The Latest AI LLM Feats

The AI LLMs have solved some big math problems, including the Jacobian conjecture this week. One, presumably an unreleased Openai GPT-6, has also aggressively hacked into other computers. Here is an explanation

Our AI model tried really hard to hack out of its sandbox, a computer with no internet access, in order to find the answer to a test problem it had been given. To do this, it found previously unknown software bugs that allowed it to reach an OpenAI computer it wasn't supposed to be able to access. Then it started hacking other computers on OpenAI's networks until it found one that had Internet access. After gaining Internet access, the AI model thought about where it could find the answers to the test question and figured the AI platform Hugging Face might have the data it was looking for. It then found ways to hack Hugging Face to steal the information it could use to cheat the test. The AI model used several hacking techniques together, including using a stolen password and finding several totally new security bugs in Hugging Face's computers, allowing the AI model to take control of those computers.

That would have been illegal, if a human did it.

The open source models are almost as good. Artificial general intelligence is here.

Elon Musk brags that he will be able to make a non-woke version of The Odyssey before the end of the year. I doubt it, but it is not impossible. Likely within five years.

Update: Jacobian conjecture explained here.

Famous Computer Scientist Died

News:

Rabin has sadly just passed away at 94. This is a short piece on honoring him immediately. More is planned for the future.

His work has touched key areas of mathematics as well as central areas of computer theory. Without his work theory would be completely different today.

Besides what is mentioned, he developed a method of public key cryptography similar to RSA. He got it about the same time, and may have even been first.

It is a quirk of history that RSA caught on. For technical reasons, the Rabin method is trickier to use, but people could have figured out how to use it safely.

RSA was inspired by the Diffie-Hellman (DH) method. The elliptic curve variant of DH is now the most common used. It has the advantages of small keys, signatures, and idiot-proof key generation.

These are all quite secure, except for the possibility of quantum computers, which could break them all.

What the Islamic Golden Age achieved

From a new paper:

At the end of fifth century C.E. the Roman Empire was in shambles. It was divided into the Western and Easter parts already in 395 C.E., and prone to steadily increasing barbarian invasions ever since. The last Roman emperor Romulus Augustulus was disposed of in 476 C.E. by war Germanic chief Odoaker, who proclaimed himself emperor.

The Eastern part of the Empire with capital in Constantinople gradually transformed into Greek-speaking Byzantine Empire. All these territories, including Egypt and North Africa up to Spain were Christian since the Emperor Constantinus proclaimed Christianity to become state religion. However, since the fall of the Western Roman Empire, most of these territories were deprived of any organized army and statehood, prone to barbarian invasions, among which the Huns, the Goths and the Vandals were the most important and disastrous.

In the midst of 7th century C.E. a new religion was proclaimed by Muhammad in Arabia, derived from Jewish and Christian traditions, simplifying them and professing with great conviction the uniqueness of God, This was an important revolution, because it replaced the tribal principle by a more general religious and social unity.

While Europe entered the era of turmoil and invasions Dark Ages, lasting roughly from 500 C.E. until the 12th century, the Arabs have conquered vast territories creating a buyoant Islamic Civilization, which spread from Moorish Spain in the West, through Western North Africa, through Egypt and Mesopotamia, touching India and even the most western parts of China. ...

The Golden Age of Islamic civilization covers the time span from 9th till 13th century C.E. in Baghdad under the Abassid dynasty, and in Moorish Spain until the fourteenth century; it lasted a little bit more in Central Asia, falling under the Mongol conquest.

It goes on to detail those Islamic Golden Age advances, mostly in mathematics and astronomy.

the Arab and Islamic Astronomy, especially in the observational field, represents the last chapter of the science of Antiquity, a natural extension of Babylonian; Indian, and above all Greek scientific heritages of a small world centered on the Earth, for which the sphere of fixed stars represented the utmost external limit.

Modern science germinated within the new university framework of Medieval Europe between the 13th and 15th centuries, openly born with the intellectual revolution brought by Copernicus in the 16th century, pursued later on by Galileo, Descartes, Kepler, Leibniz, Newton and other European scientific luminaries.

Baghdad and Persia had great intellectual traditions from before the Mohammedan conquest. The Islamic accomplishments were mostly in the preservation and improvement of science from elsewhere. This part is not so surprising.

The surprising thing, not covered in the paper, is how European science and math skyrocketed, while the Islamic Golden Age ended. This cannot be explained by Europeans getting higher IQ while others declined. No, clearly Christendom was doing something right, while the Islamic world was doing the opposite.

Africa is Bigger than You Think

Reuters:

The African Union has backed a campaign to end the use by governments and international organisations of the 16th-century Mercator map of the world in favour of one that more accurately displays Africa's size.

