Equation of love (overview image)
Left: a 2009 Flickr-style, heart icon depiction of a mathematical formulation attempt at an equation of love. [6] Right: a modern day Bergman-Goethe-Adler reaction style equation of love: that of a human combination reaction, i.e. a time-accelerated depiction of act of falling in love (relationship formation) as a chemical equation, specifically a male-female reaction (see: human chemical reaction theory).
In science, equation of love
(LR:1) refers to either a formulaic reaction describing instances of love the chemical reaction, such as depicted in the following alchemical symbol stylized chemical equation:

♂ + ♀ → ♂≡♀

wherein a single man meets a single women and fall in love into a stable relationship ♂≡♀, attached via a chemical bond ‘≡’, or to an actual mathematical or thermodynamic formulation, equation quantifying the affinity (Goethe, 1809), potential (Rankine, 1853), or the free energy change (Hwang, 2001) of a reaction, describing the process of love, quantitatively or qualitatively.

Overview | Modern view
In modern 21st century physical science terms, an individual moving animate human, according to the 1789 Sales human molecular hypothesis and the 2000 Sterner-Elser human molecular formula, is an individual reactive "molecule", and reactive molecules moving freely about on the surface of the earth, according to 1923 Lewis inequality for natural processes, which governs the nature of earth-bound chemical reactions, will tend to react in a direction that results in a free energy decrease, indicative of system stability, thus qualifying the "spontaneity" (via the spontaneity criterion) or uncontrollableness of the heightened energetic process of falling in love.

Two demons equals one angel love equation
A two demons equals one angel love equation, representative of the good (natural) and evil (unnatural) aspects of relationships, viewed as types of neutralizing reactions.

Hence, a reaction between a single male human molecule, symbol Mx, and a single female human molecule, symbol Fy, on going from an initial state (day one) Gibbs free energy Gi to a final state Gibbs free energy state Gf, over the extent of reaction, of say 2-3 years (typical transition state time period), is defined according to the following human chemical reaction equation: [5]

 Mx + Fy \rightarrow MxFy \,

and is a process quantified by the following chemical thermodynamic formula:

 \Delta G = G_f - G_i \,
Equation of love (barn)

A 2011 rustic algebra-style equation of love. [33]

or in expanded form:

 \Delta G = G_{MxFy} - (G_{Mx} + G_{Fy}) \,

in which GMxFy is the Gibbs free energy of the couple in their bonded relationship state, in the form of a dihumanide molecule (two attached humans viewed as one single molecule), GMx is the measure of the Gibbs free energy of the male as a single unattached human molecule, and GFy is the measure of the Gibbs free energy of the male as a single unattached human molecule, variable which can be determined by measure of the individual enthalpies and entropies of each of those states of existence. This logic is summarized well by the following 1999 definition of molecular bonding by American-born Canadian biophysical chemist Julie Forman-Kay: [31]

“Whether two molecules will bind is determined by the free energy change of the interaction, composed of both enthalpic and entropic terms.”

The calculated value of this so-called "marriage reaction", in human terms, Gibbs free energy change ΔG will determine the naturalness or feasibility of the potential marriage as follows:

Differential change
State change
Love (perfect equation)
dG < 0ΔG < 0Lewis inequality for a natural process (or spontaneous process), one in which the change will occur naturally or spontaneously and in which useful energy is obtainable from the system.
dG > 0ΔG > 0Lewis inequality for an unnatural process (or non-spontaneous process), one in which useful energy is required to be supplied to the given system to bring about the desired change.

The first of these criterion's, i.e. the Lewis inequality for a natural process, will energetically quantify so-called "natural marriages" and the magnitude of the Gibbs free energy change, when less than zero, will determine the so-called measure of "love" or rather Gottman stability ratio of love to hate in the structure of the stability of the bond, according to the following rules (spontaneity criterion):

State change

ΔG < 0Lewis inequality for a natural process (or spontaneous process), one in which the change will occur naturally or spontaneously and in which useful energy is obtainable from the system.
ΔG ≪ 0Lewis inequality for a "very" natural process (or "very" spontaneous process), one in which the change will occur naturally or spontaneously and in which useful energy is obtainable from the system and in which the final state (bonded couple) will be greatly favored over that of the initial state (unattached couple) and the existence of the so-called strongly "loving" marriage will ensue.

This last equation is the "actual" modern physical science equation of love, according to the science of chemical thermodynamics.
Gravitational love equation

Algarotti | 1737
In 1737, Italian natural philosopher Francesco Algarotti, in his Newtonianism for the Ladies, employed the inverse square law to calculate the power of attraction between a pair of separated lovers", as follows:

Algarotti eq 2f

meaning that the force of love decreases with distance of separation.

In 2004, someone made a Algarotti-style social gravity like equation of love (Ѻ), shown adjacent, with accompanying description “Every person in the universe attracts every other person with a commitment directed along the line of social centers for the two persons that is proportional to the product of their affections and inversely proportional to the square of the separation between the two persons”.

Elective Affinities (1996)  (s)
Left: the 1996 film adaption of German polymath Johann Goethe's 1809 Elective Affinities, which uses the equations of Swedish chemist Torbern Bergman's 1775 physical chemistry A Dissertation on Elective Attractions, to explain love and relationships.
Goethe | Affinity equation | 1809
See main: Reaction decipherment; Equation decipherment
In 1796, German polyintellect Johann Goethe began to pioneer human chemical reaction theory, in terms of the forces of chemical affinities A operating on and between people, affinity being the precursor concept to free energy, who used the chemical equations of Swedish chemist Torbern Bergman's 1775 physical chemistry textbook A Dissertation on Elective Attractions, to show, through thirty-six chapters of a novella, that human relationships are purely and simply "chemical reactions", or affinity reactions (as they were called in Goethe's day), whereby the actions and processes involved in the state (initial state and final state) of love and human actions revolving about this powerful notion are quantified by measures of the force of affinity. [2] The following is are screenshots from the 1996 film adaptation of the famous chapter four, of his his 1809 novella Elective Affinities, wherein the gist of this theory is explained:

