Terry Tao Tackles Probability and Risk

 Proposing a unit of measurement of risk:

https://terrytao.wordpress.com/2021/10/03/nines-of-safety-a-proposed-unit-of-measurement-of-risk/

A Little Backstory… the Erdos/Tao photo

A substitute ‘Sunday reflection’ today, because of my experience with a tweet last evening….

I’ve always loved the above photo (brings me a smile everytime) of a 10-yr.-old Terry Tao with Paul Erdös, which I dropped into a tweet last night — the look on the faces, the synchronous postures, the concentration, the shared passion…  It originally showed up on the ’Net in 2013 courtesy of Terry himself, and went somewhat viral at the time within math circles:

https://plus.google.com/u/0/+TerenceTao27/posts/fiZbgKv4Yew

(...and a h/t to Patrick Honner who was the first to bring it to my own awareness, back then)

Is that not great! I thought it was iconic by now and viewed by everyone multiple times. But a few folks (responding to the tweet) apparently were not familiar with it, and while usually recognizing Erdös, were unsure of the youngster involved. So just to clear any confusion, am posting the little bit of history that I know (thanks again to Dr. Tao for sharing it originally -- apparently the pic comes from the University of Adelaide in Australia at an awards ceremony of the Australian Mathematics Competition,1985).

As some responders have noted, two people, bridging a large generation gap, one originally Hungarian, one originally Australian, who both came to America, and in different manners contributed so much to our joy of mathematics, and continue to delight us, in both death and life.

p.s... among Erdös' many noted linguistic idiosyncracies, he referred to young children as "epsilons," and as one of the commenters to Terry's original post says, he had finally found an interesting "epsilon." ;-)

NY Times Meet Terry Tao

Nice profile of Terry Tao in NY Times Magazine today:

http://tinyurl.com/o6yqn4d

The Tao of Tao ;-)

Terry Tao from his blog, "What's New":

"The point of rigour is not to destroy all intuition; instead, it should be used to destroy bad intuition while clarifying and elevating good intuition. It is only with a combination of both rigorous formalism and good intuition that one can tackle complex mathematical problems; one needs the former to correctly deal with the fine details, and the latter to correctly deal with the big picture. Without one or the other, you will spend a lot of time blundering around in the dark (which can be instructive, but is highly inefficient). So once you are fully comfortable with rigorous mathematical thinking, you should revisit your intuitions on the subject and use your new thinking skills to test and refine these intuitions rather than discard them. One way to do this is to ask yourself dumb questions; another is to relearn your field."


[…If you have a favorite math-related passage that might make a nice Sunday morning reflection here let me know (SheckyR@gmail.com). If I use one submitted by a reader, I'll cite the contributor.]

Tao Tackles Riemann

Honk if you can read and understand this:

http://terrytao.wordpress.com/2013/07/19/the-riemann-hypothesis-in-various-settings/

...I'm pretty much lost from the word "meromorphically" on… :-(

But seriously, Terry Tao has put up a verrrry long entry on the Riemann hypothesis, which no doubt, serious number theorists will be scrutinizing.
For me the most interesting bit comes at the end, with the first comment posted, invoking a dose of Andrew-Wiles-deja-vu! I quote it in its entirety:

"So Terence Tao has posted a blog regarding the Riemann Hypothesis. He notes that his blog is one that makes 'no new progress' on the hypothesis, but later refers to the entry as one in which he is 'simply arranging existing facts together.'
"And THAT, ladies and gentlemen, would be the perfect way for someone as amazing as Tao to provide a subtle, suave introduction to a long series of posts, the culmination of which could be an actual proof to Riemann’s actual hypothesis.
"Has the already-brilliant Terry Tao solved the Riemann Hypothesis? Stay tuned to his quadrant of internet space to find out…."

I can't imagine that the above wishful scenario would be fulfilled… but hey, it never hurts to stay tuned. (And if Dr. Tao schedules a series of 3 lectures at an upcoming conference, well, the room will be packed to the rafters.)

Happy Tao Day

 Just a quick Happy Birthday to Dr. Terence Tao today:

In honor of his special day, I'll link again to this wonderful old photo he once shared:

https://plus.google.com/u/0/114134834346472219368/posts/fiZbgKv4Yew

And below a couple of interviews I've also previously linked to with Fields Medalist Tao:

http://www.austms.org.au/Publ/Gazette/2009/Nov09/MathMinds.pdf

http://blogs.ams.org/mathgradblog/2009/10/04/an-interview-with-terence-tao/

Two-ooo Wonderful!

