I have just returned from Basel, Switzerland, on the occasion of the awarding of the 2019 Ostrowski prize to Assaf Naor. I was invited to give the laudatio for Assaf’s work, which I have uploaded here. I also gave a public lecture (intended at the high school student level) at the University of Basel entitled “The Notorious Collatz conjecture”; I have uploaded the slides for that here. (Note that the slides here are somewhat unpolished as I was not initially planning to make them public until I was recently requested to do so. In particular I do not have full attribution for some of the images used in the slides.)

Basel has historically been home to a number of very prominent mathematicians, most notably Jacob Bernoulli, whose headstone I saw at the Basel Minster,

and also Leonhard Euler, for which I could not find a formal memorial, but I did at least see a hotel bearing his name:

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16 February, 2020 at 10:38 am

Allen KnutsonI don’t know about memorials, but Euler’s actual grave is in St. Petersburg.

16 February, 2020 at 11:37 am

RabeDid you find Hotel Hilbert as well? Thank you for sharing this!

17 February, 2020 at 1:09 pm

AnonymousIs that the one in the song? “Since my baby left me, I’ve had a new place to dwell; Its floors go to infinity, it’s the… Hilbert Hotel”.

16 February, 2020 at 12:33 pm

AnonymousEuler is also known as the solver of the Basel problem

https://en.wikipedia.org/wiki/Basel_problem

16 February, 2020 at 12:55 pm

JosephSugarThe “eadem mutata resurgo” is interesting. Wonder if he simply refers to the spiral or it was his philosophical take on life, nature, the universe, in general. The problem is that mutata is both feminine singular and neuter plural.

16 February, 2020 at 1:56 pm

Gil KalaiCongratulation to Assaf!

16 February, 2020 at 2:21 pm

MaxThanks for one more inspiring post! But you should please correct repeated instances of “Radamacher” to (Hans) *Rademacher* (in the Assaf laudatio at least, didn’t check whether it appears in the other lecture or in your arxiv.org/1909.03562). (I could imagine the Swiss already made that remark – it really hurts the eyes of a German-speaking reader!)

[Corrected, thanks – T.]17 February, 2020 at 5:18 am

Radu ZaharopolDear Professor Tao,

Many thanks for your message. Sincerely yours, Radu Zaharopol

17 February, 2020 at 7:59 am

David FryDear Terry,

What an amazing academic trip regarding Switzerland.Â But the burning question here is, HOW WAS THE CHOCOLATE? Thanks, David

Very Sincerely,

David W. Fry

18 February, 2020 at 3:42 am

Michel EveDear Prof Tao

I have a naive question regarding the Collatz conjecture. As I am just an amateur, I waited to have a low level presentation of your results to understand the progress made .I have therefore a question on your excellent slides on the subject.

You mention the work of Terras which shows that almost all initial values n iterate eventually to a value less than n and you make the point that, if it had been “all” initial values then the conjecture would have been proven. This seems to say that the conjecture is proven for all initial values except for a small subset S of initial values for which one cannot say anything.

Then you present you latest result which is tighter but still applies to “almost all” initial values but you claim that this is the closest one can get short of a full proof of the conjecture.

My question is : Do you share the same definition of “almost all” with Terras ? ie: is your subset S the same as Terras’s ? If it is the same then it is a step forward but if it is larger ..

I am sure that I must be wrong somewhere ,I would very much appreciate your comment.

18 February, 2020 at 4:10 am

Michel EveSorry I see now that my statement “the conjecture is proven for the subset N-S is wrong as some values less than n may lie in S…

18 February, 2020 at 4:29 am

AnonymousHotel Euler is not named after Leonhard. Abraham Euler established a taverna in 1867 which later became the hotel. But of course maybe Abraham was (far) family of Leonhard, born 1707.

I always enjoy reading about the Collatz Conjecture. Some 25 years ago I tried to solve it as well and created pictures of triangles representing the binary digits of the numbers. Was reminded of this when I read your new “almost all” paper.

20 February, 2020 at 1:50 am

Andrew HoweSuperb Collatz slides thanks – very accessible for aspiring mathematicians. I will be forwarding to a pre-university friend

22 February, 2020 at 1:42 am

James MoriartySo you are using the Samsung Galaxy S9 SM-G960U. Well, I suppose it’s got a reasonably safe operating system – except towards Google Inc.

23 February, 2020 at 3:20 am

Islem GhafforAn Equivalent Problem to the Collatz Conjecture

28 February, 2020 at 7:19 am

AnonymousThis is a nice idea to represent the Collatz iteration (originally given in terms of one variable) by using two (or more) variables, since the original (one dimensional) formulation of the iteration as a (deterministic) discrete-time Markov chain may have several equivalent representations using finitely many “state variables” – which may be easier to analyze than the original formulation (which is based on a single “state variable”) – the idea to use the Syracuse iteration (in order to simplify the analysis) is similar, but perhaps there are even better (perhaps multidimensional iterations) equivalent formulations which may have additional “nice properties” (to simplify the analysis) than the Syracuse iteration.

28 February, 2020 at 9:00 am

Robert SilvermanI reply here because I do not know how to start a new thread.

I am astonished that there has been no mention of Peter Montgomery’s

passing:

https://fataldeaths.com/2020/Peter-Montgomery-(mathematician)

Peter was a good friend and I am deeply saddened by his death.

28 February, 2020 at 9:35 pm

Michael Rhttps://iacr.org/people/PeterMontgomery.html

28 February, 2020 at 9:37 pm

Michael RThis is the only obit I found via google search.

2 March, 2020 at 1:16 am

Martin LotzThere is a memorial to Euler at the place of his birth, in Riehen (a suburb of Basel): https://images.app.goo.gl/W7x696Z9ieEx4Aj67

This is very close to where my parents live, used to go past this place regularly :)

3 March, 2020 at 10:18 am

.Fed cut 0.5 points. Does the fed know something we don’t? Is it trying assimilate ‘common knowledge’ in your parlance?

28 September, 2020 at 9:15 pm

collatz standing on shoulders of giants (not!) | Turing Machine[…] the quanta writeup. he also has an excellent “high school” level slideshow refd on his blog, my favorite slide is the squirrel at the end that also seems to ref Creation of Adam by […]

17 November, 2020 at 6:21 pm

john ronandnot sure if we can proof Collatz this way

https://photos.app.goo.gl/w4gGNmocgPBqPziu6