Elective Affinities (screen shots) chapter four

In short, to actuate the above scene, and each human chemical reaction per chapter, in his mind, Goethe made a human affinity table, and thus gave his readers the following equation for love:

Love = f{human elective affinities}

or in words, in 1799
comment (see: Goethe timeline) on the lack of realism in the work of French author Prosper Crebillon:

“Crebillon … treats the passions like playing cards, that one can shuffle, play, reshuffle, and play again, without their changing at all. There is no trace of the delicate, chemical affinity, through which they attract and repel each other, reunite, neutralize [each other], separate again and recover.”
Goethe love thought experiment
The 1808 Goethe "love thought experiment" according to which German polymath Johann Goethe contemplated the story of a hero simultaneously in love with four women, and had to turn to the equations of physical chemistry, affinity chemistry in particular, to explain the situation. See also: Thims thought experiment (1995).

which states that love is a function of human elective affinities or "chemical affinity" preferences between reactive people, which Goethe viewed as being chemical species. Thus, according to Goethe, for instance, in the situation in which a man ♂ in a relationship with woman ♀1 falls out of love with her and into love with a new women ♀2, as diagrammed below:
Single elective affinity (diagram)
the changes in love, for this chemical reaction, are quantified by sum forces of elective affinity preferences, or chemical affinity (modern sense), of the three people involved in the reaction. In modern terms, this ‘single elective affinity reaction’ is written as such:

♂♀1 + ♀2 → ♂♀2 + ♀1

To go through one example, the following is Bergman reaction #20 scaled up to the human-human reaction level, as explained in Elective Affinities. In modern terms, calcium sulfide CaS is decomposed by sulfuric acid H2SO4 in water calcium sulfate CaSO4, which precipitates (down full-bracket) and to produce elemental sulfur S which precipitates (downward half-bracket); which, neglecting intermediates, would be written as:

Bergman reaction 20 modern new

This reaction is an example of what is called a single elective affinity or single displacement reaction and in Bergman chemical species letter notation would be categorized as the following "type" of reaction:

Goethe (reaction models)

This outline thus explains the "symbols" and "chemical equations" Goethe had in mind in the writing of his self-defined greatest work.

Others, in the decades to follow, such as Henry Carey (1854), George Elliot (1872), and Max Weber (1878), Otto Weininger, (1903), etc., would go on to utilize similar types of chemical affinity theory in explaining various aspects of love in the wider context of embedded societal interactions.
Balzac dialogue 2
An 1834 rendition of Honore Balzac explaining to his fictional wife why the chemist, who has an understanding of human chemical theory, has a deeper sense and "feeling" of love then the general romantic person.

See main: Balzac feelings and affinity dialogue
In 1834, French realism novelist Honore Balzac, in his The Quest of the Absolute (La Recherche de l’Absolu), has Balthazar Claes, a chemist, debate with Josephine, his wife, about the underlying moral of the romantic belief that preoccupation with science atrophies the normal emotions that sustain personal relations and social responsibilities; the main dialogue of which is as follows:

Josephine: “Believe me, Balthazar, nature made us to feel; and though you will have it that we are nothing but an electrical mechanism, your gases and etherealized matter will never account for our power of foreseeing the future.

Balthazar: “Yes, by means of affinities. The power of vision which makes the poet and the deductive power of the man of science are both based on visible affinities, though they are impalpable and imponderable, so that ordinary minds look on them ‘moral phenomena’, but in reality they are purely physical. Every dreamer of dreams sees and draws deductions from what he sees. Unluckily, such affinities as these are too rare, and the indications are too slight to be submitted to analysis and observation.”

Josephine: “And this”, she said, coming closer for a kiss, to put chemistry, which had returned so inopportunely at her question, to flight again, “is to be an affinity?”

(add discussion)

Rankine | Love potential function
In circa 1845, Scottish mathematical physicist and engineer William Rankine wrote his "The Mathematician in Love" poem love song, wherein he quantified love as follows, namely as a type of potential, i.e. "potential energy" (a term he would coin in 1853) and or thermodynamic potential, as we now define things:

Rankine love poem (segment) EddingtonWilliam Rankine ns

Eq S6


Free energy and affinity | 1882
In the 1882 paper "On the Thermodynamics of Chemical Processes", German physicist Hermann Helmholtz showed that the measure of affinity A in a reaction system is equal to the negative of the free energy change
ΔG for the process of reactants going to products:

A = – ΔG

In the years to follow, others such as Walther Nernst, Theophile de Donder, and Gilbert Lewis, expanded on this view to prove unequivocally that the measure of affinity of a reaction is that of the free energy, or specifically Gibbs free energy in the case of isothermal-isobaric reactions, as are human chemical reactions.
Equation of love (tattoo) (2011)
Equation of love (Index card)
Left: a 2011 equation of love tattoo on the inner bicep of a Tumblr user woman named Chrissy. [32] Right: a 2009 index card “solve for n” style equation of love, entitled “The Equation of Love Perception”, indicating that both "time", spent working, in transit, and in affairs, and "imagination" are factors. [35]

A variant of this Helmholtz-based formula, connecting chemical affinity and free energy, is found in the 1936 booklet Thermodynamic Theory of Affinity, by Theophile de Donder, in which he gives the following expression for isothermal-isobaric affinity A: [3]

A=-\left(\frac{\partial G}{\partial \xi}\right)_{p,T}

where the affinity of the reaction is equal to the negative of the partial of the Gibbs free energy ∂G with respect to a change in the partial of the extent of the reaction ∂ξ, for a process at constant pressure P and temperature T.

Ellis’ equation | 1900
One of the first “equations” of love was put forward in the circa 1900 works of British physician Havelock Ellis, who postulated the following ball-park formula to love: [1]

Love = Sex + Friendship

which states that love is a combination of finding both hot sex and close friendship in another person.

Bazargan's equation of love
Bazargan (equation pg 71)
or need
The capacity of consumption
or total need

Available assets [items]
(Sexual inventory?)

In these early years, however, the crossover to human application, with focus on love, had not yet begun; thus would be a late 20th century insurgence (below).

