Our Thoughts on P=NP
The Clay prize anniversary is soon.
SME keynote lecture source |
Evelyn Lamb is a mathematician who is also a journalist. She has a blog called Roots of Unity on the Scientific American blog network. Also impressive is that she designed the AMS Page-a-Day Calendar on behalf of the American Mathematical Society. It is available from the AMS with member discounts and is filled with wonderful tidbits on math.
The other day she interviewed Ken and me on P=NP.
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No Password Encryption
Who can remember passwords anyway?
Real Bernie Sanders reaction source |
Larry David is an American comedian. He was the lead writer and producer of the Seinfeld TV series. During the previous and current election cycles he has played Presidential candidate Bernie Sanders in skits on Saturday Night Live. His “Bernie” rails about issues with passwords.
Today I want to talk about reducing our dependence on passwords.
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Servant: The TV Show
Using logic to try and understand the show Servant
[ M. Night ] |
M. Night Shyamalan is the creator of many wonderful horror movies, including The Village and The Sixth Sense. His films often have a twist ending.
Today I thought I would try to apply math and logic to his latest creation, the TV show called Servant.
Resolutions For 2020
Some fun about resolutions.
source |
Ben Orlin is a funny mathematician. His book title Change Is the Only Constant was selected by the blog Math-Frolic as the best mathematics book of 2019.
Today Ken and I want to try to get you to at least smile, if not laugh.
Orlin is a funny chap—okay I just got back from London—so forgive me for using “chap”. Check Orlin’s site out for proof that he is funny. Here are some of his examples of math types rewriting famous opening lines from books. We will make this into a kind of quiz. You must guess the book title from the modified quote:
- The times had high variance.
- Up to isomorphism there is one happy family.
- It was a bright cold day, and the clocks were not mod 12.
- All this happened, but not with equality.
- was spiteful, full of a baby’s venom.
- It was zero at the leading ordinal of viewing.
The third is the first hard one—I did not get it. The last one (of three from Ken not Ben) is probably unfair. All six of them, however, are on the “First Lines Literature Coffee Mug” which Ken received a year ago as a Christmas present from his sister. I did not know this when I chose the first three.
Orlin’s Resolutions
Many of us make resolutions for the new year. Here are some examples from Orlin:
Be better at explaining what I do to family and friends. I, Dick, have trouble with this one.
Not to prove by contradiction what can be proved directly. Assume that and
Stop using the word “obviously.” Here at GLL we try to avoid this, at least when it is not obvious. We posted about phrases to avoid a year ago.
Our Resolutions
Here are some of ours:
Stop doubting quantum computer claims. Unless, adds Ken, you have a possible concrete way of challenging them…
Start trying to apply AI methods to complexity theory. Could there be a new learning approach to 3-SAT? Note that PAC learning kind-of came from there. See for instance the end of this.
Stop trying to understand proofs that Peano arithmetic is inconsistent. I still do not understand what logic they use to prove that Peano is inconsistent. What if that logic is inconsistent?
Start up some fundamental research ideas and attempts on hard problems again.
And try to make GLL better, including making it appeal to a wider community.
Open Problems
The answers are:
- A Tale of Two Cities by Charles Dickens: “It was the best of times, it was the worst of times.”
- Anna Karenina by Leo Tolstoy: “Happy families are alike; every unhappy family is unlike in its own way.”
- 1984 by George Orwell: “It was a bright cold day, and the clocks were striking thirteen.”
- Slaughterhouse-Five by Kurt Vonnegut: “All this happened, more or less.”
- Beloved by Toni Morrison, who died this year: “124 was spiteful, full of a baby’s venom.” This explanation of the line continues: “We know all about numbers being spiteful. We took high school algebra. We’ve experienced the pain. But in this instance, the quote isn’t actually referring to a number. There’s not some mysterious mathematical entity that’s come to wreak havoc on the characters in our story. Here, ‘124’ refers to…”
- Lolita by Vladimir Nabokov: “It was love at first sight…” But wait—this is not the first line of the novel. The first line is maybe not suitable for a coffee mug or family-friendly blog. Instead it is the first line of chapter 29 of part II. We did say it was unfair. Update: Oops—as noted here, it is the first line of Catch-22 by Joseph Heller. Maybe Ken’s Google engine shares his tendency toward chess-playing authors…
Have a happy new year, and make some fun resolutions. Please let us know some of them, or ideas for ours.
[added Update fixing last first-line answer.]
A Math Gift For All
Happy holidays to all.
Kathryn Farley is my dear wife. We just celebrated Christmas together and then went off to London for a holiday.
Today I thought I would share a gift with you.
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Predicting When P=NP is Resolved
Has it outlasted the ability to estimate when?
Composite of src1, src2 |
Ryohei Hisano and Didier Sornette wrote in 2012 a paper titled, “On the distribution of time-to-proof of mathematical conjectures.”
Today Ken and I discuss predicting the end to mathematical conjectures. This is apart from considering odds on which way they will go, which we also talk about.
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