The Recent Trademarking of Pi: A Troubling Precedent Jonathan M. Borwein and David H. Bailey Pi Period (π.) In January 2014 the U.S. Patent and Trademark Office granted Brooklyn artist Paul Ingrisano a trademark on his design “consisting of the Greek letter Pi, followed by a period.” It should be noted here that there is nothing stylistic or in any way The many shapes of pi. particular in Ingrisano’s trademark—it is simply the standard Greek letter π followed by a period. That’s it—π period. No one doubts the enormous value of Apple’s partly eaten apple or MacDonald’s Background arch. But π period? Intellectual property law is complex and varies We live in an era of aggressive patent trolling by from jurisdiction to jurisdiction, but, roughly vulture patent firms [10]. There is a vast amount speaking, creative works can be copyrighted, while at stake. Think of the current smartphone patent inventions and processes can be patented and wars and the sometimes successful patenting of brand names thence protected. In each case the life forms. Additionally, it is often cheaper for a intention is to protect the value of the owner’s firm to pay than go to court. A vague patent can be a work or possession. “nice little earner,” and thus even established firms For the most part mathematics is excluded by such as Microsoft and Apple go patent trolling and the Berne Convention [1] of the World Intellectual successfully patent such generalities as “a method Property Organization (WIPO) [12]. An unusual to enable….” Other firms are more willing to “open exception was the successful patenting of Gray source” some of their intellectual property, such codes in 1953 [3]. More usual was the carefully as, for example, Tesla’s announcement [9] that it timed Pi Day 2012 dismissal [6] by a US judge of a will open some of its patents in an attempt to help copyright infringement suit regarding π, since “Pi spur the electric automobile industry. is a noncopyrightable fact.” We mathematicians have largely ignored patents What Happened Next? and, to the degree we care at all, have been more This is the disturbing part. To underscore that concerned about copyright as described in the he means business, Ingrisano, through his lawyer, work of the International Mathematical Union’s Ronald Millet, sent a letter to Zazzle.com, a π Committee on Electronic Information and Com- novelty company, to “immediately cease and desist” munication (CEIC) [2].1 But as the following story their “unlawful” usage of their π period trademark indicates, it may now be time for mathematicians or “any confusingly similar trademark” and within to start paying attention to patenting. 14 days: (1) provide an accounting of all sales of any products containing their trademark; Jonathan M. Borwein is laureate professor of mathemat- ics at CARMA, University of Newcastle. His email address (2) provide an inventory of all relevant prod- is [email protected]. ucts; David H. Bailey is retired senior scientist at Lawrence Berke- (3) disclose any other uses, electronic or print, ley National Lab and research fellow at University of Califor- that have been made of the trademark; nia, Davis. His email address is [email protected]. (4) provide an account of the date when the DOI: http://dx.doi.org/10.1090/noti1172 π trademark was first incorporated into 1A decade ago the CEIC wrote at some length on copyright their products, a list of all known links issues and was surprised at the relative paucity of good to Zazzle’s webpage, and a list of third information available at the time. parties who offer such products. 1224 Notices of the AMS Volume 61, Number 10 The letter threatened attorney’s fees and “treble attorney prevail in their legal actions, this would money damages.” The full text of the letter is mean, in effect, that anyone who uses the π symbol available [4]. in any context the holder views as encroaching Implied in the letter is the plaintiff’s position would live under the threat that they might receive that “any confusingly similar trademark” includes a similar “cease and desist” letter, with the threats the π symbol itself, without the period, since of significant financial loss. This would be an none of the products offered by Zazzle features unmitigated disaster for modern mathematics and a π followed by a period. Indeed, according to a science. report in Wired [13], Ingrisano’s attorney, Millet, It is not the slightest exaggeration to say that has asserted that many items for sale by Zazzle π is the most important irrational constant of “clearly have a pi sign and look similar enough that modern mathematics. Each year, the π symbol folks out there might confuse it with products that appears in thousands of published books and in my client also sells.” tens (possibly hundreds) of thousands of technical Zazzle responded by temporarily banning all