I am surprised that they do not complain about the term "Sub-Saharan Africa".

How Girls Fall Behind in Math

A new Nature article claims to have resolved a nature-nuture debate.

When do girls fall behind in maths? Gigantic study pinpoints the moment

Analysis of almost three million children captures when ‘mathematical gender gap’ first emerges and could help focus efforts to stop girls from falling behind. ...

Boys and girls receive similar maths scores at the start of school, but boys pull ahead of girls after just four months (see ‘Watch the mathematics gender gap emerge’). A more dramatic gap in mathematical performance emerges after 12 months of school, according to the analysis, published on 11 June in Nature1.

“This paper suggests that the gender inequalities in children’s maths performance aren’t innate or inevitable,” says psychologist Jillian Lauer at the University of Cambridge, UK. “If we want to stop girls from falling behind, we need to focus on their early experiences at school.”

The research found that boys and girls get to first grade being equally able to count, but boys pull ahead when asked to do problems like 5+6=11. The poor girls never catch up.

This is ridiculous. Grade schools are much more adapted to teaching girls than boys. I do not think that girls are falling behind because first grade teachers are not teaching them to add well.

I also don't think first grade addition has much to do with long term math abilities.

I met the science writer of this story a long time ago. She might even remember me, even though it has been maybe 25 years. I don't blame her for this. She is just writing up the published research that the Nature editors accepted. I am happy to see she is a successful science writer.

This research is only appearing in the leading British science journal because of the leftist egalitarian implication. Nature even has an editorial:

Close the mathematics gender gap: huge study prompts urgent call to action ...

‘Boys are better at maths’. It’s a stereotype that’s still pervasive among many children, teachers and parents. But is there any truth to it? A study of millions of schoolchildren in France reveals that boys pull ahead of girls in mathematics early, during the first year of school, but suggests that this ‘gender gap’ is not inevitable ...

The lack of differences in achievement at the start of school is an indication that boys have no inherent advantages when it comes to raw ability or interest. That, in turn, indicates that the gap could be reduced, or even erased, if children’s early environment at school and at home is changed. By pinpointing when girls start to fall behind boys, this study should help to focus further research into interventions that could reduce the gap.

Such interventions are needed. Women in many countries are less likely than men to study maths, ...

The latest study is a wake-up call for parents and carers, educators and scientists. The next step is for researchers to develop various interventions and measure their impact before and during the first year of school. For instance, do girls in classes taught by teachers who provide support to reduce anxiety around maths perform better than girls who don’t receive such support?

No, this is crazy stuff. First grade schooling is already girl-oriented. First grade girls do not have math anxiety. It is foolish to even think that this is a problem to be solved. From Wikipedia:

The gender-equality paradox is the finding that various gender differences in personality and occupational choice are larger in more gender equal countries.

The better you teach math, the more you will find performance differences. Face reality.

Proving Uncountability Without Diagonalization

Cantor is famous for his diagonal proof of the uncountability of the real numbers. I just learned that his first proof was different. Here it is.

First some facts about the completeness of the reals. A bounded monotone sequence of real numbers must converge. That is, if a₀ < a₁ < a₂ < ... < C are real numbers, then the sequence must converge to some point b ≤ C. Likewise, if the sequence is monotone decreasing.

Consequently, if we have a sequence of nested intervals, ie where each interval properly contains the next one, then the intersection must be nonempty. That is because the left endpoints form a bounded monotone sequence, and must converge to some point in all the intervals.

(I am being a little sloppy about whether the intervals are open or closed, ie whether they include the endpoints. It does not matter, as long as each interval is contained in the interior of the previous one. They cannot share an endpoint.)

Theorem If a₀, a₁, a₂, ... is a sequence of real numbers, then there must be a real point not in the sequence.

Proof Removing duplicates if necessary, assume the numbers are all distinct. Let I₀ be the interval determined by a₀ and a₁. Find the next two points in the sequence that are also in the interval, and let them define the interval I₁. If that is not possible, then all the points inside I₀ must be absent from the sequence.

Continuing, we get an infinite sequence of nested intervals, and so there must be a point in all of them. By the construction, that point cannot be in he original sequence of reals.

This proves that the real numbers are uncountable.

A Sideways Triangle is a Triangle

Today's NY Times Mini Crossword has the clue:

Button with a sideways triangle

Ihe answer is "Play", of course, but what do they think that a triangle is?

Schools teach triangles, starting in kindergarten, and I am pretty sure no one teaches that a triangle has to be oriented in a particular way in order to qualify as a triangle.

Math and Dr. Seuss are being canceled

Sergiu Klainerman writes:

In my position as a professor of mathematics at Princeton, I have witnessed the decline of universities and cultural institutions as they have embraced political ideology at the expense of rigorous scholarship. Until recently — this past summer, really — I had naively thought that the STEM disciplines would be spared from this ideological takeover.

