Nobel Prize in Mathematics

During this week, the 2019 Nobel Prize winners are announced. We can be sure that nobody will win the Nobel Prize for mathematics. The reason is simple. There is no Nobel Prize for Mathematics.

There are many urban legends regarding this. Most of them relate to an alleged love affair that Ms. Nobel had with a prominent mathematician. These stories conclude that Alfred Nobel did not want to award a prize for mathematics, since his wife’s lover is a leading candidate to win the prize. The most famous of this stories relates Ms. Nobel to the French mathematician Augustine Cauchy. Nice story, but Alfred Nobel was not married.

There is no Nobel Prize for Mathematics, but the Nobel Prize was awarded to mathematicians many times. Some of the most prominent winners were mathematicians John Nash, Robert Aumann and Kenneth Arrow, who all won the Nobel Prize of Economics. However, some will argue that the Nobel Prize in Economics is not a real Nobel Prize but a Nobel Prize. Oh well.

In addition, many mathematicians won the Nobel Prize in Physics, because in fact one cannot engage in high-level physics without proper mathematical education, and engaging in theoretical physics for themselves need to develop innovative mathematical tools.

My research has shown that four mathematicians have won Nobel Prizes that are not in Economics or Physics. Two won the Literature Prize, and two others won the Chemistry Prize. In this post I will review them and their work.

Four mathematicians who won the Nobel Prize. From left to right: Jose Echegaray (Literature, 1904), Bertrand Russell (Literature, 1950), Herbert Hauptman (Chemistry, 1985), John Pople (Chemistry, 1998).

The first mathematician to win the Nobel Prize was the Spanish Jose Echegaray. Echegaray was born in Madrid in 1832. He demonstrated his mathematical talent at a very young age, and was appointed professor of mathematics at the University of Madrid at the age of 21. In addition to his work in mathematics, he devoted his time to research in economics and worked to promote Spain’s international trade. With the abolition of the Spanish monarchy in the revolution of 1868, he retired from his academic position and was appointed Minister of Finance and Education of the Spanish Government. With the restoration of the monarchy in 1874, he retired from political life and began a new career as a writer, producing a series of successful satirical plays presented throughout Europe at the end of the 19th century. These plays earned him the Nobel Prize for Literature, awarded to him in 1904. Had Echegaray’s mathematical skills been useful to him in his literary career? Maybe. Literature scholars praise the meticulous structure of his plays. More likely, he was a very talented man who succeeded in everything he has done.

Another mathematician won the Nobel Prize for Literature 46 years later. The prize was awarded to Bertrand Russell in 1950. The prize committee noted it was awarded to him for his writings, which are “a victory for human ideals and freedom of thought”. Among these writings are the Foundations of Geometry (1897), A Critical Review of Leibniz’s Philosophy (1900), The Foundations of Mathematics — the monumental work he wrote with Whitehead between 1910 and 1913, and Introduction to Mathematical Philosophy (1919). All these books dealt with logic, along with his many other writings in many other fields. Bertrand Russell undoubtedly won the Nobel Prize for his mathematical work.

In 1985 another mathematician met with the King of Sweden. Herbert A. Hauptman , a mathematician who worked at the Institute for Medical Research in Buffalo, New York, shared the Nobel Prize with his fellow chemist Jerome Karl. Hauptman developed an algorithm that combined geometric and probabilistic methods to determine the molecular structure of materials using x-rays. This method, when applied in the 1980s by a computer, shortened the amount of time needed to determine the molecular structure of simple biological molecules from two years to two days, making it possible to determine the three-dimensional molecular structure of vitamins, hormones and antibiotic materials easily, to be used in the development of new drugs.

In 1998 another mathematician won the Nobel Prize in Chemistry: John A. Pople . He won the Nobel Prize for the development of new computational methods in the field of quantum chemistry. Pople sought and found methods for solving Schrodinger equations, the fundamental equations of quantum theory. These equations were previously considered insoluble, except for a few simple special cases. The software he developed for the implementation of his methods bears the name “Gaussian”, and is now used as the basic work tool of any chemist.