Bazargan’s equation | 1956
Iranian mechanical engineer, thermodynamicist, and 75th prime minister of Iran Mehdi Bazargan outlined a “mathematical formula for the thermodynamic expression of love and life” in his 1956 book Thermodynamics of Humans (chapter five: Life Force). Although the Persian-to-English translation of this text is only partially complete (such as adjacent), the equation he seems to use for his equation of love and life is the Helmholtz free energy:

Helmholtz free energy

where W is "demand or need", U is the "capacity of consumption or total need", and TS, the bound energy in Helmholtz terms, according to Bazargan, are the "available assets or sexual inventory". He then expands on this in his work employing various chemical thermodynamics derivatives of the free energy, such as dA =-d (U-TS), among others. The correct type of "free energy", however, as would come into view towards the end of the 20th century is the Gibbs free energy, the isothermal-isobaric free energy, as these are the general daily conditions on the surface of the earth, not the isochoric-isochoric free energy (Helmholtz free energy), as discussed further below. Nevertheless, this is not a simple discernment, as evidenced by the fact the the great Ilya Prigogine got this fact wrong in his 1977 Nobel Lecture.
Guyon | Prigogine
In 1975, Etienne Guyon sent the following letter to Ilya Prigogine where, supposedly, he discussed the premise of explaining the love affairs and relationships based on thermodynamics: [40]
This idea interaction, however, never resulted in a published paper.
Love Affairs and Differential Equations

American applied mathematician Steven Strogatz's 1988 article on differential equations and love. [1]
Partial differential equations
| 1988
See main: Mathematics of love
One of the first to begin to describe love in mathematical terms was American mathematician Steven Strogatz who in his 1988 article "Love Affairs and Differential Equations" discussed his unusual teaching approach to introducing students to the subject of systems of coupled ordinary differential equations, by formulating hypothetical differential equations to describe the love/hate ratio functions (see: Gottman stability ratio) for the interactions between William Shakespeare's Romeo and Juliet. [16]

Strogatz's formulations, however, seem to be only a fun superficial application aimed at teaching mathematics.

The correct mathematical formulation of love and hate and relationships invariable involves partial differential equations that describe that describe either changes in chemical affinity or changes in Gibbs free energy with temperature and pressure held constant.

Love equation (graph) Integral of love
Left: a graphical way of depicting love as an equation. [7] Right: 2008 integral of love tattoo, said to mean: “all values, from zero to infinity, are less than love.” [11]

Gibbs free energy | love & relationships
The first to state that human love is quantified by Gibbs free energy, in a formulaic manner was astrophysicist Christopher Hirata (IQ=225), in his circa 2000 relationship physics article "The Physics of Relationships".

This was followed by the 2001 relationship chemistry article
The Thermodynamics of Love” by American computational chemist David Hwang. Hwang states, without references and what seems to be on intuition, that for the process of a man M and women F falling in love:

M + F → M-F

that, the measure of the spontaneity or favorability of this falling in love process is determined by the following equation:

sG = sH – TsS

where the “s” seems to refer to the specific value of Gibbs free energy G, enthalpy H, entropy S, and T for temperature.
Me plus you equals lovesex equal fun (equation)

Sex equal fun shirt
A 2007 T-shirt love as type of mathematical / chemical equation: [9]
 M(e) + Y(o)^u = L^o (v)e \,
A mathematics humor "sex equal fun" derivation and T-shirt.

Hwang then states that “a reaction in which G decreases (-sG) favors formation of product because the products have less free energy than the starting compounds and are more stable. In a reaction in which G increases (+sG), reactants are not likely to make much chemical progress.” [4]
On February 17, 2009, a video entitled “Chemical Romance”, by Cacao Productions, was posted on YouTube declaring that:

Science today cannot give us an exact chemical equation to what is love, or even tell us if one exists.”

In response to this, on March 03, 2009, American chemical engineer Libb Thims posted up a response video to correct this erroneous statement.

“Chemical Romance” by Cacao Productions (17 Feb 09)
"Love | Equation of" by HumanChemistry101 (03 Mar 09)

These are shown below, respectively. Thims, to note, had previously written up a full textbook on this issue, Human Chemistry (2007), outlining the logic behind the view that human love and the activities surrounding this phenomenon are governed by the following simple expression:

A= -\Delta G \,

where, with substitution, knowing that the change in Gibbs free energy ΔG in closed system chemical reaction is equal enthalpy change ΔH less the product of the entropy change and the temperature, TΔS, we have:

A= -(\Delta H - T\Delta S) \,

A= T\Delta S - \Delta H \,

meaning that differences in love between potential mates can be determined by entropy and enthalpy changes involved in the process, and thus be able to predict, in theory, whether any given relationship is going to work; thus finding modern chemical thermodynamic corroboration with Goethe's 1809 Elective Affinities. [5]

Social thermodynamics (love equation)
Image from Jacob Leachman's 2017 blog (Ѻ) on the thermodynamics of love, wherein he gives Gibbs energy as the defining equation of love.
Leachman | Equation
In 2017, Jacob Leachman, in "Social Thermodynamics: Chapter on Love", stating things as follows: (Ѻ)

When you’ll fall in love
Falling in love is likely a form of phase change (see: social phase). You’re entering into a (hopefully) synergistic bond with another that adds to you on many levels. The Gibbs energy analysis in other chapters shows that phase change spontaneously occurs when the Gibbs energy after the event is less than the Gibbs energy before:

G = U + Pv – TS

This is promoted by:

U: simplification of values or descending to primal/familial values as a pair compared to individuals.
P: reduced stress after the change.
v: reduced volume, or increased density analogous to living together.
T: likelihood of increased resources after the event. (Dowry?)
S: becoming more empathic and understanding more things, including your partner, in more ways.

So if you find yourself only wanting to do one thing with someone, but are connecting with them on many levels, you run a chance of falling in love. But beware, empathy like entropy is irreversible, it’ll be tough to forget someone if it doesn’t work out. What’s also comforting is that we can fall in love again and again. At the higher v-Memes there is a multitude of ways to synergize and hook up. Remember too that these properties are all connected by a complex surface of state and it is possible for phase change to happen despite some of the properties moving in opposite directions. But it generally holds, and vice versa should you ever want to prevent love.