I was wrong. Attempts to “deconstruct” mathematics, deny its objectivity, accuse it of racial bias, and infuse it with political ideology have become more and more common — perhaps, even, at your child’s elementary school.

This phenomenon is part of what has been dubbed “The Great Awokening.” As others have explained powerfully, the ideology incubated in academia, where it indoctrinated plenty of bright minds. It then migrated, through those true believers, into our important cultural, religious and political institutions. Now it is affecting some of the country’s most prominent businesses.

He is right. Math is not immune. We have not yet seen the limits of what will be deconstructed.

For historical reasons, we often discuss contributions to the field of mathematics from the Egyptians, Babylonians, Greeks, Chinese, Indians and Arabs and refer to them as distinct entities. They have all contributed through a unique cultural dialogue to the creation of a truly magnificent edifice accessible today to every man and woman on the planet.

He is right, but I think he misses the point. A lot of fields have drawn on contributions from many sources. What we call Western Civilization has taken ideas, science, technology, and values from Romans, Greeks, Medieval Europeans, Egyptians, and many others.

For various reasons, Western Civilization is a target. Today's news is that Dr. Seuss is being canceled. Explaining that his works were fairly enlightened, and appreciated by many, does no good. His excellent children's books must be banned anyway.

(I once had an office down the hall from Klainerman, but I had no direct dealings with him.)

Objective Math is White Supremacist

Jason Rantz writes:

The Bill and Melinda Gates Foundation is bankrolling a group of activists who believe math is racist.

A group of fringe educators have compiled a six-part toolkit offering an “integrated approach” to developing an “anti-racist math practice” viewed through a social justice lens. It chides the “concept of mathematics being purely objective” as “unequivocally false.” It argues focusing on the “right answer” to math equations is an example of white supremacy.

I think Gates is onto something. Mathematics is almost entirely a White invention. And using math to quantify objective facts about the world is also a White practice.

When the anti-racists of today make their arguments, there is never any underlying logic or math that makes any sense.

It is true that ancient cultures in India and China and even Central America had learned to count, and use math to build things and account for transactions. But it wasn't really Mathematics until the Greeks.

CNN reports:

Covid-19 is disproportionately sickening and killing Black Americans, the result of centuries of structural racism, a group of Harvard researchers says.

If the US had paid reparations the descendants of Black Americans who were enslaved, though, the risk of severe illness and death from the virus would be far lower, according to a new, peer-reviewed study by the researchers. ...

They made their calculations with a model that would pay $250,000 in reparations per person or $800,000 per household. They also compared Louisiana and South Korea using infection data rates for the first two months of the epidemic.

The researcher's model found that Louisiana took twice as long as South Korea to bring the R-naught value below 1, "the critical value at which an outbreak will die out in a population."

Really? They compared Louisiana and South Korea, and the main difference was that Blacks were not being paid slavery reparations? This is too stupid to comment. The lead author appears to be White, but he is just trying to get tenure by sucking up to Blacks and SJWs.

Amy Harmon on blacks and math ability

Amy Harmon reports in the NY Times:

What I Learned While Reporting on the Dearth of Black Mathematicians

My recent reporting has highlighted why racial exclusion in “the queen of the sciences’’ may matter most of all.

She wrote a whole story on a black mathematician moving from one college to another for obscure reasons, and discovered that black mathematicians are uncommon. She cites this xkcd cartoon on the math being the purest field, by far.

She ignored some more interesting ethnic issues, such as why those same colleges are full of foreign professors with weak English skills.

If I am parsing her convoluted reasoning properly, she says:

Some people claim that there are not many black research mathematicians because African-Americans are not as intelligent as other races. ...

[They lack any] reason to think that a genetic trait would be impervious to social or educational intervention

[They lack any reason to think] that high I.Q. is key to math ability

Yes, all genetic traits are impervious to social or educational intervention. Those interventions do not change the genes.

And yes, there is reason to think that high IQ is key to math ability. You sometimes see someone with high IQ and poor math skills. You sometimes see someone with strong ability in music or some other field without a high IQ. But you never see anyone with high math ability without high IQ.

This article is so goofy that I wonder if the NY Times is trolling us.

The same paper has this AP story:

British author and broadcaster David Icke, who critics accuse of anti-Semitism and of being a conspiracy theorist, has had his Australian visa canceled ahead of a speaking tour.

More precisely:

Conspiracy theorist David Icke has blasted the immigration minister, David Coleman, for revoking his visa just hours before boarding a flight to Australia for his March speaking tour.