papers—not just in books and papers related to garments featuring the π symbol, which involved geometry but also in fields as diverse as statistics “thousands of products,” according to the Wired and quantum physics. report [13]. But two days later, after being flooded In fact, the numerical value of π (expressed in with complaints, Zazzle restored the products. binary digits) is contained in every smartphone Millet is consulting with Ingrisano as to their next ever produced, since the computations performed step. to process wireless signals (using the fast Fourier Along this line, it is amusing to note that transform) inherently involve π. π appears in a π design is featured [5] by the Mathematical several guises in the equations of quantum physics Association of America as a finalist for its 2014 MAA and thus is central to semiconductor electronics. π Annual T-Shirt Design Contest (and the design even arises in GPS technology, since the frequency includes one formula that one of the present of clock signals broadcast by GPS satellites must authors was instrumental in discovering). Will the be adjusted according to the formulas of Einstein’s MAA be challenged as well? Perhaps not, but we general relativity, the equations of which involve live in a very litigious world, and a given university π. The mind reels at the thought that the authors or company lawyer may well decide discretion is of every mathematical, scientific, or engineering the better part of valor and opt to keep their clients paper that uses a π symbol must live under a out of trouble by forbidding use. One of us had his cloud of worry that they too might be accused of former employer (Dalhousie) order him to desist “trademark violation” by including π symbols in from using the name of the institution on a bank their articles. account he had been advised to set up by his Dean for a research center. What to Do? True, it would take quite a stretch of trademark The Smiley Face law precedent before π characters appearing in This episode is reminiscent of a dispute over the mathematical literature would be at peril. The Ω “smiley face” between litigants Wal-Mart Stores symbol has been used to promote watches for and SmileyWorld, a London-based company that decades without litigation. The 1 symbol has been registered rights to the smiley face many years ago used to promote automobiles without run-ins with on behalf of Franklin Loufrani [7]. The dispute was mathematicians. The same is true for Yahoo’s finally settled in June 2011 under undisclosed (but trademark, which is little more than a block Y, and likely quite expensive) terms [8]. Google’s trademark, namely a capital G. Unlike the π case, no one has argued that the But even if legal hassles over π in mathematical smiley face has scientific significance! But the papers are an unreasonable worry, as the legal case does demonstrate that such disputes must advice quoted below suggests, can we really not be taken seriously. Moreover, the smiley face is freely put π on our pens, thumb drives, coffee a defined and recognizable image, and Loufrani cups, posters, and T-shirts? explicitly makes no attempt to stop the use of it in For the same reason that π is omnipresent in email as plain text, such as :). mathematical literature, it is also omnipresent in the larger cultural milieu of mathematics, and to Pi in Modern Mathematics and Science place a legal cloud over the usage of π on everyday The π period trademark, and the aggressive actions novelty items and posters would seriously hamper taken by the trademark holder, may seem amusing, the humanization of modern mathematics. though they are certainly unfortunate for Zazzle Also, if π is placed under a cloud of trademark and its owners, employees, and customers. But violation, what is next? The letter e, the base of much more is at stake here. If Ingrisano and his natural logarithms? The summation sign Σ (another November 2014 Notices of the AMS 1225 R Greek letter)? The integral sign ? Should the or any other “ornamental” use (ornamental in this American Mathematical Society or the International context meaning anything other than commercial Mathematical Union trademark all mathematical use of the mark for branding products or services symbols, including notation such as 5!, as logos offered commercially). Thus a trademark right and release them under a general public license? No in a mathematical symbol does not preclude precedent even remotely approaching this scenario its use for decorative purposes, other than as should be tolerated. a brand. And a trademark owner in a mark A lawyer familiar with trademark law (see involving a mathematical symbol would have to “Sidebar”) has advised us that “the trademark show likelihood of confusion due to the use registration for a symbol, such as a Greek letter, of a mark to obtain relief.