An Abundance of KatherinesAn Abundance of Katherines (2008)
American young adult fiction author John Green's 2006 award-winning book An Abundance of Katherines (left), and followup 2008 edition (right), which tells the story of Colin Singleton, a child prodigy who tries to turn his 19 failed encounters with girls named Katherine into a formula that will predict the outcome of all relationships.
An Abundance of Katherines | 2006
In 2006, American young adult fiction author John Green published the award-winning book An Abundance of Katherines, which tells the story of Colin Singleton, a child prodigy who tries to turn his 19 failed encounters with girls named Katherine into a formula that will predict the outcome of all relationships and elevate him into genius status. The book was a 2007 Michael L. Printz Award Honor Book, a finalist for the Los Angeles Times Book Prize, and may also, it is said, be in the works to be made into a movie in the future. The synopsis is:

"When it comes to relationships, Colin Singleton's type is girls named Katherine. And when it comes to girls named Katherine, Colin is always getting dumped. Nineteen times, to be exact. On a road trip miles from home, this anagram-happy, washedup child prodigy has ten thousand dollars in his pocket, a bloodthirsty feral hog on his trail, and an overweight, Judge Judy–loving best friend riding shotgun—but no Katherines. Colin is on a mission to prove The Theorem of Underlying Katherine Predictability, which he hopes will predict the future of any relationship, avenge Dumpees everywhere, and finally win him the girl. Love, friendship, and a dead Austro-Hungarian archduke add up to surprising and heart-changing conclusions in this ingeniously layered comic novel about reinventing oneself."

The book contains an appendix, written by American mathematician Daniel Biss, a close friend of Green, explaining some of the more complex equations Colin uses throughout the story. [21] The so-called "Theorem of Underlying Katherine Predictability", is outlined below: [23]

Green's theoremGreen equation of love tattoo
A synopsis of the Green equation of love.
A circa 2010 tattoo of the Green equation of love on someone's forearm.

To solve this formula, supposedly, one is only to plug the variables into the equation shown and calculate. At one point, to note, Green had a java applet running to make quick calculations for people at SparksFlyUp.com, but the now-archived site was only active for a few years (c.2006-2008). [25] A Q&A synopsis of the book's writing origin, according to Green (2008), is as follows: [24]
An Abundance of Katherines (draft notes)
A 2008 artistic recreation of the themes and content, e.g. anagrams, mathematics, orbitals, some type of min-max graphical method, etc., of An Abundance of Katherines. [26]

Q. Is this book like Looking for Alaska?
A. Well, yes and no. Katherines is more of a comic novel (for instance, no one dies), but I still like writing about smart kids and friendship and figuring out what if anything matters.

Q. This book has a lot of anagrams and footnotes and also some math. What's up with that?
A. The only way I can answer that question is to say that I don't think you have to like footnotes or anagrams to like Katherines. And I SWEAR you don't have to like math.

Q. It's not just cleverness for the sake of cleverness, is it?
A. I hope not. Certainly I've never taken a lot of stock in being clever.

Q. Colin believes that there are two kinds of people in this world: Dumpers and dumpees. Which kind are you?
A. I am a dumpee. In fact, before I got married, I was dumped 53 times. But never by a girl named Katherine.

Q. Is what why you picked the name Katherine?
A. Well, that had something to do with it. Also because Katherines is a great word for anagramming (it contains, after all, both heart and tear), and because it is a very common name.

An Abundance of Katherines (page)
Green's "dumber/dumpee dichotomy" shown on a bell curve, according to which he says the majority of people are lumped somewhere in the middle.

Q. Yeah I have a question about that, actually. How could Colin have been dumped by 19 Katherines? Are there even 19 Katherines in all of Chicago?
A. When I was writing the book I actually decided to sit down and figure out approximately how many Katherines there are currently living in Chicago between the ages of 16 and 18 (which I figured to be the basic pool from which Colin could draw girlfriends).

It's a very inexact science, but if you look at the frequency with which kids in America were named Katherine between 1988 and 1990, and then you look at the percentage of Cook County residents who are between the ages of 16 and 18, the numbers indicate that there are something like 275 16-18-year-old Katherines living in or very near the city of Chicago, and that's not even counting the 3 million people who live in the suburbs. So the real question is: How did Colin manage to date ONLY 19 of them?

Curiously, although only in numerical similarity, 19 was the number of girlfriends of marriage potential that American electrochemical engineering student Libb Thims, in circa 1992-1993 (see: Thims thought experiment) , plugged into an excel spreadsheet style formula to attempt to discern numerically whom he should potentially choose to marry; listing each person on the horizontal and listing a range of point ranked attributes, qualities, or factors on the vertical, in an attempt to get a numerical "marriage quality value" for each girlfriend.
An Abundance of Katherines (ertiaofsleep)Equation For Love (2012)
Left: a John Green fan 2011 "equation overlay style" book cover submission, showing Green's equation of love in the background. [27] Right: a 2012 novel entitled Equation for Love by Fae Sutherland the blurb of which is:

Sex + money (shouldn't) = love

with the tagline: "but since when does the heart follow any laws but its own?" [36]

Of note, Green has been running an ongoing Penguin publishers "An Abundance of Covers" contest (ending November 21, 2011) for reprint editions of his book; all of the many submitted designs of which can be viewed online (at Tumblr). [27]

The Attraction Equation | 2007
A spin-off of Green’s An Abundance of Katherines was the fictional 2007 book The Attraction Equation described as being written the character Charles Eppes of the popular TV show Numb3rs, described as being about the "the mathematics of friendship". [22] A summary of the episode is as follows: [23]

“Dr. Finch tells him to publish, and so he has renewed interest in old research, having decided to publish one of his eleventh-grade papers he started at nine years old, "The Mathematics of Friendship," with an addendum. A publishing company has turned his work into a classic book for those not mathematically inclined, while opting for a title with more pizazz, "Friendship, As Easy as Pi." Charlie takes joy in the belief that this book will allow his thoughts to reach a much wider audience than before.
The Attraction Equation (2007)
The cover of the fictional 2007 TV-land book The Attraction Equation, for an episode of the popular TV show Numb3rs, described as being about the "the mathematics of friendship", written by child prodigy Charles Eppes. [22]

By the episode "In Security," the published book appears with the title "The Attraction Equation" and a dapper photo on the back cover of him holding a sculpture of a stellated icosidodecahedron with bevelled edges [William Sidis lectured on something similar to this as a child]. A decision theoretic approach to relationships is covered in the book. His proud father hands copies to friends and Larry sells signed copies on eBay. He apparently has some fans and gives into a televised interview.”

To note, the first to actually write such a mathematical paper was Russian-born American thermodynamicist, theoretical biologist, and sociologist Nicolas Rashevsky who in his 1935 article turned chapter "Mathematical Theory of Human Relations" builds on the work of Alfred Lotka to attempt to derive mathematical equations for things such as ‘desire’ and ‘will’, in terms of concepts such as intensities and physical forces.

Likewise, as reality mirrors fiction and fiction reality, the character of Eppes, is similar to a number of actual prodigies. Eppes, it is said, could multiply four-digit numbers mentally at age three and at the age of four required special teachers [similar to Kim Ung-Yong (IQ=200-210)].

In the second grade, he attempted to find a 70-digit narcissistic number in base 12 [William Sidis (IQ=200-300) invented his own base 12 logarithm table] — Eppes has described himself as "quixotic" in elementary school.

A prodigy, he attended Princeton University at the age of 13 after graduating from high school [Christopher Hirata (IQ=225) won the IPO at age 13 and completed his BS in physics at Caltech and PhD at Princeton at age 23; likewise, Hirata actually did publish an actual physical chemistry based formula for love and relationships, in his 2000 article "The Physics of Relationships" written at age 20] at the same time as his brother who is five years his senior ("Soft Target"), and took Professor Lawrence Fleinhardt's quantum physics course in his first year.

They became fast friends, with Fleinhardt establishing his academic connections. Eppes published his first mathematical treatise at the age of 14 (in the American Journal of Mathematics) [similar to William Thomson (IQ=170-190) who published his first papers in the Cambridge Mathematical Journal as a teenager under the pseudonym P.Q.R.] and graduated at the age of 16. In fact, he was the youngest person to ever write a paper of importance. [23]

Extent of love
Modeling the process of love viewed as a purely chemical reaction, which is what it is, one arrives at the finding that each type of reaction between individuals in a relationship is characterized by a specific measure of "extent of reaction" or time-frame at which the reaction or relationship reaches thermodynamic equilibrium, meaning that the transformation content of the relationship, otherwise known as entropy or entropy change has reached maximum value.

man plus woman equals love

Extent of reaction
Equilibrium reactions
Left: with marriage viewed as a human chemical reaction, the factoid of 43% of marriages ending at 15-years, i.e. divorce rate, is a measure of the extent of reaction. Right: a Julius Davidson (1919) and or Christopher Hirata (2000) type depiction of human pairings as Le Chatelier type equilibrium reactions that adjust depending on reaction conditions.

Mathematically, the equilibrium point or divorce point for a relationship is quantified by Theophile de Donder's extent equation:

A=-\left(\frac{\partial G}{\partial \xi}\right)_{p,T}

where at equilibrium the affinity A, chemical affinity, elective affinity, or driving force of the reaction between the couple will equal zero, A = 0, and thus with substitution:

 \Bigg ( \frac{\partial G}{\partial \xi} \Bigg )_{T,P} = 0 \,

which means that the variation of the Gibbs free energy (available energy) of the relationship with respect to the variation of extent (time) is zero or has a near negligible change. Some relationships, however, owing to thermodynamic coupling, will be driven past the equilibrium point, meaning that not only is there no available energy, but that the relationship becomes "energy absorbing" (endergonic) or energy draining, meaning that not only is the relationship not working any more, but it is work absorbing.

Statistically, it is known that about 90% of people will enter into a marriage reaction and that of these reactions 43% will reach thermodynamic equilibrium at the 15-year mark and file for divorce.

Homosexual equation of love
See main: Queer chemistry
The first to outline and discuss chemical reaction reaction or chemical equation formulations for homosexual relationships was American astrophysicist Christopher Hirata ("The Physics of Relationships", 2000) and the first textbook section on subject homosexuality in the context of chemistry and thermodynamics was the "LGBT/Queer chemistry" chapter section of American electrochemical engineer Libb Thims' 2007 textbook Human Chemistry. [19]
Homosexual love equation
Male-male love equation
Left: an alchemy symbol stylized chemical equations for homosexual love. Right: the 2000 song "U + Me = Us" by the boy band 2ge+her.

On average, about 3-4 percent of the general male population and about 1-2 percent of the female population are homosexual in mating behavior and orientation. In these types of reactions, for the male-male pairing scenario, two male human molecules will form a mated union:

Mx + Mx → MxMx

Similarly, about 1 percent of the general female population are homosexual in mating behavior. In these types of reactions, two female human molecules will form a mated union:

Fy + Fy → FyFy

Other variations of reactions and chemical equations exist beyond these two examples.

Mathematical equation
See also: Thermodynamics humor
Related to the subject of the “equation of love” is the popular so-called ‘mathematical proof’ that a woman equals problems, which is often given as a joke-answer to the premise that, supposedly, one can reduce love to a mathematical equation. It is difficult to track down the origin of this; online versions date several years, and the actual joke seems to have originated several decades back, but it amounts to a five step proof, with alternative variations in step four:


Love is greater than money (s)
1. Women are a product of time and money
\text{women} = \text{time} \times \text{money}
2. Time is money
 \text{time} = \text{money} \,
3. (substitution of step 1 eq. into step 1 eq.)
 \text{women} = \text{money}^2 \,
4. Money is the root of all evil Bible
(Timothy, 6:10)
\text{money} = \sqrt{\text{evil}}

Money is the root of all problems
\text{money} = \sqrt{\text{problems}}
5. (substitution of step 4 eq. into step 3 eq.)
\text{women} = (\sqrt{\text{evil}}\,)^2

