**Mathematics has multiple domains**

Although I am not a mathematician, I studied mathematics at the university level. As an undergraduate, I completed two years of mathematics — Calculus followed by Discrete & Finite Mathematics. For my graduate degree, I studied Regression Analysis and Statistics/Probability. For my PhD research, I learned Cluster Analysis (Multivariate Discriminate Analysis). I needed to understand the mathematical foundations underlying Computer Science, Finance, and [Value Chain] Management, the subjects of my BSc, MBA and PhD degrees.

The various branches of mathematics are complementary. Algebra, Geometry, Calculus, Statistics/Probability, etc. are used to solve different types of mathematical problems. Sometimes they are used together. For example, to calculate the value of many financial derivative securities, one needs Algebra, Statistics / Probability and (sometimes) Calculus. In order to answer a wide range of scientific, engineering, and economic questions, one needs to know multiple areas of mathematics. Each mathematical discipline is necessary but insufficient by itself.

One needn’t be an advanced mathematician to solve business problems. Solving frequently encountered problems, though, does require understanding the “first principles” of mathematics. For example, one cannot divide a number by zero. Or one can use the associative and distributive rules when factoring algebraic equations. Or most probabilistic occurrences follow a normal distribution. Solving problems also requires understanding how the various mathematical disciplines intersect/combine. To compute the volume of a concave cone or a doughnut, one uses the formula for calculating the area of a circle (taken from Geometry) along with principles for calculating the area under / between continuous functions (taken from Integral Calculus).

One does need an advanced mathematician, however, to validate proposed solutions to very detailed (and complex) problems. University mathematics departments ensure that graduates are sufficiently trained / educated in multiple mathematical areas to a deeper degree than generalists like me. Mathematics graduates understand all the areas of Calculus for example. They also are trained to solve statistical problems that do not follow a Normal Distribution. We rely on their expertise to ensure sampling methods are robust and accurate when conducting large-scale research surveys. Or to test that statistical outcomes are significant – that they aren’t merely chance events.

**Mathematics as an analogy for business value**

An earlier article used energy (defined by physics) as an analogy for business value. It is equally useful to view business / management through the lens of mathematics. Both mathematics and business deal with numbers. Mathematics, though, recognizes that numbers alone are meaningless. One needs to understand how they are generated (e.g. the sampling method used), how they may be interpreted (i.e.. avoiding the logical pitfalls described by Darrell Huff in his 1954 book ** How to Lie With Statistics**), and what those numbers actually explain (e.g. the meaning of the R-squared measure in a regression analysis). Business similarly needs to understand the context of value, the limitations of value metrics / measures, and the caveats of monetizing value (see previous article).

Just as the field of mathematics has different subareas, so does the field of business management. Strategy, Marketing and Operations are different branches of management. They use different academic disciplines — economics, finance, decision/cognitive science, marketing, psychology, engineering, quality/lean thinking, supply chain management, etc. — to solve their respective problems. Each discipline, however, is insufficient alone to solve complex problems like managing value across an enterprise or a company’s value chain (see previous article). Yet business integration across disciplines / functions is sorely lacking.

The essence of business is value. A company’s value stream is optimized when value flows to the ultimate customer (see previous article). When flows are obstructed / blocked / impeded, value gaps result. These value gaps are black holes devouring business value. What causes value gaps? What powers value black holes? They are formed when value is mistranslated across the organization. They grow when activities / assets / people / efforts are misaligned across the value chain.

**Value Mistranslation: An academic relic perpetuated by business functions**

The field of management theory and most business school faculty departments still reflect historic academic disciplinary silos established decades ago. Business school students follow discipline-based programs and graduate with functional degrees: MBAs in Finance (like me), Marketing, Operations, etc. These graduates are then hired to work in company departments corresponding to those degrees: Finance, Accounting, Logistics, Sales, etc. Professionals generally progress via discrete career paths to assume functionally distinct leadership roles: CIO, CFO, CMO, COO, etc. Some even attain the coveted role of CEO, after having spent much – if not all– of their careers in a single discipline.

