The Mathematics of the Ph.D. Glut

I recently had a conversation at a get-together with someone whose sister had just started a Ph.D. program in biology. I discussed some of the unpleasant realities of graduate school today and referenced Brian Vastag’s July 7, 2012 article in the Washington Post “U.S. pushes for more scientists, but the jobs aren’t there”.

I have touched briefly on the Ph.D. glut in two previous articles — The Government Did Too Invent the Internet and Top Secret Rosies: The Female Computers of World War II Video Review. Since many people including prospective graduate students still don’t realize there is a Ph.D. glut, this post gives more details on the Ph.D. glut as well as more references in the appendices below.

The Ph.D. glut is certainly a bad thing for graduate students and others who want to become scientists or mathematicians. There is also considerable and growing evidence that, far from accelerating the rate of scientific and technological progress, it has slowed the rate of progress and with it the growth of the US and global economy.

Yes, There is a Ph.D. Glut

Brian Vastag’s article represents one of the few times the Ph.D. glut and dismal career prospects in scientific research has been reported in a major media outlet like the Washington Post. In general, the major “mainstream” media reports on explicitly claimed or implied shortages of scientists, Ph.D., and all manner of STEM (Science, Technology, Engineering, and Math) workers, even though a Ph.D. glut has been the reality in most fields including mathematics and physics since about 1970 (forty-two years ago!). Even more remarkably, extensive, well-documented, verifiable, and steadily growing information on the Ph.D. glut has been readily available on the Internet since the mid 1990s (fifteen years ago!). Nonetheless both reporters and op-ed piece writers at major media outlets seem unable to use Google or other search engines to find this information!

Vastag’s article focused primarily on the current situation in biology and medicine. However, a Ph.D. glut has been the reality in almost all scientific and mathematical fields since about 1970. From time to time, the situation gets especially bad and attracts some comment. This happened in physics in 1970 and in 1992/1993 (I received my Ph.D. in Physics in 1993). The National Institutes of Health’s budget was doubled in the 1990s resulting in the recruitment of huge numbers of graduate students who now form an especially large cohort of Ph.D.’s unable to find jobs. In addition the so-called fiscal stimulus in 2009 included several billion dollars for the NIH. Both of these developments translated into more graduate students and more post-docs, but few, if any, permanent positions. Thus, biology and medicine suffers from an especially large glut at present. Smaller but still substantial Ph.D. gluts exist in virtually every STEM field.

It is worth considering some basic arithmetic. A typical professor has at least two graduate students at any time, sometimes many more. A Ph.D. programs in the United States usually lasts 5-7 years. A professor will take on and “advise” students from about age 30 as a starting assistant professor to retirement or death (say 65). This means a typical professor produces at least ten Ph.D.’s during his or her academic career in his or her academic specialty. If all the students pursue an academic career, certainly the ambition of many, this means an additional nine (9) new positions must be created over 35 years on top of the professor’s own position. Even with a fifty percent drop out rate, at least four or five new positions must be created to absorb the new Ph.D.’s. Of course, nothing of the kind has been the case for over forty years. This requires an exponential increase in the funding for an academic field relative to the size of the economy as a whole, something that occurred only briefly during and after World War II and in the early post-Sputnik days of the Cold War.

Over thirty-five years, increasing the number of faculty members in a scientific field by a factor of ten (10) corresponds to a 6.8 percent annual growth rate. A five-fold increase corresponds to a 4.7 percent annual growth rate. The World Bank gives the annual growth rates of the United States Gross Domestic Product (GDP) for the years 2007-2011 as 1.9 percent (2007), -0.4 percent (2008), -3.5 percent (2009), 3.0 percent (2010) and 1.7 percent (2011). It is rare for a GDP to grow by more than five percent in one year, let alone continuously for 35 years.

The two figures below show the United States Real Gross Domestic Product (GDP) data from 1947 to 2011 from the St. Louis Federal Reserve which is one of the major sources of official economics statistics in the United States. One can easily see that the annual real GDP growth rate in the United States has rarely exceeded the 6.8% rate needed to absorb the Ph.D. production. In fact, the average GDP growth (smoothed red curve) is substantially lower. Note also that the real (inflation-adjusted) growth rate of the US economy has been declining for decades.