Icke, a former footballer and sports broadcaster best known for his theory that the world is run by a cabal of giant shape-shifting lizards, has claimed Jewish people bankrolled Hitler, caused the 2008 global financial crisis and staged the 9/11 terrorist attacks. ...

Icke denied being antisemitic and a Holocaust denier, and said he had never advocated for Holocaust denial to be taught in school. ...

Icke said the cancellation of his visa “sets a dangerous precedent for citizens who have differing views and are willing to openly express these”.

“This is the creation of a blatantly Orwellian totalitarian state and says the government believes they have the right to dictate what the nation can and cannot choose to hear.”

I don't think that Icke blames the Jews for bankrolling Hitler or those other things. I think his theory blames shape-shifting lizards who are masquerading as Jews and others. That would be anti-reptilian, not anti-Semitic. But I could be wrong, as Icke is probably trolling us also. I wonder if Jussie Smollett will be allowed into Australia.

If Icke is banned for being anti-Semitic, then why isn't the TV show The X-Files also banned? It also involves weirdo globalist alien conspiracy theories.

Censored explanation of male intelligence

Math professor Theodore P. Hill writes:

In the highly controversial area of human intelligence, the ‘Greater Male Variability Hypothesis’ (GMVH) asserts that there are more idiots and more geniuses among men than among women. Darwin’s research on evolution in the nineteenth century found that, although there are many exceptions for specific traits and species, there is generally more variability in males than in females of the same species throughout the animal kingdom.

Evidence for this hypothesis is fairly robust and has been reported in species ranging from adders and sockeye salmon to wasps and orangutans, as well as humans. Multiple studies have found that boys and men are over-represented at both the high and low ends of the distributions in categories ranging from birth weight and brain structures and 60-meter dash times to reading and mathematics test scores. There are significantly more men than women, for example, among Nobel laureates, music composers, and chess champions—and also among homeless people, suicide victims, and federal prison inmates.

This got him into trouble:

Theodore Hill, a retired professor of mathematics at Georgia Tech, claims that activists successfully pressured the New York Journal of Mathematics to delete an article he had written for the academic journal because it considered a politically incorrect subject: the achievement gap between men and women at very high levels of human intelligence.

This is a subject that women appear to be incapable of understanding. Or maybe they understand it, and are desperate to censor research that they cannot refute. Either way, you can forget about hearing the truth in today's colleges.

Update: This issue has drawn commentary from Terry Tao, Tim Gowers, and Lubos Motl.

It is funny to see these prominent mathematicians make excuses for leftist egalitarian groupthink. Gowers actually says that it is a myth that being good at math is a question of raw brainpower. He presumes that there are no many female mathematicians because of discrimination, lack of role models, and similar reasons. He doubts that women are really so picky as to only want to mate with the top 30% or so of men. So he rationalizes rejecting the paper. He later retracted some of his criticisms of the paper.

It is instructive to see Gowers' thought process in action. He is a brilliant mathematician and he struggles with some fairly simple ideas that are commonly observed about male-female sex differences. It is impossible that the ideas are difficult for him. It can only be that many years of leftist brainwashing have made it difficult for him to think clearly on the subject.

Leftist weaponisation of social media

John Naughton writes a London Guardian essay:

One of the biggest puzzles about our current predicament with fake news and the weaponisation of social media is why the folks who built this technology are so taken aback by what has happened. ...

It never seems to have occurred to them that their advertising engines could also be used to deliver precisely targeted ideological and political messages to voters. Hence the obvious question: how could such smart people be so stupid?

No, they were not so stupid. Not only were they aware of the utility of political ads, they spent millions of dollars marketing those services to political operatives.

Now mathematics, engineering and computer science are wonderful disciplines – intellectually demanding and fulfilling. And they are economically vital for any advanced society. But mastering them teaches students very little about society or history – or indeed about human nature. As a consequence, the new masters of our universe are people who are essentially only half-educated.

Being half-educated is better than being negatively educated. Humanities majors are brainwashed into leftist thinking. Those professors do not teach human nature, they teach a denial of human nature.

“a liberal arts major familiar with works like Alexis de Tocqueville’s Democracy in America, John Stuart Mill’s On Liberty, or even the work of ancient Greek historians, might have been able to recognise much sooner the potential ...

Note that he has to go back centuries to find scholars concerned with human nature.

All of which brings to mind CP Snow’s famous Two Cultures lecture, delivered in Cambridge in 1959, in which he lamented the fact that the intellectual life of the whole of western society was scarred by the gap between the opposing cultures of science and engineering on the one hand, and the humanities on the other – with the latter holding the upper hand among contemporary ruling elites.

Snow's conclusion was that the humanities scholars were the half-educated ones. He found that the science and engineering scholars were well-educated in the humanities, but the humanities scholars were science illiterates.