Academics understandably specialize in particular areas of business. The associated problems / issues they confront “frame” the research questions they ask as well as the theories they develop / use. A distinct terminology and language is often developed by each department to describe / communicate its respective subject area. As a consequence, these languages / theories describe value (the essence of business) using autonomous definitions of value. Seemingly incompatible value perspectives result. A Tower of Babel generally ensues, since definitions / terminologies / theories don’t mesh / “fit together” in both academe and the business world. Since faculty and professionals are functionally educated / trained, they are often unaware of other perspectives and/or do not understand those alternative value viewpoints. Instead, increased specialization reinforces “value silos”.

**Value Misalignment: A Cartesian relic perpetuated by disconnected business practice**

Many business schools were founded in an earlier age of mass industrialization. Company executives generally used top-down, command-and-control approaches to management. They also adopted prevailing Cartesian logic: think about a problem, break it up into its constituent parts, solve each independently, and implement solutions (with appropriate management controls). It was hierarchical, top-down, linear, and compartmentalized. As corporations grew into conglomerates, specialized functions and departments assumed these roles and followed these practices. It was an effective approach, relevant and appropriate for stable domestic economies with few external shocks.

Such a business environment no longer exists. Trade liberalization and deregulation opened domestic economies, global trade provided new customers but also new competitors, computers increased transaction processing and enabled the automation of business activities (sometimes making workers redundant), and the Internet sped information flows around the clock and globe. Global competition also changed the underlying economics of industries as new entrants competed for scarce resources (sometimes increasing costs as demand outstripped supply) and for customers (often reducing margins by commoditizing offerings and/or reducing a company’s market share). These factors were inter-related and inter-linked producing dynamic feedback loops that furthered business complexity.

A linear, top-down, unidirectional management approach is inappropriate to, inefficient for, and ineffective in such market conditions. Sometimes companies and entire sectors do not adapt quickly enough, leading to corporate reorganizations / takeovers / bankruptcies and / or restructuring of entire economic sectors. In 1995, Adrian Zlywotsky predicted the economic ** Value Migration** that would — and did — ensue. A dynamic, iterative and systemic way of thinking is needed today in order to manage companies in the face of such complexity. See previous article.

*Principia Valorem*** – Synthesizing value theory for a changing economy**

Generally “ways of thinking” develop over time, building on preceding ideas. Entire disciplines form via the accretion of intellectual concepts over years. Take mathematics, for example. The Pythagoreans were an order of Greek philosophers who held that number theory and geometry were fundamental to understanding the universe. The Pythagorean Theory takes its name from the group and its founder, Pythagoras (circa 540 BCE). Euclid (circa 300 BCE) wrote thirteen books, complied into his treatise ** Elements**, describing solid geometry, elementary number theory and the concept of lines. Archimedes (circa 250 BCE) surpassed Euclid; he “developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus” (Wikipedia entry for Mathematics). Algebra comes from the title of a book (circa 820 CE) by the Persian astronomer and mathematician Muhammad ibn Musa al-Khwarizmi who outlined the rules for solving quadratic equations. His book was translated into Latin in 1145 CE and used by European students for centuries.

Periodically, revolutionary developments in mathematics occur. For example, Isaac Newton and Gottfried Wilhelm Leibniz simultaneously developed the field of Calculus in the sixteenth century. Newton focused on Differential Calculus (instantaneous rates of change and the slope of curves at a given point); Leibniz focused on Integral Calculus (areas under or between curves for a given interval). In the early twentieth century, Alfred Whitehead and Bertrand Russell published their three-volume ** Principia Mathematica** on the foundations of mathematics. It advanced the field of symbolic logic used by mathematics, philosophy and engineering. Modern algebraic geometry, developed later in the twentieth century, uses abstract

*algebraic*techniques to solve

*geometrical*problems. In 1967, Robert Langlands outlined what has become known as the Langlands program, a Rosetta Stone-like method for

*translating*between different fields of mathematics.

