Can Math be Patented?

Gabrielle Birchak/ January 25, 2022/ Ancient History, Contemporary History, Modern History, Post Classical, Uncategorized

Pod­cast / Show Transcripts

Is math­e­mat­ics invent­ed or dis­cov­ered? And if it is invent­ed, can it be patent­ed? Has it ever been patent­ed? I will dis­cuss this in today’s episode.

In my pod­cast intro­duc­tion, I say that the his­to­ry of math is our intel­lec­tu­al foun­da­tion for under­stand­ing sci­ence. In oth­er words, I think that math is the foun­da­tion of sci­ence and helps us to build upon our dis­cov­er­ies, which then lead to incred­i­ble tech­ni­cal and sci­en­tif­ic devel­op­ments. In the world of sci­ence and math­e­mat­ics, we con­sid­er that math is a pla­ton­ic real­i­ty. It is not just the real­i­ty of the phys­i­cal world. Pla­ton­ic real­i­ty gives real­i­ty to the con­cepts that cre­ate our phys­i­cal world. How­ev­er, we do not force this Pla­ton­ic real­i­ty into our phys­i­cal world. It is just already in exis­tence thanks to the bril­liance of Euclid, Men­ach­mus, Pythago­ras, and the many oth­er bril­liant math­e­mati­cians from ancient times. So back to my first ques­tion, is math­e­mat­ics invent­ed or dis­cov­ered? Because if you think about it, sci­ence, tech­nol­o­gy, and engi­neer­ing, are fun­da­men­tal to our exis­tence. They have helped us cre­ate a world that pro­vides us a world of com­fort, a world of dis­cov­ery, and hope for the future. The appa­ra­tus you are using to lis­ten to this pod­cast or watch this video was cre­at­ed with the help of sci­ence, tech­nol­o­gy, and engi­neer­ing. All of this could not have been pos­si­ble with­out the foun­da­tions of math­e­mat­ics. The cars we dri­ve, the com­put­ers we use, the stoves that make our food, the microwaves that heat the food, the phones that we use, the cam­eras in our phone, pen­cil sharp­en­ers, screw­drivers, water­mel­on tre­buchet, all these things require math­e­mat­ics to cre­ate them. So, if all of these things can be patent­ed, can math­e­mat­ics be patent­ed? Because, unlike ancient times that had already assumed the truth to the pla­ton­ic real­i­ty of math­e­mat­ics, today, the algo­rith­mic struc­ture of math­e­mat­ics is imple­ment­ed, applied, and uti­lized in com­put­er-imple­ment­ed inven­tions. So, with this in mind, can math­e­mat­ics be patented?

In the third cen­tu­ry BCE, the ancient his­to­ri­an Phy­larchus wrote that in the ancient city of Sybaris, which is in south Italy in the province of Cosen­za, the gov­ern­ment would pro­vide annu­al exclu­sive mon­e­tary rights to the chefs of Sybaris who cre­at­ed culi­nary mas­ter­pieces. They would have the rights to their recipes for an entire year. This was the begin­ning of patent law, as far as I have cur­rent­ly researched.

By the sec­ond cen­tu­ry BCE, the archi­tect and engi­neer Vit­ru­vius served as a judge over a lit­er­ary con­test held in Alexan­dria. Part of his role includ­ed expos­ing the poets who were vio­lat­ing the copy­rights of oth­er poets. Vit­ru­vius would expose the poets who pla­gia­rized the works of oth­er poets and then try them and con­vict them for their theft.[1] Then, approx­i­mate­ly 200 years lat­er, there were indi­ca­tions of patent and copy­right laws among Roman jurists who exam­ined and debat­ed own­er­ship rights with intel­lec­tu­al works. These dis­cus­sions cen­tered around what made an intel­lec­tu­al work the prop­er­ty of the own­er. For exam­ple, the dif­fer­ence between who owned a paint­ing ver­sus who owned the table that the paint­ing was sit­ting on.

Around the same time one of the very first ref­er­ences to lit­er­ary pla­gia­rism was brought to legal atten­tion. In the first cen­tu­ry CE, a Roman poet named Mar­tial was slow­ly gain­ing fame for his works. How­ev­er, Mar­tial dis­cov­ered that anoth­er poet, Fidenti­nus, was recit­ing his poet­ry and claim­ing it as his own. Mar­tial then dis­cov­ered that his poet­ry was being copied and recit­ed by oth­er poets as well. But because there was no prece­dence that gave him legal recourse, Mar­tial had to find a way to pub­licly accuse Fidenti­nus of steal­ing his poet­ry. So, Mar­tial authored a poem about a lit­er­ary thief who was guilty of “pla­gia­rus.” This Greek word, “pla­gia­rus,” was used to define some­body who was kid­nap­ping some­one else’s slaves. Mar­tial then wrote, Fame has it that you, Fidenti­nus, recite my books to the crowd as if none oth­er than your own. If you’re will­ing that they be called mine, I’ll send you the poems for free. If you want them to be called yours, buy this one, so that they won’t be mine.”

The first statute that was writ­ten to pro­tect the rights of the inven­tors was pub­lished on June 9, 1421, and was writ­ten to pro­tect the works of the archi­tect Fil­ip­po Brunelleschi. By 1450, Venice declared that inven­tions had to be con­veyed to the Repub­lic so that inven­tors could receive legal pro­tec­tion should anoth­er inven­tor attempt to steal their work. About twen­ty years lat­er, this led to the dis­tri­b­u­tion of gov­ern­ment statutes that pro­tect­ed the works of archi­tects, inven­tors, and writ­ers. These statutes allowed for incen­tive, com­pen­sa­tion for infringe­ment, and a term lim­it. Inter­est­ing­ly, these patent laws in Italy influ­enced Euro­pean laws as Vene­tians emi­grat­ed to oth­er parts of Europe, ask­ing for sim­i­lar patent pro­tec­tion from oth­er governments.

Thus, by the 16th cen­tu­ry, Queen Eliz­a­beth I was grant­i­ng patents to ver­i­fi­able sci­en­tists and inven­tors and indi­vid­u­als who were finan­cial­ly sup­port­ing the monar­chy. In the 17th cen­tu­ry, specif­i­cal­ly in 1624, Eng­land passed the statute of monop­o­lies, which grant­ed that the monop­oly on the inven­tion was only good for 14 years. Fur­ther­more, the statute of monop­o­lies stat­ed that these inven­tions had to be new and not built on the con­cept of pre­vi­ous patents. How­ev­er, these patents did not cov­er lit­er­ary works. Lit­er­ary works weren’t pro­tect­ed by gov­ern­ment statutes until 1710 with the statute of Anne. This statute pro­tect­ed the works of authors who were los­ing prof­it due to pub­lish­ing hous­es copy­ing their works with­out the authors’ con­sent. Final­ly, by 1790, patent rights reached the Unit­ed States when the Unit­ed States gov­ern­ment pro­vid­ed patents for 14 years to those who cre­at­ed “use­ful, impor­tant, and new inven­tions.” Today, the patent is only good for 20 years, just two decades.

This is where we get into the his­to­ry of patents as it relates to math­e­mat­ics. By 1849, patents were required to be “non-obvi­ous to oth­er pro­fes­sion­als in the same field.” In oth­er words, in the Unit­ed States, inven­tions had to prove nov­el­ty, use­ful­ness, and non-obvi­ous­ness. This con­cept of non-obvi­ous­ness in Europe is referred to as the inven­tive step. Well, math­e­mat­ics is often used in the appli­ca­tions of com­put­er engi­neer­ing. For com­pu­ta­tions, algo­rithms are often used for devel­op­ing software.

In some cas­es, though, if you take an algo­rithm that, on its own, could not be patent­ed and apply it to a tech­ni­cal appli­ca­tion that unleash­es a use­ful out­come, it could poten­tial­ly be patent­ed. For exam­ple, on Novem­ber 26, 1996, the Unit­ed States grant­ed patent num­ber 5,579,430 to Germany’s Fraun­hofer Insti­tut for the “dig­i­tal encod­ing process” used on the MPEG Audio Lay­er III, the MP3. The dig­i­tal encod­ing process goes like this: sound is a com­plex wave­form. And it’s con­stant­ly vary­ing between high peaks and low val­leys. Com­put­ers oper­ate using bina­ry num­bers. To cre­ate dig­i­tal audio, the sound waves must be mea­sured at reg­u­lar inter­vals. How­ev­er, these inter­vals dic­tate the qual­i­ty of the sound. As a result, the qual­i­ty will depend on how often the mea­sure­ments are gath­ered. This is known as the sam­pling rate. Addi­tion­al­ly, the qual­i­ty depends on how many val­ues are assigned to the wave­form, oth­er­wise known as the bit depth.

