end this list with the Newton-Leibniz Rap (see here).

(I am sure there are more songs about famous mathematicians. If you know any that are better than the BW Rap, that is, any of them, please leave a comment.)

Side note: There are poems about Fermat's last theorem, as discussed in my post here.

So what do Mandelbrot, Lobachevsky, Gauss, Galois, Bolzano, Weierstrass, Hamilton, Newton, Leibniz, and Fermat have in common?

They are all famous and for a good reason- they all did math worth doing that is remembered many years later.

Bill Gasarch- not so much (unless the Muffin Problem is the key to solving world hunger).

In the past the EFFORT to write a song about someone was enough so that one would only bother for famous people.

With AI it is now EASY, as Lance did with his song THE BILL. He used ChatGPT for the lyrics and Suno for the song itself.

So what does this say about the future? It will be so easy to write songs about ANYBODY that it will be done. So having a song about you will no longer be a sign that you are famous or special. We are RIGHT NOW in a transition. If I tell my nephew that there is a song about me and that I have a Wikipedia page, he is impressed. My great niece- not so much.

24 July 2024 | 1:07 pm

Computational Complexity conference. I attended the first 26 meetings (1996-2011) and 30 of the first 31. I chaired the conference committee from 2000-2006. According to DBLP I still have the most papers appearing in the conference (32). I even donated the domain name for the conference (with the caveat that I could keep the subdomain for this blog).

Only Eric Allender had a longer streak having attended the first 37 conferences through 2022 in Philadelphia (if you count the two online during the pandemic) before he retired.

But I haven't been back to Complexity since that 31st conference in Tokyo in 2016. Due to my administrative roles, various conflicts and changes in the field you just start missing conferences. But with the conference at the University of Michigan in Ann Arbor within driving distance of Chicago it was time to go home for the 39th meeting. And it's a good thing I drove as more than one person had flight delays due to the Crowdstrike bug.

The complexity conference remains relatively stable at about 75-100 registrants, the majority students and young researchers. I've moved from wise-old sage to who is that guy. But I'm having great fun talking to old acquaintances and new. I'm impressed with the newer generations of complexity theorists--the field is in good hands.

Best paper goes to Michael Forbes Low-Depth Algebraic Circuit Lower Bounds over Any Field. the work of Limaye, Srinivasan and Tavenas I talked about last month gave an explicit polynomials with superpolynomial-size over constant depth algebraic circuits but it required polynomials over large fields. Forbes extended the lower bounds to all field sizes.

Best student paper goes to Ted Pyne from MIT for Derandomizing Logspace with a Small Shared Hard Drive for showing how to reduce space for randomized log-space algorithms on catalytic machines.

Check out all the papers in the online proceedings.

From a relatively quiet business meeting: 36 papers accepted out of 104 submissions, a bit up from previous years. 75 attendees including 42 students, similar to recent years. 2025 conference at the Fields Institute in Toronto August 5-8. 2026 in Lisbon or Auckland.

The loss of Luca Trevisan, PC Chair 2005 and local arrangements chair in 2013 in San Jose, loomed large in the business meeting and at the conference.

21 July 2024 | 1:00 pm

On June 21, 1993, at the Issac Newton Institute for Mathematical Science, Andrew Wiles announced that he had proven Fermat's Last Theorem. That wasn't quite right- there was a hole in the proof that was later patched up with the help of Richard Taylor (his former grad student). A correct proof was submitted in 1994 and appeared in 1995. Wiles is the sole author.

June 21, 2024 was the 31st anniversary of the announcement. (So today is the 31-years and 1-month anniversary). I COULD have had ChatGPT write some poems about it. But there is no need. There are already some very nice poems about it written by humans. Will humans eventually lose the ability to write such things? Would that be a bad thing? Either ponder those questions or just enjoy the poems. (My spellcheck still thinks ChatGPT is not a word. It needs to get with the times.)

1) A link to a set of poems about FLT: here.

2) Here is a poem that is not in that set but is excellent.

A challenge for many long ages

Had baffled the savants and sages

Yet at last came the light

Seems that Fermat was right

To the margins add 200 pages

(I don't know who wrote this or even where I read it. If you know anything about where it was published or who wrote it, please let me know. ADDED LATER:Eric Angelini left a comment telling me that this limerick was written by Paul Robert Chernoff. The commets also has a link to lots of limericks that Paul Robert Chernoff wrote. Thanks!)

3) Here is a poem by Jonathan Harvey that mentions the gap in the original proof.

A mathematician named Wiles

Had papers stacked in large piles

Since he saw a clue

He could show Fermat true

Mixing many mathematical styles

He labored in search of the light

To find the crucial insight

Young Andrew, it seems

Had childhood dreams

To prove Mr. Fermat was right

He studied for seven long years

Expending much blood, sweat, and tears

After showing the proof

A skeptic said “Poof!

There’s a hole here”, raising deep fears.

This shattered Mr. Wiles’s belief

His ship was wrecked on a reef

Then a quick switcheroo

Came out of the blue

Providing his mind much relief.

Mr. Wiles had been under the gun

But the obstacle blocking Proof One

Fixed a much older way

From an earlier day

And now Wiles has his place in the sun

4) Here is a poem by John Fitzgerald that mentions other unsolved problems including P vs NP

Fermat’s theorem has been solved,

What will now make math evolve?

There are many problems still,

None of which can cause that thrill.

Years and years of history,

Gave romance to Fermat-spree,

Amateurs and top men too,

Tried to push this theorem through.

Some have thought they reached the goal,

But were shipwrecked on the shoal,

So the quest grew stronger still;

Who would pay for Fermat’s bill?

So what is now the pearl to probe,

The snark to hunt, the pot of gold,

The fish to catch, the rainbows end,

The distant call towards which to tend?

One such goal’s the number brick,

where integers to all lengths stick:

To sides, diagonals, everyone,

Does it exist or are there none?

Then there are those famous pearls,

That have stymied kins and earls:

Goldbach, Twin Primes, Riemann Zeta;

No solutions, plenty data.

Find a perfect number odd;

Through 3n + 1 go plod;

Will the P = N P ?

Send a code unbreakably.

Are independence proofs amiss;

Continuum Hypothesis;

Find a proof which has some texture

of the Poincaré conjecture.

And so, you see, onward we sail,

there still are mountains we must scale;

But now there’s something gone from math,

At Fermat’s end we weep and laugh.