H/T to Patrick Honner who tweeted this delightful photo of a 72-yr.-old Paul Erdös with a 10-yr.-old Terence Tao (from Terry Tao's Google+ account):

https://plus.google.com/u/0/114134834346472219368/posts/fiZbgKv4Yew

(so great, made my day!... love the two right arms, in synchrony and thought, held to chins)

The Practical... and the Philosophical

1) Guillermo Bautista recently posted a list of 13 online sites giving calculus tutorials... might be useful for some (I'm not necessarily endorsing them, but just passing along, and also adding the link to the right-hand column "math instruction" list):

http://tinyurl.com/ajjy54d

2) A different blogger has interestingly spotlighted an older post by Terry Tao on 'rigor in mathematics' and intuitions:

http://m-phi.blogspot.com/2013/03/terry-tao-on-rigor-in-mathematics.html

May be a bit too philosophical for some, but anything from Dr. Tao of course is worth consideration.

Tao divides mathematical education into three stages: the "pre-rigorous," "rigorous," and "post-rigorous" stages. I like the approach he takes:

"The point of rigour is not to destroy all intuition; instead, it should be used to destroy bad intuition while clarifying and elevating good intuition. It is only with a combination of both rigorous formalism and good intuition that one can tackle complex mathematical problems; one needs the former to correctly deal with the fine details, and the latter to correctly deal with the big picture. Without one or the other, you will spend a lot of time blundering around in the dark (which can be instructive, but is highly inefficient). So once you are fully comfortable with rigorous mathematical thinking, you should revisit your intuitions on the subject and use your new thinking skills to test and refine these intuitions rather than discard them. One way to do this is to ask yourself dumb questions; another is to relearn your field."

Read the entire post here:

http://terrytao.wordpress.com/career-advice/there%E2%80%99s-more-to-mathematics-than-rigour-and-proofs/

An Interview with TERENCE TAO...

(via WikimediaCommons)

...well, okay, not by me :-( (maybe some day), but wonderful nonetheless. I stumbled across this 2009 interview with Dr. Tao from an Australian mathematics gazette, and (though I often avoid linking to pdfs) it's tooooo good not to pass along; many great responses from Terence (and no math required!):

http://www.austms.org.au/Publ/Gazette/2009/Nov09/MathMinds.pdf

Here's one interesting little Q & A exchange:

"Gazette: What was the best career advice you have ever received?

Tao:  Mostly people have led by example other than explicitly giving advice. I do remember one thing my advisor told me once, which was very useful. I was writing my first paper, and I put a little joke in it. I thought I was being smart. He took a look at me and said: ‘When you write a paper, this is something that will stay in the record for ever. Thirty years from now people will still read it. What you think is funny now, may not be funny thirty years from now’. He told me not to put jokes in my papers. Looking back, that was actually pretty good advice: don’t be a smart alec when you write. And it wasn’t a very good joke anyway."

And here's a second (non-pdf) interview with Dr. Tao from the Web (not as good as the above, but still good):

http://mathgradblog.williams.edu/an-interview-with-terence-tao/

If perchance you're not familiar with him, Dr. Tao (Wikipedia page HERE) is one of the world's foremost mathematicians (a former Australian child prodigy of Chinese ancestry), a Fields Medalist, and currently professor at UCLA. A Smithsonian Magazine article on him here:

http://www.smithsonianmag.com/science-nature/tao.html?c=y&page=1

And his own mathematics blog here (which on rare occasions includes posts even I can understand! ;-):

http://terrytao.wordpress.com/

Finally, another fascinating (and longish) piece below on Terence, his two gifted brothers, and the parents that raised them. It delves into both gifted and autistic children and is, I think, a super-read:

http://www.theaustralian.com.au/news/features/beautiful-minds/story-e6frg8h6-1111114147837

An excerpt:

"Billy Tao [the father] recalls that early on he and his wife were helped by the Gifted and Talented Children’s Association of South Australia, but they became uncomfortable with the fixation some parents in the association had with their children’s achievements and IQ ratings. The Taos had already seen the pitfalls of this approach during a trip to the US when they met Jay Luo, a prodigy who had earned a university science degree at age 12, but later dropped out during his PhD studies.
"'Many parents of gifted children tend to overestimate their children’s ability, they want to maximise speed,' says Billy. 'One thing I disagree about with the gifted-children movement is the emphasis on acceleration. Many gifted-education people, particularly teachers who have diplomas in gifted education, are all brainwashed with this idea of acceleration, acceleration, acceleration. What about lateral thinking? What about creativity?'
"In contrast to the effusive praise other parents heaped on their little Mozarts, the Taos avoided excessive flattery and downplayed the importance of winning."

 -----------------------------------------------

[p.s... sorry to sound like a broken record, but if anyone (math blogger) is willing to be interviewed here for my series pleeease don't hesitate to let me know that -- it's far more efficient for me to contact people who have already consented to the process than to blindly send out inquiries and not know whether they'll be returned or are even received. I really like throwing a little extra attention to folks who are out there actively promoting math to a wider audience.]

Terence Tao on Prime Numbers

Mathematical prodigy and MacArthur Fellow Terence Tao gives a talk (~50 mins.) on prime numbers: