# Jonathan Borwein quotes

We give below a very small number of short extracts from various articles by Jonathan Borwein. Since Borwein is known as 'Doctor Pi' we have included three articles about Pi which begin our collection. It is not easy to extract from any of the articles short pieces which stand alone, so we give these short extracts in the hope of encouraging the reader to read the complete article. We give 12 examples, a tiny example of Borwein's output. His CV lists 388 papers in journals, 103 conference proceedings, 84 published blogs, 28 books and software, 13 reviews, and 25 other manuscripts.

**1.**

**Authors:**Jonathan Borwein and David H Bailey.

**Title:**Pi Day Is Upon Us Again and We Still Do Not Know if Pi Is Normal.

**Source:**

*The American Mathematical Monthly*

**121**(3) (2014), 191-206.

**Date:**2014.

The number

*π*, unique among the pantheon of mathematical constants, captures the fascination both of the public and of professional mathematicians. Algebraic constants such as √2 are easier to explain and to calculate to high accuracy (e.g., using a simple Newton iteration scheme). The constant

*e*is pervasive in physics and chemistry, and even appears in financial mathematics. Logarithms are ubiquitous in the social sciences. But none of these other constants has ever gained much traction in the popular culture.

In contrast, we see

*π*at every turn. In an early scene of Ang Lee's 2012 movie adaptation of Yann Martel's award-winning book

*The Life of Pi*, the title character Piscine ("Pi") Molitor writes hundreds of digits of the decimal expansion of

*π*on a blackboard to impress his teachers and schoolmates, who chant along with every digit. This has even led to humorous take-offs such as a 2013 Scott Hilburn cartoon entitled "Wife of Pi," which depicts a 4 figure seated next to a

*π*figure, telling their marriage counsellor "He's irrational and he goes on and on."

This attention comes to a head on March 14 of each year with the celebration of "Pi Day," when in the United States, with its taste for placing the day after the month, 3/14 corresponds to the best-known decimal approximation of

*π*(with 3/14/15 promising a gala event in 2015). Pi Day was originally founded in 1988, the brainchild of Larry Shaw of San Francisco's Exploratorium (a science museum), which in turn was founded by Frank Oppenheimer (the younger physicist brother of Robert Oppenheimer) after he was blacklisted by the U.S. Government during the McCarthy era.

Originally a light-hearted gag where folks walked around the Exploratorium in funny hats with pies and the like, by the turn of the century Pi Day was a major educational event in North American schools, garnering plenty of press. In 2009, the U.S. House of Representatives made Pi Day celebrations official by passing a resolution designating March 14 as "National Pi Day," and encouraging "schools and educators to observe the day with appropriate activities that teach students about

*π*and engage them about the study of mathematics."

As a striking example, the March 14, 2007

*New York Times*crossword puzzle featured clues, where, in numerous locations,

*π*(standing for Pi) must be entered at the intersection of two words. For example, 33 across "Vice president after Hubert" (answer: SπRO) intersects with 34 down "Stove feature" (answer: π LOT). Indeed, 28 down, with clue "March 14, to mathematicians," was, appropriately enough, PIDAY, while PIPPIN is now a four-letter word.

*π*Mania in popular culture include the following:

- On September 12, 2012, five aircraft armed with dot-matrix-style skywriting technology wrote 1000 digits of
*π*in the sky above the San Francisco Bay area as a spectacular and costly piece of*piformance*art.

- On March 14, 2012, U.S. District Court Judge Michael H Simon dismissed a copyright infringement suit relating to the lyrics of a song by ruling that "Pi is a non-copyrightable fact."

- On the September 20, 2005 edition of the North American TV quiz show Jeopardy!, in the category "By the numbers," the clue was "'How I want a drink, alcoholic of course' is often used to memorise this." (Answer: What is Pi?).

- On August 18, 2005, Google offered 14,159,265 "new slices of rich technology" in their initial public stock offering. On January 29, 2013 they offered a
*π*million dollar prize for successful hacking of the Chrome Operating System on a specific Android phone.

- In the first 1999
*Matrix*movie, the lead character Neo has only 314 seconds to enter the Source. Time noted the similarity to the digits of*π*.

- The 1998 thriller "Pi" received an award for screen play at the Sundance film festival. When the authors were sent advance access to its website, they diagnosed it a fine hoax.

- The May 6, 1993 edition of The Simpsons had Apu declaring "I can recite
*π*to 40,000 places. The last digit is 1." This digit was supplied to the screenwriters by one of the present authors.

- In Carl Sagan's 1986 book
*Contact*, the lead character (played by Jodie Foster in the movie) searched for patterns in the digits of*π*, and after her mysterious experience sought confirmation in the base-11 expansion of*π*.

**2.**

**Author:**Jonathan Borwein.

**Title:**Are Pi's days numbered?

**Source:**https://theconversation.com/are-pis-days-numbered-39

**Date:**4 May 2011.

Some people have argued that Pi's days are numbered and that other tools, such as tau, could do its job more efficiently. As someone who has studied Pi throughout his entire working life, my response to such challenges is unwavering: Pi is the gift that keeps on giving.

People call me Doctor Pi. I have played with Pi since I was a child and have studied it seriously for 30 years. Each year I discover new, unexpected and amusing things about

*π*, its history and its computation. I never tire of it.

- Without
*π*there is no theory of motion, no understanding of geometry or space/time. -
*π*occurs in important fields of applied mathematics. -
*π*is used throughout engineering, science and medicine and is studied for its own sake in number theory. - It fascinates specialists and hobbyists alike.

...

Although it is very likely we will learn nothing new mathematically about

*π*from computations to come, we just may discover something truly startling.

*π*has seen off attacks in the past. It will see off attacks in the future.

*π*, like its inherent magic, is infinite.

The battle continues.

**3.**

**Authors:**Jonathan Borwein and David H Bailey.

**Title:**Prepared for Pi Day? This year it's a once in a century celebration.

**Source:**https://theconversation.com/prepared-for-pi-day-this-year-its-a-once-in-a-century-celebration-38576

**Date:**12 March 2015.

Pi Day - on March 14 - will be particularly memorable this year: the date can be written 3/14 by those who opt for the month then day format, which is

*π*to two decimal places, 3.14. If you include the year this year then that gives 3/14/15, which is Pi to four decimal places, 3.1415.

This happens only once a century, and the Museum of Mathematics in New York City, among others, is taking Pi Day 2015 one step further, by celebrating at 9:26pm, adding three more digits to Pi, 3.1415926.

You can personally celebrate the event 12 hours earlier at 9.26am, wait a further 53 seconds to get 3.141592653 Pi to nine decimal places. That's probably the best time and date approximation to

*π*you can get with your typical time piece, although the digits of

*π*continue on indefinitely ...

Chicagoans plan to celebrate Pi Day this year by running in a Pi-K race of 3.14 miles. Numerous city bakeries are offering special pies for the occasion at US$3.14 per slice.

Not as well known perhaps is the fact that March 14 this year is also the 136th birthday of physicist Albert Einstein, and that 2015 is the 100th anniversary of the publication of Einstein's paper on general relativity.

To commemorate this doubly significant event, Princeton University is planning its usual gala event, including a pie eating contest, a performance by the Princeton Symphony, a contest to see who can recite the most correct digits of

*π*(the current Guinness world record is 67,890 places), a guided Einstein tour and even an Einstein look-a-like contest.

**4.**

**Author:**Jonathan Borwein.

**Title:**If I had a blank cheque I'd … turn IBM's Watson into a maths genius.

**Source:**https://theconversation.com/if-i-had-a-blank-cheque-id-turn-ibms-watson-into-a-maths-genius-1213

**Date:**8 July 2011.

You're offering me a blank cheque, so what would I do? A holiday in Greece for two? No, not this time. Here's my manifesto:

Google has transformed mathematical life (as it has with all aspects of life) but is not very good at answering mathematical questions - even if one knows precisely the question to ask and it involves no symbols.

In February, IBM's Watson computer walloped the best human Jeopardy players in one of the most impressive displays of natural language competence by a machine.

I would pour money into developing an enhanced Watson for mathematics and would acquire the whole corpus of maths for its database.

Maths ages very well and I am certain we would discover a treasure trove. Since it's hard to tell where maths ends and physics, computer science and other subjects begin, I would be catholic in my acquisitions.

Since I am as rich as Croesus and can buy my way out of trouble, I will not suffer the same court challenges Google Books has faced.

I should also pay to develop a comprehensive computation and publishing system with features that allow one to manipulate mathematics while reading it and which ensures published mathematics is rich and multi-textured, allowing for reading at a variety of levels.

Since I am still in a spending mood, I would endow a mathematical research institute with great collaboration tools for roughly each ten million people on Earth.

Such institutes have greatly enhanced research in the countries that can afford and chose to fund them.

Content with my work, I would then rest.

**5.**

**Author:**Jonathan Borwein.

**Title:**The Future of Mathematics: 1965 to 2065.

**Source:**

*S F Kennedy, D J Albers, G L Alexanderson, D Dumbaugh, F A Farris, D B Haunsperger and P Zorn (eds.), A Century of Advancing Mathematics*(MAA Press, 2015), 313-330.

**Date:**2015.

A few things are certain. First, I am willing to predict that - as both Felix Browder (in his final address as AMS President) and Tim Gowers (at a meeting of Fields medalists) have said - the future of mathematics is intimately coupled to computing. (But then, so is everything else.) We should proudly consider ourselves one of

*The Sciences of the Artificial*.

As a reminder of the youth of computer science as a discipline, I recall that the University of Toronto undergraduate computer science (CS) programme was founded as late as 1971.

In the case of mathematical research, this tight coupling with computational-science - as opposed to computer-science - presages more emphasis on algorithms and constructive methods, visualisation, aesthetics and the like; and less focus on abstraction for its own sake. These are trends we can already observe.

The increasing role of collaborative research, which can be exaggerated (mathematicians have always needed to talk to each other) may help make the subject more attractive as a career for women, by keeping them in the STEM stream long enough to develop

*A passion for science*. As it stands why would bright and articulate young women (including my own three adult daughters and my brother's three) with many options be likely to opt for a STEM Career?

Second, we shall assuredly know vastly more about the working of the brain and in particular neurology of mathematical creativity but whether that will resolve the

*mind-body problem*to the satisfaction of philosophers like Thomas Nagel only time will tell. In consequence, one may also hope that 'evidence-based' mathematical education will become the rule not the exception.

Finally, as the economic transformation of South America, Asia, and Africa accelerates, the geographic dispersal of mathematical research is certain to grow; we are a pretty cheap science. As any editor can attest the sheer quantity of submissions originating in Asia is now stunning. One may hope a corresponding increase in quality is not far behind. The rapid development of first-rate universities in places such Hong Kong, Singapore, Korea and China is a positive sign. But building robust cultural traditions of academic enquiry is a long and difficult job.

...

After 60 years with really only two input modalities: first via keyboard and command line computing; and then thirty years later with Apple's adoption of Douglas Engelbart's mouse along with iconic graphical user interfaces (GUI), we are now in a period of rapid change. Speech, touch, gesture, and direct mental control are all either realised or in prospect. As noted, the neurology of the brain has developed in twenty-five years from ignorance to a substantial corpus.

It is barely twenty years since the emergence of the World Wide Web and it would be futile to imagine what interfaces will look like in another twenty. We are still exploring the possibilities suggested by Vannevar Bush in his seminal 1945 essay "As We May Think" and some parts of Leibniz's dream still seem very distant.

In any event, in most of the futures, mathematics will remain important and useful, but those of us who love the subject for its own sake will have to be nimble. We cannot risk leaving the task of looking after the health of our beautiful discipline to others.

**6.**

**Authors:**Jonathan Borwein and David H Bailey.

**Title:**When things don't add up: statistics, maths and scientific fraud.

**Source:**https://theconversation.com/when-things-dont-add-up-statistics-maths-and-scientific-fraud-4185

**Date:**14 November 2011.

From time to time, the scientific community is rocked by cases of scientific fraud. Needless to say, such incidents do little to instil confidence in a public that's already predisposed to be sceptical of inconvenient scientific findings, including biological evolution and human-induced global warming.

...

Let us emphasise here - in case it's not completely obvious - that scientific fraud is the exception, not the rule. Our cursory search of Science's archive showed about half-a-dozen headline cases in the past ten years. Business, politics or law would not fair as well.

In any event, it's clear that:

(a) more care needs to be taken in using statistical methods in scientific and mathematical research.

(b) statistical methods can and should, to a greater extent, be used to detect fraud and manipulation of data (deliberate or not).

Perhaps the considerable attention drawn to recent incidents will lead to more rigorous analyses, and more circumspect behaviour by scientists. We shall see.

**7.**

**Author:**Jonathan Borwein.

**Title:**A Short Walk can be Beautiful.

**Source:**

*Journal of Humanistic Mathematics*

**6**(1) (2016), 86-109.

**Date:**2016.

The story I tell is of research undertaken, with students and colleagues, in the last six or so years on short random walks. As the research progressed, my criteria for beauty changed. Things seemingly remarkable became simple and other seemingly simple things became more remarkable as our analytic and computational tools were refined, and understanding improved. I intentionally display some rather advanced mathematics as it is my contention - as with classical music - that one can learn to appreciate and enjoy complex formulas without needing to understand them deeply.

Beauty in mathematics is frequently discussed and rarely captured precisely. Terms like 'economy', 'elegance', and 'unexpectedness', abound but for the most part a research mathematician will say "I know it when I see it" as with US Supreme Court Justice Potter Stewart's famous 1964 observation on pornography.

As Bertrand Russell writes, mathematics is the most austere and least accessible of the arts. No one alive understands more than a small fraction of the ever growing corpus. A century ago von Neumann is supposed to have claimed familiarity with a quarter of the subject. A peek at Tim Gowers'

*Companion to Pure Mathematics*will show how impossible that now is. Clearly - except pictorially - one can only find beautiful what one can in some sense apprehend. I am a pretty broadly trained and experienced researcher, but large swathes of modern algebraic geometry or non commutative topology are too far from my ken for me to ever find them beautiful.

Aesthetics also change and old questions often become both unfashionable and seemingly arid (useless and/or ugly) - often because progress becomes too difficult as Felix Klein wrote over a century ago about elliptic functions. Modern mathematical computation packages like

*Maple*and

*Mathematica*or the open source SAGE have made it possible to go further. This is both exciting and unexpected in that we tend to view century-old well studied topics as large barren. But the new tools are game changers.

An

*n*-step uniform random walk in $\mathbb{R}^{d}$ starts at the origin and takes

*n*independent steps of length 1, each taken in a uniformly random direction. Thence, each step corresponds to a random vector uniformly distributed on the unit sphere. The study of such walks originates with Pearson, whose interest was in planar walks, which he looked at as migrations of, for instance, mosquitos moving a step after each breeding cycle. Random walks in three dimensions ('random flights') seem first to have been studied in extenso by Rayleigh, and higher dimensions were mentioned in G N Watson A Treatise on the

*Theory of Bessel Functions*.

Self-avoiding random walks are now much in vogue as they model polymers and much else. While for both random walks and their self-avoiding cousins, it is often the case that we should like to allow variable step lengths, it is only for two or three steps that we can give a closed form to the general density. Thence, as often in mathematics we simplify, and in simplifying hope that we also abstract, refine, and enhance.

While we tend to think of classical areas as somehow fully understood, the truth is that we move on because, as Klein said, progress becomes too difficult. Not necessarily because there is nothing important left to say. New tools like new theorems can change the playing field and it is important that we teach such flexibility as suggested by Keynes.

**8.**

**Authors:**Jonathan Borwein and David H Bailey.

**Title:**Why Are So Many Mathematicians Also Musicians?

**Source:**https://www.huffpost.com/entry/why-are-so-many-mathemati_b_9814796

**Date:**3 May 2016.

As the present authors will readily attest, introducing oneself as a mathematician is generally not an effective way to start a social conversation. But, as Cambridge mathematician Tim Gowers explains, there is a "miracle cure": just explain that you, as well as many other mathematicians, are also a musician or at least are deeply interested in music.

The present authors are not the best examples of this, because neither is very good at musical performance, although both have an abiding interest in listening to music. One of us listens to an eclectic collection of mostly modern music while he works (rock, jazz, classical, singer-song-writer, show tunes, alternative, folk, country, adult contemporary and world music to name a few - plus an Apple music subscription). The other one of us has a large collection of classical music, including the entire works of Bach (nearly 200 hours total), on his iPhone, all of which he has listened to many times.

Perhaps the best real-life example of a mathematician-musician was Albert Einstein, who, as many who knew him personally would attest, was also an accomplished pianist and violinist. His second wife Elsa told of how Albert, while during deep concentration on a mathematical problem, would sit down at the piano and play for a while; after one two-week period, interspersed with random piano playing, Einstein emerged the first working draft of general relativity. He once said, "If ... I were not a physicist, I would probably be a musician. I often think in music. I live my daydreams in music. I see my life in terms of music."

So why is it that a remarkable number of professional mathematicians are also into music? Are the two disciplines so similar? Or is there a genetic link? Or is it simply that both mathematicians and musicians are likely to have been raised in households where mathematics, music and other scholarly, artsy subjects were valued, and where the mathematicians and/or musicians were encouraged on by eager parents? Good questions.

...

In short, while it is problematic to claim any kind of innate link between mathematical ability and musical ability, it is clear that the two disciplines have a deep commonality.

One of us (Borwein) has taught many students who were vacillating between musical, medical, and academic careers. And at many mathematical conferences, entertainment is provided by international-level pianists or violinists whose day job is mathematics.

What's more, in the era of modern high-performance computing, the future may bring the two disciplines together in ways that we can scarcely imagine at the present time. May your mathematical future also be a musical one!

**9.**

**Authors:**Jonathan Borwein and David H Bailey.

**Title:**School maths is failing children - a US and Australian perspective

**Source:**https://theconversation.com/school-maths-is-failing-children-a-us-and-australian-perspective-8397

**Date:**24 July 2012.

Those that can't do, teach - or so goes the famous saying. But what of those who want to do teaching. What of those who do maths teaching? Can we be sure the job they are doing is the best one for our children, or the training they are getting as teachers is adequate? Sadly, we cannot.

We, the present authors (Jon, from Australia, and David, from the USA) are research mathematicians and computer scientists. We are also the proud fathers of seven adult daughters, and a gamut of grandchildren of whom the oldest is starting school.

Together with our spouses, we have attended a multitude of PTA meetings, sports games, concerts and science fairs. We have read almost as many report cards (and not all of them have been glowing). But, at the end of the day, our daughters include PhDs, veterinary doctors, lawyers, teachers, web designers, postgraduate students and one senior undergraduate. We have also acquired four sons-in-law.

We have firm opinions, both as professionals and as parents. So what have we learned about teaching - and specifically about maths teaching?

...

It is undeniably important that mathematics teachers have mastered the topics they need to teach. The new Australian national curriculum is misguidedly increasing the amount of "statistics" of the school mathematics curriculum from less that 10% to as much as 40%. Many teachers are far from ready for the change.

But more often than not, the problem is not the mathematical expertise of the teachers. Pedagogical narrowness is a greater problem. Telling that there is a correct idea in a wrong solution to a problem on fractions requires unpacking of elementary concepts in a way that even an expert mathematician is not usually trained to do.

One of us - Jon - learned this only too well when he first taught future elementary school teachers their final university mathematics course.

Australian teachers at an elite private school could not understand one of Jon's daughter's Canadian long-division method nor her solution techniques for many advanced school topics. She got mediocre marks during the year because of this.

The school also scheduled advanced mathematics at 7:30am and 4:30pm. Despite, or perhaps because of this, she was the only female at the school to complete state-wide advanced mathematics school leaving exams, and did so with distinction.

One of Jon's grandsons, who had learned to read by the whole word route, was classified as "slow" by a phonics-based teacher in his new country. The experience demolished the confidence of a previously robust little boy.

...

One thing seems clear: more, better trained, better paid, and better respected teachers are a big part of the solution. As is the time and freedom to experiment.

**10.**

**Authors:**Jonathan Borwein and David H Bailey.

**Title:**Danger, you're at serious risk of … no, sorry, it's all relative

**Source:**https://theconversation.com/danger-youre-at-serious-risk-of-no-sorry-its-all-relative-12218

**Date:**14 February 2014.

We assess risk every day. But very few of us receive any formal training in the requisite mathematics and statistics, and, partly as a result, poor decisions are made, both by individuals and governmental bodies.

Evolutionary biologist Richard Dawkins suggests we may be neurologically ill-equipped to make the sort of decisions called for by modern society; and Nobel prize-winning behavioural economist and psychologist Daniel Kahneman makes it clear in his book Thinking Fast and Slow that making careful (slow) judgements is a very complicated mental process.

Many have presumed that, in the wake of the threat of terrorism, not to mention recent questions about the safety of airliners, that air travel remains a rather dicey proposition.

...

Similar behaviour can be seen in the fanatical and often counter-productive measures taken by parents to protect children. In 1970, 67% of American children walked or biked to school, but today only 10% do, in part out of fear of abductions.

But the number of cases of true child abduction by strangers (as opposed to, say, a divorced parent) has dwindled to only about 100 a year in the US today.

Even if one assumes that all of these children are harmed (which is not by any means true), this is still only about $\large\frac{1}{20}\normalsize$ the risk of drowning and $\large\frac{1}{40}\normalsize$ of the risk of a fatal car accident.

Such numerically absurd thinking can also be seen in the recent international hysteria over childhood vaccinations.

This mania stemmed from a 1998 study in the British medical journal

*Lancet*, which claimed that vaccination shots with a certain mercury compound may be linked to autism.

But a few years later the finding was completely debunked, and in 2011 the original study was exposed as an elaborate fraud.

In the intervening years, many thousands of parents in both the US and the UK jumped on the anti-vaccination bandwagon and, tragically, several childhood diseases began to re-appear.

Last year, measles outbreaks rose to an 18-year high in England and Wales, while in 2011 California experienced its worst whooping cough epidemic in 60 years.

In spite of these grim statistics and pleas from health agencies, many parents still resist vaccinations for their children.

**11.**

**Authors:**Jonathan Borwein and David H Bailey.

**Title:**Will computers replace humans in mathematics?

**Source:**https://theconversation.com/will-computers-replace-humans-in-mathematics-60168

**Date:**1 June 2016.

Computers can be valuable tools for helping mathematicians solve problems but they can also play their own part in the discovery and proof of mathematical theorems.

Perhaps the first major result by a computer came 40 years ago, with proof for the four-colour theorem - the assertion that any map (with certain reasonable conditions) can be coloured with just four distinct colours.

This was first proved by computer in 1976, although flaws were later found, and a corrected proof was not completed until 1995.

In 2003, Thomas Hales, of the University of Pittsburgh, published a computer-based proof of Kepler's conjecture that the familiar method of stacking oranges in the supermarket is the most space-efficient way of arranging equal-diameter spheres.

Although Hales published a proof in 2003, many mathematicians were not satisfied because the proof was accompanied by two gigabytes of computer output (a large amount at the time), and some of the computations could not be certified.

In response, Hales produced a computer-verified formal proof in 2014.

...

So what do these developments mean? Are research mathematicians soon to join the ranks of chess grandmasters, Jeopardy champions, retail clerks, taxi drivers, truck drivers, radiologists and other professions threatened with obsolescence due to rapidly advancing technology?

