Making the most of world talent for science? The Nobel Prize and Fields Medal experience

Opportunities in science largely affect the accumulation of scientific knowledge and, therefore, technological change. However, there is little evidence of how much of people’s talent is actually wasted. Here we focus on scientists with the highest performance, the recipients of the Nobel Prize and Fields Medal. We found that the average age of scientists at the time of the breakthrough was higher for researchers from less developed countries. Moreover, individual opportunities in the world were extremely unequal by country of birth, gender significantly conditioned any participation in research, and the probability of becoming a top researcher more than doubled for individuals with parents belonging to the most favoured occupational categories. Thus, inequality of opportunity in science at the highest level was higher than in sports excellence (Olympic medals) and educational attainment. These findings would not be so negative if opportunities in science at the highest level had increased over time. Contrary to the expectations, our results show that opportunities in science, in contrast with humanities, have stagnated.

Negative grey relational model and measurement of the reverse incentive effect of fields medal

PurposeThe purpose of this paper is to construct some negative grey relational analysis models to measure the relationship between reverse sequences.Design/methodology/approachThe definition of reverse sequence has been given at first based on analysis of relative position and change trend of sequences. Then, several different negative grey relational analysis models, such as the negative grey similarity relational analysis model, the negative grey absolute relational analysis model, the negative grey relative relational analysis model, the negative grey comprehensive relational analysis model and the negative Deng’s grey relational analysis model have been put forward based on the corresponding common grey relational analysis models. The properties of the new models have been studied.FindingsThe negative grey relational analysis models proposed in this paper can solve the problem of relationship measurement of reverse sequences effectively. All the new negative grey relational degree satisfying the requirements of normalization and reversibility.Practical implicationsThe proposed negative grey relational analysis models can be used to measure the relationship between reverse sequences. As a living example, the reverse incentive effect of winning Fields Medal on the research output of winners is measured based on the research output data of the medalists and the contenders using the proposed negative grey relational analysis model.Originality/valueThe definition of reverse sequence and the negative grey similarity relational analysis model, the negative grey absolute relational analysis model, the negative grey relative relational analysis model, the negative grey comprehensive relational analysis model and the negative Deng’s grey relational analysis model are first proposed in this paper.

Elitism in mathematics and inequality

The Fields Medal, often referred as the Nobel Prize of mathematics, is awarded to no more than four mathematicians under the age of 40, every 4 years. In recent years, its conferral has come under scrutiny of math historians, for rewarding the existing elite rather than its original goal of elevating under-represented mathematicians. Prior studies of elitism focus on citational practices while a characterization of the structural forces that prevent access remain unclear. Here we show the flow of elite mathematicians between countries and lingo-ethnic identity, using network analysis and natural language processing on 240,000 mathematicians and their advisor–advisee relationships. We present quantitative evidence of how the Fields Medal helped integrate Japan after WWII, through analysis of the elite circle formed around Fields Medalists. We show increases in pluralism among major countries, though Arabic, African, and East Asian identities remain under-represented at the elite level. Our results demonstrate concerted efforts by academic committees, such as prize giving, can either reinforce the existing elite or reshape its definition. We anticipate our methodology of academic genealogical analysis can serve as a useful diagnostic for equity and systemic bias within academic fields.

Sir Michael Atiyah OM. 22 April 1929–11 January 2019

Michael Atiyah was the dominant figure in UK mathematics in the latter half of the twentieth century. He made outstanding contributions to geometry, topology, global analysis and, particularly over the last 30 years, to theoretical physics. Not only was he held in high esteem at a worldwide level, winning a Fields Medal in 1966, the Abel Prize in 2004 and innumerable other international awards, but his irrepressible energy and broad interests led him to take on many national roles too, including the presidency of the Royal Society, the mastership of Trinity College, Cambridge, and the founding directorship of the Isaac Newton Institute for Mathematical Sciences. His most notable mathematical achievement, with Isadore Singer, is the index theorem, which occupied him for over 20 years, generating results in topology, geometry and number theory using the analysis of elliptic differential operators. Then, in mid life, he learned that theoretical physicists also needed the theorem and this opened the door to an interaction between the two disciplines that he pursued energetically until the end of his life. It led him not only to mathematical results on the Yang--Mills equations that the physicists were seeking, but also to encouraging the importation of concepts from quantum field theory into pure mathematics.

Conclusion

This book offers a survey of mathematical topics. However, there is much more for you to explore. Catastrophe theory, the Chinese Remainder Theorem, combinatorics, and complex analysis. Equivalence relations, Euclid’s elements, and Euler’s formula. The Fields Medal and Four-color Theorem. Galois theory, the gambler’s fallacy, geodesic domes, the geometry of spacetime, and group theory. The Ham Sandwich Theorem. Isomorphisms. Linear algebra. The Mandelbrot set, mathematical induction, matrices, and the monster group. The parallel postulate, Pascal’s triangle, perfect numbers, permutation groups, pi, the Poincare Conjecture, projective geometry, public-key cryptography, and Pythagoras’ Theorem. Quaternions. Regression analysis. Set theory, squaring the circle, and surreal numbers. Truth tables, turning machines, and turning a sphere inside out. Venn diagrams. Wavelets. Zero. The list never ends....