A brief history of clinical trials

The earliest report of a clinical trial is probably provided in the Book of Daniel. Daniel and a group of other Jewish people who stayed at the palace of the king of Babylon, did not want to eat the king’s non-Kosher food and preferred a vegetarian diet. To show that vegetarian and Kosher diet is healthier, Daniel suggested to conduct an experiment. There were two “treatment group” in this trial. One group ate the royal Babylonian food, the other kept the vegetarian diet. The health of the groups was compared after a follow-up period of 10 days. The conclusion was that the vegetarian diet is healthier.

The first modern clinical trial is James Lind’s scurvy trial, which many consider to be the starting point of modern medicine. This is the first documented controlled clinical trial (if you ignore Daniel’s trial). Lind conducted an experiment to test possible treatments for scurvy, the leading cause of death among sailors by the end of the 18th century. In a relatively brief voyage in the Mediterranean in 1749, Linde divided the 12 sailors who fell sick during the voyage to six equal groups. They were all hosted in the same place on the ship and were given the same menu, which was distinguished only by the experimental treatment given to them. The treatments were: drinking a liter of cider a day, drinking 25 drops of sulfuric acid three times a day, drinking two tablespoons of vinegar three times a day, drinking half a liter of seawater a day, an ointment made of garlic, mustard, and radish, or eating two oranges and lemon a day. The citrus patients had recovered completely, and the condition of cider patients improved slightly. The comparison between the groups allowed Lind to evaluate the efficacy of each treatment in relation to other therapeutic alternatives.

The next milestone is William Watson’s trial of treatments to reduce the risk of smallpox. Already in the 11th century it was known that anyone who had this disease and survived would not get sick again. As a result, a practice of immunization of the disease by “mild infection” of healthy people was developed. However, among the doctors there were disagreements about optimal adhesion and treatment for infection. Watson conducted a series of three clinical trials at London Children’s Hospital in 1767. His methodology was similar to that of Lind: The children participating in each trial were divided into groups, and in each group, controlled infection was performed using a bladder from an early stage of the disease. Each group was given a different adjuvant treatment that was supposed to reduce the risk of infection. Watson’s experiments had a number of innovations compared to Lind’s experiment. Watson ensured that in each treatment group there was an equal number of boys and girls to avoid possible bias in case the response to treatment was different between the genders. In addition, one group in each trial did not receive supplementary treatment but served as a control group. Most importantly, Watson was the first to report a quantitative measurement of results. The measure of success of treatment was the number of smallpox that occurred in each child participating in the trial. He also performed a basic statistical analysis and published the average number of blisters per child in each group. Watson concluded that conventional treatments to reduce risk, including mercury, various plants and laxatives, were ineffective.

The next significant milestone is the milk experiment in the Lancashire county of Scotland in the early 20th century. The purpose of the trials was to determine whether daily milk intake improves the growth of children compared to children who did not drink milk on a daily basis, and to check whether there is a difference in growth rates between children fed fresh milk and those fed in pasteurized milk. The experiment, conducted in 1930, was large-scale and included a total of about 20,000 children aged 6–12, who studied in 67 schools. About 5,000 were fed in fresh milk, about 5,000 in pasteurized milk, and approximately 10,000 children were assigned to the control group. The height and weight of the children were measured at the beginning of the experiment (February 1930) and at the end (June 1930). The conclusion was that a daily diet of milk improves the growth of children, and that there is no significant difference between fresh milk and pasteurized milk. The researchers also concluded that children’s age had no effect on the effect of growth rate.

This experiment entered my list because of the criticism leveled at it. The critics included Fisher and Bartlett, but the most comprehensive criticism was cast by William Sealy Gosset, also known as “Student”. In an article published in Biometrika, Gosset actually set rules that were necessary to ensure the validity of a clinical trial. First, he noted that in each school the children were treated with fresh milk or pasteurized milk, but the two groups were not represented in any school. As a result, it is not possible to directly compare fresh and pasteurized milk, due to differences between the different schools. He also noted that the treatments were assigned by the teachers in each class and not randomly. As a result, students in the control group were larger in their body size than students in the treatment groups. Thirdly he notes that although the measurements were conducted in February and June, the weight measurements did not consider the weights of the children cloths. Winter clothes are heavier than spring / summer clothes, and the weight difference between clothes offset the real weight differences. The researchers assumed that the difference in the weight of the clothes would be similar among the groups, but Gosset argued that the bias in the distribution of students to economically affected groups — children from affluent families were usually included in the control groups — meant that the weight of the control group’s winter clothing would be higher.

