### The Nobel Prize delay

The 2013 Nobel Prize in Physics was awarded to Peter Higgs and François Englert for their descriptions of the mass-bestowing Higgs mechanism. Although the corresponding Higgs boson was discovered at CERN in 2012, the original theoretical works were published in 1964. Thus, confirmation of the prediction took half a century.

Long time lags between discovery and recognition are not unusual. In fact, such lags have been significantly increasing over the years, as we shall demonstrate with our analysis of publication and biographical data.

Let Δ^{D→N} be the time between the discovery and the award of a Nobel Prize. We model the variation of Δ^{D→N} with time *t* as an exponential:

Δ^{D→N} = *c _{α}* exp(

*αt*)

where *α* is the rate of increase in Δ^{D→N} and *c _{α}* is a proportionality constant.

Figure 1 shows that our exponential model tracks the data on Nobel time delays. It also shows that Δ^{D→N} is increasing for all three Nobel science fields.

Figure 1. Time difference between the discovery and the awarding of the Nobel Prize, plotted against the year when the award was received. Each plot shows the raw data, the five-year average, and the exponential fit with its confidence interval. The lag is increasing for the three fields, with rates of 0.012 ± 0.002, 0.008 ± 0.002 and 0.008 ± 0.001 for physics, chemistry, and physiology or medicine, respectively.

To validate our regression analysis, we checked the residuals, as measured by the difference between the observed and the predicted values. The linear regression model shows nonrandom patterns in the residual plots. A piece-wise linear regression shows that the slopes of the curves consistently increase with time for all the fields.

We conclude that the observed increase is faster than linear.

Applying our model, we find that the rate of increase in Δ^{D→N} is the highest for Nobels in physics, followed by chemistry, and then physiology or medicine.

To further investigate the growing time lag between discovery and prize, we consider the frequency of awards within *T* years of discovery (20 years in figure 2). Using a logistic regression model, we measure whether the frequency is decreasing with time and in what way.

Figure 2. The frequency of prizes awarded 20 years or more years after the discovery is increasing for all disciplines. The growth is fastest for physics and slowest for physiology or medicine.

Simple logistic regression is analogous to linear regression, except that the dependent variable is nominal, not a measurement. In our case, the variable is "prize within 20 years of discovery" or "prize after 20 years of discovery." The goal is to see whether the probability of getting a particular value of the nominal variable (a binary one in our case) is associated with the measurement variable (time).

We estimate first-degree logistic polynomial regressions for all the fields and show the predicted values and 95% confidence intervals. The conditional probability of the discovery being awarded within *T *years is given by

Pr(Δ^{D→N} < *T*|*t*) = 1/{1 + exp[−(*μ* + *νt*)]},

where the parameters *μ* and *ν* are estimated using the maximum likelihood method.

After 1985 about 15% of physics, 18% of chemistry, and 9% of medicine prizes were awarded within 10 years of the corresponding discoveries. By contrast, before 1940 about 61% of physics, 48% of chemistry, and 45% of medicine prizes were awarded within 10 years of the corresponding discoveries.

What's more, after 1985 about 60% of physics, 52% of chemistry, and 49% of medicine prizes were awarded following a post-discovery delay of more than 20 years. By contrast, before 1940 only about 11% of physics, 15% of chemistry, and 24% of medicine prizes were awarded after a delay of more than 20 years.

In all fields, the frequency of the prize being awarded more than 20 years after discovery is increasing. The rate of increase in the frequency of receiving the award after 20 or more years is fastest for physics and slowest for medicine.

As a result of the increasing time to recognize a Nobel discovery, the age at which laureates receive the award is increasing. This is also determined by the increasing age at which major discoveries are made.

We consider how the age at which scientists are awarded the Nobel prize, *a*^{N}, is changing with time. An exponential increase is represented by

*a*^{N}(*t*) = exp(*γt*),

where *γ* is the rate of increase of the age and *c*_{γ} is a proportionality constant.

Figure 3 shows that *a*^{N} is increasing for the three science fields. We also used the regression model to project the age of the laureates at the time of the award until the end of the 21st century. The predicted values and indicated 95% confidence intervals are given by the exponential regression model.

Figure 3. Change in the age of the recipient at the time the Nobel Prize is awarded. For all fields there is an increasing trend. For physics and chemistry the rate of increase is similar (0.0040 ± 0.0005 and 0.0034 ± 0.0004), whereas for physiology or medicine the increase is much smaller (0.0020 ± 0.0005). The progression of the average life expectancy in the US is shown in gray.

The figure also shows the projected life expectancies of men and women combined across the 21st century. We used US data as a proxy for the global life expectancy of future winners, because US citizens have been awarded the majority of Nobel prizes.

We found that by the end of this century, potential laureates in physics and chemistry would most likely die before they could receive a Nobel Prize.

**Is fundamental research stalling?**

What is the reason for the increasing delay between discovery and recognition? One should first take into account changes in society, which may affect the awarding of Nobel prizes. The increasing number of scientists, their increasing life expectancy, changing research and career policies, and so on must all play a role.

Yet it is reasonable to assume that those factors affect all disciplines to a comparable extent; they also cannot explain the remaining differences, such as the ones we found between physics and medicine. It is possible, therefore, that frequency of groundbreaking discoveries in physics is decreasing.

Fundamental physics has indeed undergone major changes over the past century; it has become a highly collaborative endeavor requiring a sustained effort by large teams over many years. However, that trend might just be another facet of an underlying problem: an increasing difficulty in achieving progress.

An alternative interpretation of the difference in Nobel Prize awards between physics and medicine could be its converse: Because no more than two discoveries in any one field can be awarded the prize at the same time, it could be that the number of important discoveries is in fact increasing, that in order not to lose worthy winners, the Royal Swedish Academy of Sciences is forced to dig deeper and deeper into the past.

However, we tend to reject that interpretation. First, on the average, recognition is taking longer. But even in modern times some major discoveries—such as graphene and the accelerating expansion of the universe—have been quickly recognized and awarded.

Second, if the frequency of breakthroughs were stable or even increasing in time, the fluctuations with respect to the average importance of each awarded discovery would likewise increase in time. Thus, one would expect in recent times a comparable or higher frequency of exceptional advances, such as high-temperature superconductivity. But that increase does not seem to have occurred. Recognition of such ultra-important discoveries is not obviously being held back at the expense of less important discoveries of the past.

**Data**

We collected data on dates of birth of recipients, the years of Nobel prize awards, and years of publication for the prize-winning work. As a primary data source we used the Nobel Foundation's website. In the cases where the information was not sufficient to accurately identify year of prize winning publication, we used Google Scholar to consult all the publications of the Nobel Laureates. We then determined the year of the most relevant publication related to the topic of the Nobel Prize award. We also consulted the biographies of the laureates and other resources, such as Caltech's Nobel laureates webpage and the American Physical Society's Letters from the Past—a *PRL* Retrospective. We obtained our life expectancy estimates from *World Population Prospects: The 2012 Revision*, published by the United Nations Department of Economic and Social Affairs.

*Francesco Becattini works at the University of Florence and at the National Institute of Nuclear Physics, both in Florence, Italy. Arnab Chatterjee, Santo Fortunato, Raj Kumar Pan, and Pietro Della Briotta Parolo all work at Aalto University in Finland. Marija Mitrovic works at the University of Belgrade in Serbia.*

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