\text{women} = (\sqrt{\text{problems}}\,)^2
A "love > money" equation spray painted onto a public wall (22 July 2010): Love equation, graffiti artist (and place) unknown; alluding to the intimate and generally unwritten relation that exists between money (wealth) and love. [29]

Therefore, by the mathematical rule that  (\sqrt{\text{x}}\,)^2 = x, depending on one's prerogative, one can concluded to have proved that either all woman equal problems:

\text{women} = \text{problems} \,

or that women are evil:

\text{women} = \text{evil} \,

An alternative spin on this might start out by arguing that love is a product of time and energy:


1. Love is a product of time and energy Libb Thims (2007) \text{love} = \text{time} \times \text{energy}
2. Energy and mass are equivalent Albert Einstein (1905) \text{energy} = mc^2 \,
3. Love is a force Empedocles (400BC) \text{love} = \text{force}_L \,
4. (substitution of step 3 eq. and step 2 eq. into step 1 eq.)
 \text{time} = \frac{\text{force}_L}{mc^2} \,

Equation of love (relativity)
which leads one to the humorously conclusion that time is a function of the force of love divided by the product of the change in the mass of one's connected relationships and the speed of light squared. Another popular math-themed joke about love goes something along the lines of: [18]

“Sex is a matter of math: Add a woman. Subtract her clothes. Divide her legs. And Multiply.”

Physics of love
See main: Physics of love; Thermodynamics of love
A humorous particle physics of love poem is:

Bosons are red
Mesons are blue
I like to classify
Hadrons with you

Shown adjacent, is a humorous relativity-themed Valentine's Day card equation of love, themed on the premise of explaining love via physics. [28]

Two swans forming a heart
Two swans forming a heart shape, both a common historical symbol of love. Modern symbols, however, involve chemical symbols: bonding brackets “{“, reaction arrows “”, reaction conditions, i.e. in water “∇” or heated “Δ”, individual chemical species, A, B, c., etc., attached species, Ab, Ac, etc., and movements and reactions of species due to affinity tendencies (affinity reactions), depicted diagrammatically.
Emotional imaging
In science-based matching sites, in circa 2009, building on Sigmund Freud and Carl Jung's psychodynamic theories and Libb Thims' 2007 human chemistry and human thermodynamics theories, the Russian biometrist Viktor Minkin launched a prototype emotional recognition compatibility program designed to test for love based on thermodynamic principles. The site, Psymaker.com (see: video matching exampleExternal link icon (c)), supposedly tests couples in politics via vibraimage matching algorithms, giving a free test on which to give three politics view agreements with the best "energy compatibility" percentage with potential match. This logic is found at PsyMaker.comExternal link icon (c), which uses a fingerprint compatibility test.

Fiancée formula
In 2010, in what seems to have been a Valentine’s day math joke that gained a significant amount press following, Australian mathematics professor Tony Dooley sent out a press release of the School of Mathematics and Statistics of the University of New South Wales, for a so-called newly discovered ‘fiancée formula’, as shown below, said to be an equation helpful in determining the right moment to get serious: [12]

Fiancée formula
Equation of love (dtevent-formula) s
A 2010 equation overlay depiction of Australian mathematician Tony Dooley's so-called ‘fiancée formula’ equation of love. [34]

As to what the variables of this equation stand for, however, the explanation seems to be lacking, as the press release seems to have retracted as of 2011, possibly being a joke? In any event, all that remains in the derivative news clippings is a three step handout, by the UNSW School of Mathematics and Statistics, for the process for determining whether to ask someone to marry you, which amounts to the following:

1. Set out the last possible age by which you want to get married (e.g. age 39). Call this number 'n' for age at which marriage is a necessity.
2. Decide the earliest age at which you'll start to consider women as potential wife material (e.g. age 20 onwards). This age becomes 'p' or age at marriage becomes a possibility.

Then plug these numbers, n and p, into the following formula to get your age of optimal proposal:

 A_{o} = p + 0.368(n - p) \,

The result Ao is your "optimal" proposal age. Using the example number, n = 39, p = 20, gives Ao = 27, which essentially yields the age of the average world man at first marriage. [13] Ideally, according to Dooley, you should not propose to anyone before you hit this age, but afterwards you should prepare to pop the question to the very next girl you date – as long as she's the best of the bunch so far.
Conley equation of love (c)
American well-being theorist Chip Conley's 2012 emotional equation of love. [30]

Complex Numbers (2011)

Couple distance equation of love
Left: poster for the 2011 play Complex Numbers written by Canadian playwright Nadine Thornhill and her husband mathematician Phil Eisen, in which the main character attempts to derive equations for love. [17] Right: a 2010 “Love vs. Distance” theory equation of love, where the love symbol represents the amount of love between the couple at an instantaneous time, X represents the distance between the couple, and C is a constant; according to which at a high value of X, the couple is far apart and love decreases, whereas at a low value of X, couples are nearer and love increases. [38]
Emotional equations
In the 2012 book Emotional Equations, American Hotelier turned well-being theorist Chip Conley built on Abraham Maslow’s theory of needs, following his emotional roller-coaster on how he was going to pay his thousand plus hotel employees following the dot com bust, to pen out a number of various “emotional equations”, as he calls them, from topics such as flow to fear, among which his chapter sixteen gives the following equation for love: [30]

Joy = Love – Fear

or reordered algebraically:

Love = Joy + Fear

the latter of which becomes a bit tenuous, as far as equations of love go, boiling love down to a summation of joy and fear.

The 2011 play Complex Numbers, written by Canadian playwright Nadine Thornhill, tells the story of a main character Fiona, a mathematician, tries to navigate the complexities of an office romance. “She tries to solve the equation of first dates, kinky sex, and long-term commitment,” said Thornhill.