Gosset concluded that the results did not support the conclusion that there is no difference between a diet with fresh milk and a pasteurized milk diet, and claimed that it is impossible to conclude that there is no connection between age and the change in growth rate. He also mentions the analysis of Fisher and Bartlett that showed that fresh milk has an advantage over pasteurized milk as to the rate of growth.

Following his criticism, Gosset made a number of recommendations, including a proposal to conduct the experiment in a group of twins, one of whom will be fed milk and the other will serve as a control (or one of them will be fed in fresh milk and the other in pasteurized milk to compare the two types of milk). I think that such planning is not accepted ethically today. A more practical recommendation is to re-analyze the data collected to try to overcome the bias created in the non-random allocation to treatment and control groups. His ultimate recommendation was to re-conduct the experiment, this time using randomization, considering bias due to the weight of the clothes worn by each student, and planning the experiment so that each school has representation for the three treatment groups.

The main recommendation of Gosset, to ensure random allocation of patients to groups, was not immediately accepted, as this idea was perceived by some of the scientific community as “unethical”. It should be noted that the principle of randomization was only presented by Fisher in 1923, and there was still insufficient recognition of its importance.

The first clinical trial with random assignment to a treatment and control groups was conducted only in 1947, and is the fourth in my list. This is an experiment to test the efficacy of streptomycin antibiotics to treat pneumonia. Due to the short supply of antibiotics, there was no choice but to decide by “lottery” between the patients who will receive antibiotic treatment and who will not, and thus the planning of the experiment overcame the ethical barrier. However, the experiment was not double blind, and placebo was not used.

It should be noted that there has already been a precedent for a double blind trial: the first clinical trial using the double-blind method was conducted in 1943 to test the efficacy of penicillin as a treatment for common cold. Patients did not know whether they were treated with penicillin, or whether they were treated with placebo. The doctors who treated the patients did not know what treatment each patient received. Such a design prevents bias that may result from doctors’ prior judgment about the efficacy of the treatment, and in fact forces them to give an objective opinion about the patient’s medical condition. However, this trial did not randomize patients for treatment or control.

The debate regarding the importance of the principles outlined by Gosset and Fisher was finally decided in the trial to test the efficacy of Salk’s vaccine against polio virus, carried out in 1954. In fact, two trials were conducted. The main trial, led by Paul Meier, was a double-blind randomized trial, showing a 70% reduction in Polio-related paralysis in the treatment group compared to the control group. The size of the large sample (about 400,000 children aged 6–8) helped to establish external validity of the results. At the same time, another trial was conducted, in which the allocation of treatment (vaccination or placebo) was not random. 725,000 first and third graders who participated in the experiment served as a control group, to which 125,000 second grade children whose parents refused the vaccine were added. Their data were compared with the data of 225,000 second graders whose parents agreed to vaccinate them. A total of more than one million students participated in the experiment, almost three times the size of Meier’s trial. However, this trial results showed a decrease of only 44% in polio-related paralysis. Later analysis found that the effect was reduced due to bias related to the socioeconomic status of the treatment group. Many children in this group belonged to more affluent families, and in this population stratum polio incidence was higher because the proportion of children vaccinated naturally (the polio was mild and recovered without documentation) was lower due to the higher level of sanitation in their environment. The polio trails established the fact that the most important feature of a clinical trial is the randomization , and that only a random and double-blind allocation ensures the internal validity of the experiment.

References

• Boylston, AW (2002). Clinical investigation of smallpox in 1767.New England Journal of Medicine, 346 (17), 1326–1328.
• Leighton G, McKinlay P (1930). Milk consumption and the growth of school-children. Department of Health for Scotland, Edinburgh and London: HM Stationery Office.
• Student (1931). The Lanarkshire Milk Experiment. Biometrika 23: 398–406
• Fisher RA, Bartlett S (1931). Pasteurised and raw milk. Nature 127: 591–592.
• Medical Research Council Streptomycin in Tuberculosis Trials Committee. (1948).
• Streptomycin treatment for pulmonary tuberculosis. BMJ, 2 , 769–82.
• Hart, PDA (1999). A change in scientific approach: from alternation to randomized allocation in clinical trials in the 1940s.BMJ, 319 (7209), 572–573.
• Meier, Paul. “Polio trial: an early efficient clinical trial.” Statistics in medicine 9.1–2 (1990): 13–16.