The raw US real GDP data from the St. Louis Federal Reserve and the GNU Octave script used to generate the plots is provided below in Appendices III and IV.

Figure 1

United States Real GDP

United States Real GDP

Figure 2

US GDP Growth Versus PhD Production

US GDP Growth Versus PhD Production

Note that for illustrative purposes I am actually understating the size of the problem. First, I assumed seven years to a Ph.D. whereas the range is typically five to seven years. More importantly, I ignored that if each student becomes a professor and takes on graduate students as well, creating even more Ph.D.’s, the growth rate will be even greater than ten times in thirty-five years! This is an exponential process like the exponential overpopulation of rabbits without a predator.

As I can attest from personal experience, STEM students in the United States, despite being mathematically inclined, often do not perform the arithmetic above and think through what it means. This does not just happen. As mentioned, the major “mainstream” media in the United States has been filled for over forty years with repeated false claims of a shortage of scientists and mathematicians. Most science and mathematics education is very positive and never mentions the Ph.D. gluts. Similarly, career placement offices at many universities and colleges, while providing information on applying to graduate school, rarely mention the Ph.D. gluts in most STEM fields.

Political leaders in both major political parties such as President George W. Bush (Republican) and President Barack Obama (Democrat) frequently promote STEM shortage claims and may sincerely believe them. Both business leaders and senior scientists frequently claim or imply a shortage of Ph.D.’s and/or scientists (see the Wall Street Journal editorial “Our Ph.D. Deficit” by Lockheed CEO Norman Augustine and Nobel Prize-winning physicist Burton Richter below, for example).

Ph.D.’s and High Tech Jobs

It is important to understand a subtlety of STEM worker shortage claims in discussing both the actual Ph.D. glut and the Ph.D. shortage claims. Most Ph.D.’s receive specific training in their specialty. In almost all academic disciplines, it is factually false, demonstrably false that there is a shortage of Ph.D.s trained for each discipline.

When high tech companies and their lobbyists claim there is a shortage of skilled high technology workers, they usually use general language such as “there is a shortage of engineers,” “there is a shortage of programmers,” or “there is a shortage of technology talent.” However, when pressed about seemingly highly qualified, often older workers who cannot find jobs, they refer to both extensive and very narrowly defined specific skills that they claim they must have. Older often means over forty or even over thirty-five. As in the case of the forty year old husband of Jennifer Wedel, who confronted President Obama about the shortage claims, these older workers who encounter problems finding work despite seemingly strong qualifications are often not very old.

One can always assert a shortage of workers by narrowly specifying the skills required. Consider digging a ditch. Suppose I demand that prospective ditch diggers must: have at least three years paid professional experience digging ditches using the Big Box Mart Super Squabo 2.0 shovel which my company uses. A Black and Decker shovel won’t do. Not just any ditch digging, it must be three years paid professional experience digging ditches for gas pipelines in a medium sized city with a population from 50-200,000 people. Ditches for sewage lines won’t do. Digging ditches for gas pipelines in New York City won’t do because New York has a population over 200,000. And so on. Even though ditch diggers are surely not in short supply, I can find a shortage by narrowing my standards for ditch diggers. This sort of narrowing of standards is surely a symptom of either gross irrationality or an actual surplus of qualified applicants that makes it possible to impose such narrow requirements.

Of course, most people know or believe they know enough about ditch digging and other low status, frequently manual jobs that this sort of argument would provoke only laughter and disbelief. Hence similar worker shortage claims about low status, generally lower paying jobs in the United States usually involve claims that spoiled Americans are unwilling to do such hard manual labor. It is harder to evaluate the plausibility of such ultra-narrow job specifications where technical jobs such as software engineering are concerned.

A recent article by Wharton business school professor Peter Cappelli Why Companies Aren’t Getting the Employees They Need: The conventional wisdom is that our education system is failing our economy. But our companies deserve a lot of the blame themselves. discusses this excessive focus on specific skills.