The inspiration for the play came in the way of Thornhill’s husband, mathematician Phil Eisen, who works for Kanata-based security company Irdeto. “The main character is a mathematician and I'm married to a mathematician,” said Thornhill. “I wanted to explore the idea of the office romance and do it in a way that is different then the way you see in romantic comedies. “I wanted to explore what would happen if you had a relationship where people did the exact opposite…I would call it radical communication.” Eisen helped Thornhill write certain parts of the script, throwing in technical jargon that lends credibility to the characters but that’s also easy for the public to understand. [17]

Thornhill’s Complex Numbers might remind us of British playwright Tom Stoppard’s 1993 Arcadia, an attempt at a modern rewrite of Goethe’s famed physical chemistry of love based novella, the 1809 Elective Affinities.

The following is a noted quote from the 2001 film A Beautiful Mind based on the life of American mathematician John Nash:

"I've always believed in numbers. In the equations and logics that lead to reason; but after a lifetime of such pursuits I ask, what truly is logic? Who decides reason? My quest has take me through the physical, the metaphysical, the delusional and back, and I have made the most important discovery of my career... the most important discovery of my life. It is only in the mysterious equations of love that any logical reasons can be found. I'm only here tonight because of you. You are the only reason I am... you are all my reasons."

Left: a short 2007 film entitled “Kirby and the Love Equation”, about a 13-year-old boy genius named Kirby who spends five minutes each day attempting to derive an equation that will predict the odds the older girl he likes will go for him, Written by Brandon Goodwin, Nate Black and Grant Heugel. Right: the scene from the 2001 film A Beautiful Mind, wherein John Nash (starring Russell Crowe) gives his fictional Nobel Prize acceptance speech and mentions the "mysterious equation of love", something he never seems to have done in reality.
This is a quote from John Nash's fictional Nobel Prize speech. In actual fact, Nash was never asked to speak upon his acceptance of the 1994 Nobel Prize in Economics.

Other quotes are as listed:

“I've made the most important discovery of my life. It's only in the mysterious equation of love that any logical reasons can be found.”
Erich Fromm, German-born American social psychologist

A related film by title, albeit only in namesake, is the 2008 movie The Equation of Love and Death, which is described as a pompous English re-title of the original Chinese: "Li Mi's guesses", a suspense-thriller film about why the boyfriend of Li Mi, an undistinguished taxi driver, left her. The film has no equations in it, nor it seems anything to do with a scientific explanation of love.

The following are a few recently-found equations of love stylized images. The following, e.g., is a DreamsTime.com (Ѻ) " equation of love" wedding symbol, which shows a mixture of math (love + love) equals marriage, and possibly human bonding (M=F) theory, couple tightly bound:

Equation of love (dreamstime)
The following, below left, is 2013 The Times “equation of love” like image, showing: heart overlap, which may be representative of human molecular orbital theory, a martini squared, representative of alcohol's ability to lower inhibitions, thus giving wiggle room at the activation energy barrier, a reaction arrow, representative of transition state, an inequality sign (≥), which in the direction shown, would seem to be quantitatively indicative of the premise that good (natural) loves have greater Gibbs free energy in the initial state (left side of inequality sign) than final state (right side of inequality sign), some type of neurochemical, etc., for a book review article on Graeme Simsion’s new book The Rosie Project, about a guy with Asperger’s syndrome named Don Tillman who wants to find the “Perfect Wife” via questionnaires and DNA samples, a fictional spinoff, it seems, of recent non-fictional “Sweaty T-shirt study” based science-based dating sites: (Ѻ) (Ѻ)

Equation of love (heart overlap)Dr love
A 2013 The Times “equation of love” like image showing: heart overlap. A circa 2011 Dr. Love cartoon, by artist Jaime Huxtable (Ѻ), trying to find the formula or equation for love. (Ѻ)

The following are other examples:

What is love? (math, history, chemistry, art)Love equation (barns15)
The following is a recent 2013 math, history, chemistry, art tale on the: what is love? query:Right: A 2010 DeviantArt.com (computer modified) rendition of two people discussing a mathematical-like poetic style love equation. [15] In realty, to note, by virtue of tendencies of Beckhap's law, the probability of a physically "hot" blond being able to write such an equation on a dry erase board would be very rare.

Others include:

Equation of love (male female views)

A 2010, Beckhap's law themed, equation infographic of love created by Audrey Fukuman, representing the differences in how men and women rate each other when looking for a potential mate. [8]

Throw pillow
The following is a circa 2014 “Chemical Thermodynamic Equation for Love” fine art design, by artist Paulette Wright, based on the circa 2003 Gibbs energy male-female reaction formulations of American electrochemical engineer Libb Thims, such as outlined above, available in the formats of: canvas print, framed print, iphone case, throw pillow, among others: (Ѻ)

Chemical Thermodynamic Equation For LoveChemical Thermodynamic Equation For LoveThims equation of love (pillow) 2015

The 2015 photo (right) shows the equation of love pillow on the Thims' couch below biographical books on Hermann Helmholtz, Willard Gibbs, and William Thomson, by Helge Kragh, Muriel Rukeyser, Lynde Wheeler, David Lindley, among others, some of the thinkers behind the shown equation of love.

The following are related quotes:

“No poet, ancient or modern, not even Shakespeare or Dante, has more clearly divined or expressed with more profound utterance the nature of love than Emerson, though the poems in which he has expressly dealt with that passion are few. To be a poet is to be a lover, and the feminine Muse is but the unknown quantity in the poet's algebra, by which he expresses now this element, now that, in the indeterminate equation of love. Or, as Emerson better announces this mystery: ‘The sense of the world is short; Long and various the report — To love and be beloved’.”
— Franklin Sanborn (1879), “The Homes and Haunts of Emerson” [39]

“Polymerization + Love = You
Clifford Pickover (2016), Great Chain of Being Image Tweet (Ѻ), Nov 26

See also
● Elective Affinities | IAD: Love theories
Equation overlay method
Gottman stability ratio
Ostwald happiness formula
Love equation (beers)Equation of love (Shutterstock)
2009 humorous take on a love equation: in which a man plus a woman times five beers equals love. [10]A 2011 ShutterStock.com rendition of a male plus female equals love chalkboard equation of love. [14]
man plus woman plus coffee equals love
A man plus woman plus coffee equals love equation, alluding to the underlying chemical-amphetamine nature of love.