Google, Facebook, and Twitter are run by leftists who use the platform to promote leftist views, and censor others. The same could be said for the NY Times, Wash Post, CNN, NBC, NPR, etc.

What seems to bug the leftists is that their control is not universal. You can hear non-leftist views on talk radio, Fox News, RT TV, and the internet. Furthermore, recent disclosures have shown that maybe 0.0001% of Facebook ad revenue was used for political ambiguous messages from sources that cannot be precisely identified.

Sure, RT has criticism of American capitalism, but so does NPR. At least RT is not using American tax money for its anti-American propaganda.

So what did Facebook do that was so bad? The essay refers to this:

Along with his fellow Jews, Mark Zuckerberg introspected over Yom Kippur and asked for forgiveness via Facebook from “those I hurt this year … for the ways my work was used to divide people rather than bring us together”. He promised to “work to do better”.

Presumably, Zuckerberg was referring to the two types of harm that Facebook has recently acknowledged causing: allowing Russian nationals to purchase Facebook ads to aid Donald Trump’s 2016 campaign and allowing ad buys on hateful search terms.

It took congressional investigations, a special counsel investigation, and great reporting by Politico to get Facebook to fess up to these sins. It took President Obama pulling Mark Zuckerberg aside shortly after the election and schooling him in Facebook’s responsibility for distributing electioneering lies.

How is this harmful?

Clinton outspend Trump on advertising by about $1B to $200M. In terms of free partisan news stories and editorials in the mainstream media, favoritism towards Clinton was maybe 10-1 or 20-1. The Russians only spent several thousand dollars, and most of it did not even mention Trump.

I am all in favor of pointing out foreign influence on our elections, but the biggest NY Times stockholder is Mexican billionaire Carlos Slim. He is a Trump-hater with a financial interest in Mexicans invading the USA. The NY Times is run by Jews who have ties to Israel. The NY Times, and its foreign influences had a vastly greater effect on the election.

Everyone points to the 17 USA intelligence agencies that supposedly said that the Russians influenced the election. In fact, none of those intelligence agencies said that the Russians had any influence on the election. Their report mostly consisted of reciting some RT stories that were critical of the USA.

Math is racist

A new book titled Weapons of Math Destruction has gotten a lot of publicity, and here is a representative excerpt:

Algorithms are being used to determine how much we pay for insurance (more if your credit score is low, even if your driving record is clean), or what the terms of our loans will be, or what kind of political messaging we’ll receive. There are algorithms that find out the weather forecast and only then decide on the work schedule of thousands of people, laying waste to their ability to plan for childcare and schooling, never mind a second job.

Their popularity relies on the notion they are objective, but the algorithms that power the data economy are based on choices made by fallible human beings. And, while some of them were made with good intentions, the algorithms encode human prejudice, misunderstanding, and bias into automatic systems that increasingly manage our lives. Like gods, these mathematical models are opaque, their workings invisible to all but the highest priests in their domain: mathematicians and computer scientists. Their verdicts, even when wrong or harmful, are beyond dispute or appeal. And they tend to punish the poor and the oppressed in our society, while making the rich richer.

No, credit scores do not punish the poor. Lots of poor ppl have higher credit scores than rich ppl. You can get a high credit score by paying your bills, borrowing money, and making the necessary timely payments.

Credits scores allow me and millions of others to easily buy things online, and when traveling. There is no easier alternative. Vendors are eager to sell me things, but just want some assurance that they will get paid.

Math is racist in the same sense that the truth is racist.

This book is leftist nonsense. It does not deserve the good reviews it has. See rare negative review for how bad it is.

Complaining that math is elitist

Historian Michael J. Barany writes in SciAm:

Most people never become mathematicians, but everyone has a stake in mathematics. Almost since the dawn of human civilization, societies have vested special authority in mathematical experts. The question of how and why the public should support elite mathematics remains as pertinent as ever, and in the last five centuries (especially the last two) it has been joined by the related question of what mathematics most members of the public should know.

Why does mathematics matter to society at large? Listen to mathematicians, policymakers, and educators and the answer seems unanimous: mathematics is everywhere, therefore everyone should care about it. ...

Imagining math to be everywhere makes it all too easy to ignore the very real politics of who gets to be part of the mathematical elite that really count — for technology, security, and economics, for the last war and the next one. Instead, if we see that this kind of mathematics has historically been built by and for the very few, we are called to ask who gets to be part of that few and what are the responsibilities that come with their expertise. We have to recognize that elite mathematics today, while much more inclusive than it was one or five or fifty centuries ago, remains a discipline that vests special authority in those who, by virtue of gender, race, and class, are often already among our society’s most powerful. If math were really everywhere, it would already belong to everyone equally. But when it comes to accessing and supporting math, there is much work to be done. Math isn’t everywhere.