Not quite. Mathematicians, like many other professionals, have for the large part embraced computation as a new mode of mathematical research, a development known as experimental mathematics, which has far-reaching implications.

So what exactly is experimental mathematics? It is best defined as a mode of research that employs computers as a "laboratory," in the same sense that a physicist, chemist, biologist or engineer performs an experiment to, for example, gain insight and intuition, test and falsify conjecture, and confirm results proved by conventional means.

...

There is every indication that research mathematicians will continue to work in respectful symbiosis with computers for the foreseeable future. Indeed, as this relationship and computer technology mature, mathematicians will become more comfortable leaving certain parts of a proof to computers.

**12.**

**Authors:**Jonathan Borwein and David H Bailey.

**Title:**Hype Now, Hide Later: No Way to Do Scientific Research.

**Source:**https://www.huffpost.com/entry/scientific-research_b_3340682

**Date:**28 May 2013.

The scientific world is suffering through a rash of examples of the sad consequences of the "hype now, hide later" approach to scientific news.

...

An episode was seen on May 23, 2013, when in a feature article in the UK

*Guardian*, eminent Oxford mathematician Marcus du Sautoy described the work of his "colleague" Eric Weinstein, who, according to du Sautoy, may have found the long-sought grand unified theory successfully describing all the fundamental particles and forces of the universe simultaneously.

In his article, du Sautoy explains how Weinstein's theory is fundamentally anchored in symmetries (his own field of research):

Weinstein's theory does this by revealing the presence of a new geometric structure involving a much larger symmetry at work, inside which the symmetry of the Standard Model sits. What is so compelling about the geometry involving this larger symmetry group is that it explains why you get two copies of something with 16 particles but also that the third generation is something of an imposter. At high energies it will actually behave differently to the other two.Du Sautoy also asserts that Weinstein's theory is the "first major challenge" to the validity of Einstein's field equations.

Marcus du Sautoy himself is an internationally known mathematician, studying group theory and number theory. He is the Simonyi Professor for the Public Understanding of Science at Oxford, and also President of the U.K. Mathematical Association. He is certainly no stranger to the public stage, and in this capacity knows very well the principles and standards for scientific announcements. Thus his report had substantial credibility.

So has Weinstein finally found the "theory of everything"?

Sadly, du Sautoy's report was immediately criticised. In a

*New Scientist*commentary, physicist Andrew Pontzen noted that neither du Sautoy nor Weinstein have provided the expected set of detailed technical papers, or even a single paper, outlining the theory. Weinstein himself is not known to the mathematical physics community - he received a PhD in the field from Harvard twenty years ago, but left academia soon after and now works in the financial community. Pontzen acknowledges that Weinstein may have something to say, but most certainly he must go through proper channels, and he has not.

Pontzen notes that:

Physicists are inherently conservative. New claims, especially bold ones, face stiff resistance. That's for a good reason: faster-than-light neutrinos, anyone?Pontzen's mention of faster-than-light neutrinos is a reference to the 2012 episode where a well-respected team of researchers announced that they had measured neutrinos racing between their experimental facility in the Italian alps and the CERN facility near the French-Swiss border 60 nanoseconds faster than light. The measurement was later attributed to a faulty connector handling GPS data.

Pontzen also faulted du Sautoy and Weinstein for giving a technical presentation at Oxford without inviting anyone from the physics department. Indeed, while Weinstein was presenting his theory in one hall, theoretical physicists were in another room listening to a speaker discuss charge-parity violation. As physicist Subir Sarkar explained, "It's surprising that the organisers did not invite the particle physicists to attend - if indeed the intention was to have a discussion."

Pontzen notes that while there may be no firm standard for announcing a claimed breakthrough, du Sautoy has clearly "short-circuited science's basic checks and balances."

It is hard to avoid the conclusion that both the

*Guardian*and de Sautoy have some significant explaining to do. A story of this magnitude on most topics would require some serious fact checking and further assessment by the editors. The most charitable construction suggests that du Sautoy, through excitement, abused his easy access to global media, while the

*Guardian*was more than happy for the splashy headline.

Last Updated September 2023