1. (a) Tennov, Dorothy (1979). Love and Limerence. Maryland: Scarborough House.
(b) Article: “On Being Limerent” – flatrock.org.
(c) Havelock Ellis (1859-1939) – Kirjasto.sci.fi.
2. (a) Goethe, Johann. (1809). Elective Affinities. Penguin Classics.
(b) Adler, Jeremy. (1987). “Eine fast magische Anziehungskraft”. Goethe’s “Wahlverwandtschafte” und die Chemie seiner Zeit (“An almost Magical Attraction”). Goethe’s Elective Affinity and the Chemistry of its Time), Munich.
(c) Thims, Libb. (2007).
Human Chemistry (Volume Two), (preview), (ch. 10: "Goethe's Affinities", pgs. 371-422). Morrisville, NC: LuLu.
(d) Smith, P.D. (2000). “
Elective Affinity: a Tale of Two Cultures
”, Prometheus, 46-65.
3. De Donder, T. (1936). Thermodynamic Theory of Affinity: A Book of Principles. Oxford: Oxford University Press.
4. Hwang, David. (2001). "The Thermodynamics of Love", Journal of Hybrid Vigor, Issue 1, Emory University.
5. (a) Thims, Libb. (2007). Human Chemistry (Volume One), (preview), (Google books). Morrisville, NC: LuLu.
(b) Thims, Libb. (2007).
Human Chemistry (Volume Two), (preview), (Google books). Morrisville, NC: LuLu.
6. ShMany. (2009). “Love Equation”, Flickr.com, Mar 16.
7. Ainikeciq. (2009). “Mathematics of Love: How to Draw a Heart Shape in Math terms”, Eyenieekeciqslipsis.onSugar.com, Dec 30.
8. Tsotsis, Alexia. (2010). “Equation: the Difference between Girls and Guys”, Blogs.SFWeekly.com, Jan 29.
9. GotSingh. (2007). “Love Nerd: Love Equation: a way for Nerds to Express Their Love”, Zazzle.com, Feb 02.
10. David. (2009). “Love Equation”, MyLaughingBlog.com, Oct 07.
The Love Equation (2010)
A 2010 love equation poster. [37]
11. Talk like a physicist (2008).
12. Anon. (2010). “Math Professor Bares ‘formula for love’”, Reuters, Feb 12.
13. Age of first marriage – Wikipedia.
14. Male plus female equals love (2011) – ShutterStock.com.
15. The love equation (by barns15) (2010) – DeviantArt.com.
16. Strogatz, Steven H. (1988). "Love Affairs and Differential Equations", Mathematics Magazine, 61(1): 35.
17. (a) Cunha, Jessica. (2011). “New Play Tries to Solve the Equation of Love”, Jun 09, Your Ottawa Region Article.
(b) Thornhill, Nadine. (2011). “Complex Numbers: Why I Write Plays about Sex”, June 09. WordPress.
18. Clayton, Michal. (2009). “Love is a Matter of Chemistry, but Sex is a Matter of Physics. Is this True?”, Yahoo Answers.
19. Thims, Libb. (2007). Human Chemistry (Volume Two) (LGBT/Queer chemistry, pgs. 622-28), (preview), (Google books). Morrisville, NC: LuLu.
20. (a) Green, John. (2006). An Abundance of Katherines. Dutton.
(b) An Abundance of Katherines – Wikipedia.
(c) An Abundance of Katherines (poster) – Glogster.com.
21. Daniel Biss – Wikipedia.
22. Liz B. (2007). “Numb3rs & Abundance of Katherines, A Chair, A Fireplace & A Tea Cozy, blogspot, Nov. 04.
23. Charlie Eppes – Wikipedia.
23. Colin’s Equation from an Abundance of Katherine’s – EffYeahNerdFighters.com.
24. Katherines (SparksFlyUp.com) – WayBack Machine.
24. SparksFlyUp.com – WayBack Machine.
25. (a) Green equation of love – EffYeahNerdFighters.com.
(b) Green equation of love – BellesParoles.Tumblr.com.
26. An Abundance of Katherines (note) – Flickr.com.
27. An Abundance of Covers (design contest) – JohnGreenBookCovers.Tumblr.com.
28. Einstein’s equation of love (2011) – AbstruseGoose.com.
29. Love greater than money (2010) - MyStillLife.Wordpress.com.
30. (a) Conley, Chip. (2012). Emotional Equations (pgs. 185-). Free Press.
(b) Conley, Chip. (2010). “Measuring what makes life worthwhile”, TED, Feb.
31. Forman-Kay, Julie D. (1999). “The ‘Dynamics’ in the Thermodynamics of Binding.” Nature Structure Biology, 6: 1086-87
32. Equation of love tattoo (2011) – Don’t Walk in time (original), Tumblr.com.
33. Equation of love (rustic style) – wedpicstodiefor.blogspot.com.
34. (a) Kneene, Neil. (2010). “Follow this Formula for True Love”, The Telegraph, Feb 11.
(b) Photo (description): “Timing ... Ben Devonshire, 20, and girlfriend Cathy Clarke, 20 / Pic: Liam Driver Source: The Daily Telegraph”.
35. The Equation of Love Perception (2009) – Flickr.com.
36. Equation of Love (2012) – GoodReads.com.
37. The Love Equation (poster) (2010) – The Patter Connection, WordPress.com.
38. Author. (2010). “Love vs Distance Theory”, Driftneland.Blogspot.com, Jan 26.
39. Sanborn, Franklin B. (1879). “The Homes and Haunts of Emerson” (Ѻ) (library, pg. 505; soul, pg. 505; equation, pg. 506), The Century, 17:496-511, Feb.
40. Rinaldi, Sergio, et al (2015). Modeling Love Dynamics (pg. 20-21). World Scientific.
Further reading
● Bryner, Jeanna. (2008). “Wanted: The Equation of Love”, LiveScience.com, Jan 30th.

External links
Formula of Love (1984 film) – Wikipedia.
Is there a mathematical equation for love? (2009) – Yahoo! Answers.
What is the chemical formula for love? (2009) – Yahoo! Answers.

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