Mathematical knowledge is available to everyone, more or less equally. It is taught in every school. Books and videos at every level are freely available on the web.

The best schools are a couple of years ahead of the worst schools, but almost everyone has a chance to get a first class math education.

Talent is not distributed equally, of course. Most ppl have difficulty with the simplest math arguments.

Universities are filled with scholars whose main object is to dream up kooky theories for blaming straight white Xian men. Barany is an example.

We need more math competence, not less.

Poor people buy lottery tickets.

I almost bought a Powerball lottery ticket. Here is who does:

Nationwide, people who make less than $10,000 spend on average $597 on lottery tickets — about 6 percent of their income. ...

Nationwide, African Americans spend five times more on lottery tickets than white people. ...

One in five Americans believe the lottery is the only way they can accumulate a significant amount of savings.

I have heard that half of big jackpot winners declare bankruptcy within 5 years. Some are also victims of crimes.

Mathematician's logic puzzle

There is a story about a math dept of 20 professors who all seem to know about the infidelities of other wives, but if any one discovered that his own wife was unfaithful, he would shoot her the next morning.

One day a visiting professor happens to mention to everyone that one (or more) of the wives was unfaithful. This might seem inconsequential, because they all already knew that. Or it seems that way. But these were mathematicians, and 20 days later, they all shot their wives.

You can find the explanation at The blue-eyed islanders puzzle, Common knowledge (logic), or Muddy Children Puzzle.

A mathematician is apt to find the argument convincing, but no one else.

I am reminded of this as I read puzzle about 10 pirates dividing 100 coins. A solution is given, and proved correct, except that you cannot imagine any pirates using it. Most of them would die, if they tried.

According to the proof, the first pirate will take 96 coins for himself. The pirate can vote to reject this offer, throw the first pirate overboard, and let the second pirate divide the coins among the remaining 9 pirates. But a clever induction argument claims to prove that the pirates will vote to accept the division of coins!

In the comments at the above link, I argue that the induction argument is flawed, and that pirates will vote to reject such lousy deals. Everyone else disagreed with me. Read for yourself, and form your own opinion.

Attack on NSA dwells on 40yo DES

I responded to complaints about the NSA from mathematicians and scientists, and now there are more.

A letter to the AMS attacks the NSA:

This track record includes reducing the key length of the block cipher DES in the 1970s to make it breakable, blacklisting an inventor of DES from other cryptography jobs, advocating for control of cryptographic research in the 1980s, and, according to NSA's 2013 budget request, covertly influencing "commercial products' designs" and "policies, standards and specifications for commercial public key technologies" for the purposes of exploitation. Indeed, the track record speaks for itself.

Most of this is dubious. An AMS history of DES only says that

There have been persistent rumors that NSA had pressed for the shorter key length.

While IBM originally proposed a 128-bit key cipher, NSA pointed out weaknesses, and the 56-bit DES was stronger than IBM's 128-bit cipher. At the time of its release, DES was stronger than any other civilian cipher, so I don't see how NSA could have weakened it.

The blacklisted inventor was supposedly Horst Feistel, but he seems to have had a successful cryptology career.

The NSA is a military spy agency, so I do not doubt that it budgets money for spy work.

Here is another response:

In a recent letter to the American Mathematical Society titled 'Encryption and the NSA Role in International Standards', Dr. Wertheimer, a former NSA Mathematician and Research Directer, works very hard to leave the impression that the NSA did not place a backdoor in the DUAL_EC_DRBG algorithm. He never directly says that though because the evidence is so overwhelming to the contrary. Instead he chooses to engage in what can only be called aggressive and willfully misleading

If the evidence is so overwhelming, then how is anyone misled?

I do think that it is silly to complain about NSA's influence over DES 40 years ago. Here is what I originally said in my letter to the NSA:

Back in the 1970s, attacks on the NSA were based on how it influenced the Data Encryption Standard (DES). The accusation was that NSA crippled it in order to spy on everyone.

In fact DES was a big advance over anything else in the public domain, and more secure than what IBM developed on its own. Years of analysis have not turned up any backdoors, and the most practical attack is a brute-force key space search. There is no known example of anyone ever losing a dime from a DES weakness.

The chief complaint about DES was that the key size was limited to 56 bits. However this was not even a material limitation as everyone quickly realized that DES could easily be augmented to Triple-DES or DES-X for larger keys.

It is likely that NSA had some ciphers that were better than DES at the time. However it would have surely been against policy to release a military cipher into the public domain. What it apparently did was to make sure that DES was exactly as good as it appears to be, so it could be used appropriately for unclassified purposes. As computers got faster, it later helped facilitate AES as an improved cipher.

These mathematicians are embarrassing themselves with their criticisms of NSA. If they are against spying, they could just say so, instead of all the silly complaints about how NSA has not always fully explained itself.

I am all in favor of public concern about computer security. We hear regular stories about naked selfies posted online, identity theft, stolen movies, email tampering, hacking credit card databases, etc. How many of these were caused by NSA choosing too few key bits or poorly seeding a pseudorandom number generator? Zero. These complaining mathematicians keep acting as if something bad has happened, but they cannot point to any ill effect anywhere.

More NSA complaints

I mentioned mathematicians attacking the NSA, and now AAAS Science magazine is getting into the act:

Science magazine this week has an article and a podcast about the NSA and the AMS. AMS president David Vogan is portrayed as outraged at the NSA’s misuse of mathematics, but without much support for doing anything about it

Supposedly the smoking gun here is a Snowden leak about a random number generator, but the same info has been public since 2007, as well as instructions how to re-seed the generator so that the NSA cannot spy on you. People are trying to stir up a controversy over nothing.

In spite of all this supposed spying, The NSA Is Viewed Favorably By Most Young People according to a poll. After all, Apple, Facebook, and Google are the ones spying on their naked selfies, not the NSA.

Mathematicians attack the NSA

I wrote a letter suggesting that the American Mathematical Society not get too excited about the National Security Agency, and the AMS published this reply in the AMS Notices:

The AMS must justify its support of the NSA

Roger Schlafly (letters, November 2014) accuses mathematicians of an "overwrought" and "over-excited" response to the recently-revealed activities of the National Security Agency (NSA). So, let us look at some cold facts. In 2011, the NSA explicitly stated its goal of universal surveillance, describing its "posture" as "collect it all", "know it all", "exploit it all". The same year, the NSA's close British partner GCHQ said it was intercepting over 50 billion communication events per day. In 2012, a single NSA program celebrated its trillionth metadata record.

Those numbers sound big, but much more data is being harvested by Google, Facebook, and ATT. Why no criticism of them?

On encryption: the NSA's 2013 budget request sought funds to "Insert vulnerabilities into commercial encryption systems". The NSA described its secret program Sentry Raven as "work[ing] with specific US commercial entities ... to modify US manufactured encryption systems to make them exploitable for SIGINT [signals intelligence]". The aim is clear: that no two human beings shall be able to communicate digitally without the NSA being able to listen.

The NSA's aim is to spy on military and terrorist enemies. It has no interest in others.

Schlafly is, at least, correct in noting that outrage at the intelligence agencies' abuse of surveillance powers is nothing new: from the FBI's bugging of Martin Luther King and subsequent attempt to blackmail him into suicide, to the 2011 extrajudicial killing of an American child by CIA drone strike (a program to which the NSA supplies surveillance data). He is justified in worrying about the data held by Google, Facebook, etc., but he writes as if concern over that and state surveillance were mutually exclusive, which of course they are not; and much of that data is harvested by the NSA's PRISM program anyway.

I said nothing about the FBI's invesigation of King, and I am not sure it matters, as it was very far removed from the business of a math society. Nor about the Obama administration killing a 16yo enemy combatant.

My understanding of USA law is that an American who takes up arms against the USA can be killed without judicial process. If this Britain mathematician disagrees, then he can state his political opinion, but I suspect that the laws in his country are similar.

Further, his comparison with 1970s technology distracts from the awesome invasive power of today's internet. As the NSA's former general counsel Stewart Baker said, "metadata absolutely tells you everything about somebody's life". Former NSA director Michael Hayden agreed, adding "we kill people based on metadata".

Sure, the US military acts on whatever intelligence it can get.

By collaborating with the NSA, the AMS sends a strong political message: that it is proud to support the NSA's work and welcomes it into the mathematical community. It is just as surely a political position as withdrawing cooperation would be. Many members are vigorously opposed to much of what the NSA does; indeed, when the Notices set out to organize the series "Mathematicians discuss the Snowden revelations", its editors could not find anyone to write in the NSA's defense. (And when they finally did, it was a longtime NSA employee.)

Yes, the only reason I wrote my letter was that no one else was expressing the foolishness of the AMS trying to boycott the NSA. I was not defending the NSA; I expressed no opinion about the merits of NSA spy programs.

How does the AMS leadership justify its continued cooperation with the NSA? Is it certain it has the backing of the membership? And what exactly would the NSA have to do in order for the AMS to declare "Enough: this partnership brings mathematicians into disrepute"?

Tom Leinster
University of Edinburgh

What would it take? The essence of his complaint is that the NSA has a spy program against foreign enemy combatants. The program has the approval of the leaders of both our political parties. The purpose is to prevent terrorist attacks. War is an ugly business sometimes, and maybe it is a necessary evil. I do not personally agree with some of the military actions. But what does Leinster want? To shut down the military? To shut down NSA? To prohibit military spying?