The alleged shortages of high technology workers such as software engineers are thus difficult to disprove due to the specific skills issue. But in the case of Ph.D.’s, a Ph.D. represents a certification that a Ph.D. holder is qualified and trained in their specialty. Thus, this excuse does not work for Ph.D.’s, whether biologists, physicists, or mathematicians, who cannot find work in their field. It is really factually untrue, not a matter of opinion, that there is a shortage of Ph.D.s either in general or in most specific fields such as biology, physics, or mathematics where shortages are often claimed or implied.

Where are the Fact Checkers?

It is striking that the Ph.D. shortage claims have been widely repeated for over forty years by most major media including the New York Times, the Wall Street Journal, and many other companies and organizations although these claims are demonstrably false and have been demonstrably false for over forty years. Extensive information on the falsity of these claims has been available on the Internet for about fifteen (15) years. Yet, so far, articles like Brian Vastag’s recent article in the Washington Post have been extremely rare.

Newspapers and similar organizations are supposed to have fact-checkers whose job is to verify facts. The Ph.D. glut is really a matter of fact, not opinion. It can be verified by a small amount of serious investigation. What happened to the fact checkers?


Yes, there is a Ph.D. glut. In fact, there has been a Ph.D. glut for over forty years, since about 1970. This is inherent to the structure of the current government funded system of scientific research. It is a matter of public policy. Sometimes the Ph.D. gluts get especially bad as in physics in 1970 and 1992/1993 and now in biology and medicine, but there has always been and are sizable Ph.D. gluts in almost all scientific disciplines since 1970.

The remarkable persistence of Ph.D. and scientist shortage claims in the major “mainstream” media should raise questions about the reliability and independence of the major media. This evident lack of basic fact-checking is not what one should expect of a “free press.”

Finally and most importantly, there is considerable evidence that the Ph.D. glut has not worked. Far from accelerating the rate of scientific and technological progress, it has contributed to a slowing rate of progress.

As can be seen in the Federal Reserve data on real GDP, the real annual growth rate of the United States economy has declined over the last forty years. This is a long term trend. This decline probably reflects the limited scientific and technical progress in most fields outside of computers and electronics, especially in power and propulsion technology, since 1970.

© 2012 John F. McGowan

About the Author

John F. McGowan, Ph.D. solves problems using mathematics and mathematical software, including developing video compression and speech recognition technologies. He has extensive experience developing software in C, C++, Visual Basic, Mathematica, MATLAB, and many other programming languages. He is probably best known for his AVI Overview, an Internet FAQ (Frequently Asked Questions) on the Microsoft AVI (Audio Video Interleave) file format. He has worked as a contractor at NASA Ames Research Center involved in the research and development of image and video processing algorithms and technology. He has published articles on the origin and evolution of life, the exploration of Mars (anticipating the discovery of methane on Mars), and cheap access to space. He has a Ph.D. in physics from the University of Illinois at Urbana-Champaign and a B.S. in physics from the California Institute of Technology (Caltech). He can be reached at [email protected].

Appendix I: Selected Internet Resources on the Ph.D. Glut

“U.S. pushes for more scientists, but the jobs aren’t there”

The disposable academic: Why doing a PhD is often a waste of time from The Economist, December 16, 2010

What Scientist Shortage? The Johnny-can’t-do-science myth damages US research by Beryl Lieff Benderly, Columbia Journalism Review, January/February 2012

We Don’t Need More Scientists—We Need Better Ones A chemist responds to Slate’s David Plotz’s claim that not enough students are going into science and engineering. by Derek Lowe in Slate, June 17, 2012

Scientist shortage? Maybe not by Greg Toppo and Dan Vergano, USA Today, July 9, 2009

How and Why Government, Universities, and Industry Create Domestic Labor Shortages of Scientists and High-Tech Workers
By Eric Weinstein

Toil, Trouble, and the Cold War Bubble: Physics and the Academy since World War II
MIT Science Historian David Kaiser Presentation at the Perimeter Institute