The process of com­pres­sion involves ana­lyz­ing what the human ear can hear. Whales and ele­phants can hear excep­tion­al­ly low sounds. These low sounds math­e­mat­i­cal­ly are rep­re­sent­ed with an excep­tion­al­ly large, long, com­plex wave­form. Alter­na­tive­ly, birds, and tiny ani­mals like mice, can hear extreme­ly high sounds. Math­e­mat­i­cal­ly, these high sounds are rep­re­sent­ed by the slope of the line of the wave­form. The high­er the slope, the high­er the fre­quen­cy. How­ev­er, humans can’t hear some of these fre­quen­cies. Our range is lim­it­ed to 20 Hertz to 20 Kilohertz.

So, with the MP3 com­pres­sion, a math­e­mat­i­cal process is applied called the Fouri­er series. The Fouri­er series looks at a peri­od of com­plex waves and sums them up into a peri­od­ic func­tion. By cre­at­ing this peri­od­ic func­tion, the math allows us to find those fre­quen­cies that sit out­side of range than humans can hear and there­by remove them. This cre­ates a wave with less infor­ma­tion and data than the orig­i­nal, there­by com­press­ing the information.

So, even though the Fouri­er series was not, per se, patent­ed, the com­pres­sion process that uses it was. Such is also the case of the Fast Fouri­er Trans­form (FFT). The FFT algo­rithm was devel­oped in 1965 by two Prince­ton math pro­fes­sors, James Coo­ley and John Tukey. Like the Fouri­er series, the FFT reduces the steps required to ana­lyze curves. How­ev­er, the FFT reduces the num­ber of steps to ana­lyze a curve by an extra­or­di­nary amount. As a result, it has become com­mon­place and rou­tine­ly used in com­pu­ta­tion process­es. How­ev­er, even though this math­e­mat­i­cal method is a valu­able tool in com­put­ers, it is not unique. This is because the FFT was built upon the Fouri­er series, which was first imple­ment­ed and pub­lished in 1807 by Jean-Bap­tiste Joseph Fouri­er in his book Trea­tise on the prop­a­ga­tion of heat in sol­id bod­ies. Though the con­cept was bril­liant, accord­ing to patent law, because it is math, it is con­sid­ered “obvi­ous.”

So, back to my orig­i­nal ques­tion, is math­e­mat­ics invent­ed or dis­cov­ered? Well, in the case of the FFT, it was invent­ed for the pur­pose of reduc­ing com­pu­ta­tion­al process­es. But, in the case of Jean-Bap­tiste Fouri­er, it was dis­cov­ered. But, as we have dis­cov­ered, it can­not be patent­ed. In his book, Patent­ly Math­e­mat­i­cal, Jeff Suzuki­writes about this. He shows that though one can­not patent a math­e­mat­i­cal algo­rithm, one can attempt to patent the appa­ra­tus that exe­cutes the algorithm.

This was the case in the 2014 Supreme Court deci­sion of Alice Corp ver­sus CLS bank inter­na­tion­al. Between 1999 and 2010, the Alice Cor­po­ra­tion obtained four patents for an alleged com­put­er that could auto­mate and reduce “set­tle­ment risk,” which is the risk that one par­ty in a finan­cial agree­ment will per­form the duty imposed by the agree­ment while the oth­er par­ty will not. Accord­ing to Alice Cor­po­ra­tion, this com­put­er could track the bal­ances of both par­ties’ bank accounts. This com­put­er would then have the bank accounts for both par­ties com­plete the finan­cial trans­ac­tion. It would only autho­rize the trans­ac­tion if both par­ties had the capac­i­ty to per­form the transactions.