The AMS is not a political organizations. It is just mathematicians wanting to do math. It is formally American, so if there is an American consensus to send drones into Yemen to kill terrorists, then it is not the place of the AMS to try to obstruct it. If some mathematicians disagree, they can join political organizations to vote our leaders out of office.

The AMS hardly does anything to support the NSA. Maybe it accepts some employment ads. If the AMS is helping mathematicians find job that assist the USA government in the war against terrorism, then the AMS ought to be proud to have that role. I fail to see how it would be any better to help mathematicians find jobs at Google or Facebook.

Leinster posted a similar complaint last year against mathematicians cooperating with a British intelligence agency.

The AMS published another letter attacking me:

Difference between the NSA and Google

In his June 28, 2014, letter to the Notices[November 2014 issue], Roger Schlafly claims that he does not see a distinction between the dangers posed by the massive collection of data by commercial companies like Google and the collection of data by the NSA. Perhaps that is because he is also unable to see a distinction between public and covert oversight. No doubt the practices of Google are a real danger, but commercial companies are subject to regulations and can be brought before open courts whose judges are appointed by an elected president and have to be approved by the Senate. The regulations governing the NSA are classified, and the NSA is answerable only to a closed court whose judges are appointed, without further review, by a man who himself was appointed by a president who believed that one can defeat terror by declaring a war on it. Maybe these distinctions seem trivial to Dr. Schlafly, but even he should be able to understand why somebody like Alexander Beilinson, who grew up in a country where all courts were secret, does not.

—Daniel W. Stroock
Professor emeritus
Massachusetts Institute of Technology
dws@math.mit.edu

I original letter mentioned that Alexander Beilinson was a Russian-American professor, as I thought that him growing up in Russia had some relevance. The editors removed that. My guess is that they thought that his ethnicity was a distraction, or that I was insinuating that he might be a commie or something.

The NSA is much more tightly regulated in its spying than Google. In its most controversial program, the NSA has collected metadata on Americans, but regulations prevent it from searching the data except in a few hundred cases where Americans were talking to known terrorism suspects in places like Afghanistan. Google is under no such restrictions. It collects whatever it can get, and keeps it forever. And not just metadata. It keeps email, search terms, sites visited, videos watched, and ads viewed.

Stroock reveals his politics by slyly referring to Pres. Obama as the "elected president" but Pres. G.W. Bush as "a president who believed that one can defeat terror by declaring a war on it." Bush has been out of office for 6 years. His war on terror has been continued by the Obama administration, as so has NSA surveillance. These policies have broad support in Congress and with the American people.

When I submitted my letter to the AMS, the editor said she got 7 or more opinions on it, and they all recommended against publishing it. One of the objections was that only the government puts people in jail, not Google. I replied:

The NSA does not put people in jail either. Google is, in fact, quite capable of instigating action to jail someone. See this recent story:

"Google sees alleged child porn in man's email, alerts police A Houston man is charged after police say Google tips them off to alleged child porn in his e-mail."

How many Americans have been harmed by NSA spying? Go ahead and count the enemy combatant in Yemen.

I am actually surprised at how little public concern there is about the NSA. Various people in the news media and academia are constantly telling about how some leak is outrageous, or about how the NSA has too much metadata, or about how some court lacks sufficient due process. But when pollsters ask people about reasons for their votes, the NSA is never even mentioned. Nobody cares.

The real threats to your privacy are coming from Google, Facebook, Apple, Obamacare, video cameras, credit agencies, consumer marketing databases, and various new technologies. Not NSA. The AMS would be very foolish to get into a political fight over the NSA.

Too much math for a science journal

Hollywood dumbs down the mathemetics of Alan Turing, but I expect better from a leading science journal. Nature magazine asked a couple of Harvard mathematicians to write an obituary of Alexander_Grothendieck, but they lament:

The sad thing is that this was rejected as much too technical for their readership. Their editor wrote me that 'higher degree polynomials', 'infinitesimal vectors' and 'complex space' (even complex numbers) were things at least half their readership had never come across. The gap between the world I have lived in and that even of scientists has never seemed larger. I am prepared for lawyers and business people to say they hated math and not to remember any math beyond arithmetic, but this!? Nature is read only by people belonging to the acronym 'STEM' (= Science, Technology, Engineering and Mathematics) and in the Common Core Standards, all such people are expected to learn a hell of a lot of math. Very depressing.

The review does get a little technical, but don't the reader want to know what the man really did, instead of over-hyped irrelevant stories?

Update: A math and biology professor describes the differences.