The Theory of Value also has a long history. See previous article where I visualize the theory’s development by economics writers over the centuries. Other academic disciplines also contributed to value theory: marketing, finance, accounting, lean / quality, etc. Unfortunately, business management lacks a comparable Rosetta Stone that enables academics and researchers to translate between different theories of value. A map is needed to navigate within and across these areas. See previous article where I discuss value theory mind maps. Business, in other words, needs a ** Principia Valorem** to synthesize the many alternative definitions / theories of value it has developed and uses.

**Integrated Value Management – A synthesis of management / business value theory**

In an earlier article, I noted that value management is multi-dimensional. Managing value is like solving a Rubik’s Cube. To solve a Rubik’s Cube, one needs to: (a) sense how “scrambled” the puzzle currently is, (b) understand how the cube can be conceptually solved (unscrambled), (c) apply the relevant solution (the appropriate moves), and (d) focus intently until the desired result emerges (the cube is unscrambled / the puzzle is solved).

A Rubik’s Cube is three-dimensional. Any approach to value also needs to be three dimensional, based on the scope of the company’s “value puzzle”, the desired degree of “value knowledge”, and the intended “value objective.” A Rubik’s Cube has multiple colors. In Integrated Value Management: “Mind the flow!” I noted that knowledge is the product of multiple types of “smarts”: conceptual / theoretical intelligence, encoded intelligence, experiential intelligence, and socio-emotional intelligence.

To truly understand and manage business value on these multiple levels, I developed the Integrated Value Process (IVP) framework in ** An Empirical Framework for Evaluating, Implementing and Managing a Value-based Supply Chain Strategy** (my PhD thesis accepted by the University of Bath School of Management — ProQuest publication number 3121355). IVP incorporates the four types of intelligence. It consists of (1) a conceptual framework explaining the intra- / inter-firm value management process, (2) a methodology to ‘decode’ value gaps present in that process, (3) five value ‘first principles’ underlying value chain activities, and (4) a ‘meta’ definition of value to communicate effectively across functions within the firm and with the firm’s customers / suppliers.

IVP promotes an integrative and holistic approach to value management. A “new way of thinking” about value — one that is interdisciplinary, multifunctional, and systems-based. The framework meets rigorous academic standards: it is conceptually sound (based on existing theory), empirically tested (supported by quantitative and qualitative evidence from research into US and UK value chains), and practice-relevant (appropriate and contingent to specific company situations). Its power lies in its ability to synthesize and address value thinking and business management across multiple domains and functions.

To solve complex mathematical problems, one uses multiple branches of mathematics. To use those different branches properly, however, one needs to understand how they fit together. The same is true for solving / managing complex value problems. One needs to understand how different but complementary value theories and definitions – from strategy, marketing and operations – are interlinked and interrelated. Managing value in business requires synthesis and integration. The activities, assets, people and initiatives of a company and its value chain will be sub-optimized without such an integrated approach. Use the Integrated Value Process (IVP) framework as the basis for your Integrated Value Management (IVM) program!

Andrew Swan, PhD is a multidisciplinary and cross-functional integrator of strategy, processes, and information technology. His focus and expertise center on helping executives increase value creation and optimize value flows in business. Dr. Swan holds four degrees in Management, Accounting & Finance, Information & Knowledge Strategy, and Computer Science from the University of Chicago Booth School of Business, the University of Bath School of Management, and Columbia University.

He frequently publishes articles on value chains, value streams / flows, and Integrative Value Management on his website __www.andrewjswan.com__. Dr. Swan created the Integrated Value Process (IVP) Framework to help companies optimize the flow of goods & services, funds, and information across their respective value chains for multiple stakeholders. He can be reached at andrew.swan@columbia.edu or at +1.773.633.7186. He lives in Chicago.

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