In 2002, Alice Corp accused CLS bank of using sim­i­lar tech­nol­o­gy and accused CLS Bank of infringe­ment of their patents. CLS respond­ed by suing Alice Cor­po­ra­tion in Fed­er­al Dis­trict Court. To prove that they did not infringe upon Alice, CLS pur­sued a declara­to­ry judg­ment that Alice’s four patents were unen­force­able because the patents did not have any source code, nor did Alice cre­ate a pro­to­type of the com­put­er that is ref­er­enced in the patents. The dis­trict court ruled in favor of CLS, stat­ing that abstract con­structs such as escrow can­not be patent­ed, stat­ing that a “com­put­er sys­tem mere­ly ‘con­fig­ured’ to imple­ment an abstract method is no more patentable than an abstract method that is sim­ply ‘elec­tron­i­cal­ly’ imple­ment­ed.”[2]  

The Alice Corp appealed, in which the appel­late court ruled in Alice’s favor. How­ev­er, the Fed­er­al Court vacat­ed the rul­ing, which then led the case to the Cir­cuit Court. How­ev­er, the Fed­er­al Cir­cuit court couldn’t agree on whether an inven­tion imple­ment­ed by a com­put­er is an abstract idea and inel­i­gi­ble for a patent.

As a result, the con­cept of patent­ing a com­put­er or a com­put­er pro­gram became unclear. The rea­son is that, in a patent, the con­cept can­not be a nat­ur­al phe­nom­e­non or a nat­ur­al act. How­ev­er, a com­put­er, its soft­ware, and the math­e­mat­i­cal algo­rithms are not nat­ur­al phe­nom­e­na. As a result, this Supreme Court deci­sion pro­vid­ed lit­tle sup­port for defin­ing what kind of soft­ware, source code, and algo­rithms can be patented.

Here’s where it leads into math­e­mat­ics. Algo­rithms are built on math­e­mat­ics. And now that we are cre­at­ing machine learn­ing algo­rithms that are crunch­ing Big Data, these algo­rithms need to be pro­tect­ed. And luck­i­ly, today, algo­rithms can be patent­ed in some coun­tries. But because of cas­es like Alice ver­sus CLS, it’s not a straight­for­ward process. In the Unit­ed States, patent­ing an algo­rithm requires break­ing down the soft­ware algo­rithm into a series of math­e­mat­i­cal steps that show a process. By mak­ing it a process, the algo­rithm is no longer an abstract idea but a pro­ce­dure. As a result, today, the math still can­not be patent­ed, but the series of math­e­mat­i­cal appli­ca­tions can. Regard­less, patent­ing algo­rithms and soft­ware is a com­plex process, which, on some lev­el, is unfor­tu­nate for soft­ware companies.

Even though soft­ware is built on math­e­mat­ics, soft­ware is not math­e­mat­ics. Soft­ware is the con­struct of math­e­mat­i­cal algo­rithms. By not patent­ing these algo­rithms, soft­ware com­pa­nies become sus­cep­ti­ble. Unpatent­ed soft­ware stacks the odds against their busi­ness, which is bad for inno­va­tion. Soft­ware com­pa­nies are not try­ing to patent num­bers or equa­tions. They are try­ing to patent the process by which the math­e­mat­ics is applied. And, just like the chefs of Sybaris whose recipes were pro­tect­ed by the gov­ern­ment, these devel­op­ers deserve to have their cre­ations pro­tect­ed as well.

Final­ly, back to my orig­i­nal ques­tion, is math­e­mat­ics invent­ed or dis­cov­ered? Or both? Why couldn’t it be both for the sake of our future?

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[1] “Intel­lec­tu­al Prop­er­ty (Stan­ford Ency­clo­pe­dia of Phi­los­o­phy),” Stan­ford Ency­clo­pe­dia of Phi­los­o­phy, accessed Decem­ber 28, 2021, https://plato.stanford.edu/entries/intellectual-property/.

[2] CLS Bank Inter­na­tion­al v. Alice Cor­po­ra­tion Pty. LTD, 768 F. Supp. 2d 221, 99 U.S.P.Q.2d (BNA) 1898 (D.D.C. 2011)