PhD’s Org’s Collection on Links and Resources on Scientist and Ph.D. Shortage Claims

Bridges to Independence: Fostering the Independence of New Investigators in Biomedical Research (National Research Council 2005)

Women in Science by Philip Greenspun

Appendix II: Selected Internet Examples of the Never Ending STEM Shortage Claims

Our Ph.D. Deficit (Op-Ed by Norman Augustine and Burton Richter, Wall Street Journal, May 4, 2005)

Rising Above the Gathering Storm: Energizing and Employing America for a Brighter Economic Future (2005)

Heading Off a Ph.D. Shortage. by John Vaughn and Robert Rosenzweig in Issues in Science and Technology, v7 n2 p66-73 Win 1990-91

EDUCATION; Shortage of Ph.D.’s Imminent, Report Says (January 24, 1990)


This is data downloaded from the St. Louis Federal Reserve at

1947    1793.3
1948    1868.2
1949    1838.7
1950    2084.4
1951    2192.2
1952    2305.3
1953    2314.6
1954    2379.1
1955    2535.5
1956    2582.1
1957    2589.1
1958    2654.3
1959    2782.8
1960    2800.2
1961    2975.3
1962    3097.9
1963    3262.2
1964    3429.0
1965    3720.8
1966    3881.2
1967    3977.6
1968    4174.7
1969    4259.6
1970    4253.0
1971    4442.5
1972    4750.5
1973    4948.8
1974    4850.2
1975    4973.3
1976    5187.1
1977    5446.1
1978    5811.3
1979    5884.5
1980    5878.4
1981    5950.0
1982    5866.0
1983    6320.2
1984    6671.6
1985    6950.0
1986    7147.3
1987    7451.7
1988    7727.4
1989    7937.9
1990    7982.0
1991    8062.2
1992    8409.8
1993    8636.4
1994    8995.5
1995    9176.4
1996    9584.3
1997   10000.3
1998   10498.6
1999   11004.8
2000   11325.0
2001   11370.0
2002   11590.6
2003   12038.6
2004   12387.2
2005   12735.6
2006   13038.4
2007   13326.0
2008   12883.5
2009   12873.1
2010   13181.2
2011   13441.0

Appendix IV: GNU Octave Script Used to Make Figures

This is the GNU Octave script used to process the US REAL GDP data from the St. Louis Federal Reserve and generate the figures in the article.

% script to compute annual growth rate of US REAL GDP
% (C) 2012  By John F. McGowan, Ph.D.
data = dlmread('us_real_gdp.txt');  % federal reserve data
year = data(:,1);
gdp = data(:,2);
h1 = plot(year, gdp);
set(h1, 'linewidth', 3);
delta = conv(gdp, [1 -1]);
growth = delta(1:end-1) ./ gdp(1:end);

[p, s] = polyfit(year(2:end), growth(2:end)*100, 3);
fit = polyval(p, year(2:end));

target = ones(size(fit))*6.8;  % need average growth rate of 6.8% to absorb new Ph.D.'s

h2 = plot(year(2:end), growth(2:end)*100, '+', year(2:end), fit, '-r', year(2:end), target, '-g');
set(h2, 'linewidth', 3);

disp('ALL DONE');


  1. Piltdown Proof August 11, 2012
    • Piltdown Proof August 11, 2012
      • Piltdown Proof August 11, 2012
  2. gappy August 11, 2012
    • jimbo jones November 27, 2012
  3. John F. McGowan August 11, 2012
  4. Benjamin Cummings August 12, 2012
  5. Clark August 13, 2012
  6. John F. McGowan August 13, 2012
  7. John Regehr August 13, 2012
    • John F. McGowan August 14, 2012
      • John Regehr August 20, 2012
        • John F. McGowan August 20, 2012
  8. Christian Marks August 18, 2012
    • Christian Marks August 19, 2012
      • John F. McGowan August 20, 2012
  9. John F. McGowan December 29, 2012
  10. John McGowan April 12, 2013

Leave a Reply