Francisco Sánchez and the Quaestio de certitudine mathematicarum: A sceptical approach.

In this paper I analyse Francisco Sánchez's role in the Quaestio de certitudine mathematicarum debate. Despite some studies on the philosophical and medical scepticism of Sánchez and, his extant letter with Christopher Clavius, a participant in the debate, we have few analyses about Sánchez's position regarding the certainty of mathematics. Sánchez discussed some problems that Clavius analysed in his Prolegomena to propose an empirical basis for mathematics through a questioning of its certainty. I will trace the conceptual connections between Sánchez's 1589 letter to Clavius and the Quaestio debate, to introduce Sánchez's sceptical approach to analysing the certainty of mathematics.

En torno a la correspondencia internacional de Zoel García de Galdeano / On the international correspondence OF Zoel García de Galdeano

En este trabajo presentamos avances relacionados con el estudio de la intensa actividad epistolar de Zoel García de Galdeano con destacados matemáticos extranjeros de su época. En particular aportamos un listado y una revisión general de todas las cartas localizadas hasta el momento y abordamos un estudio más detallado del contenido de algunas de ellas

In this work we present progress regarding the study of the intense epistolary activity between Zoel García de Galdeano and some of the most important foreign mathematicians of his time. In particular, we list all the letters known up to date, we provide a general overview of them, and we perform a more detailed content analysis of some of them.

Vladimir Voevodsky on mathematics and life.

This is a brief overview of Vladimir Voevodsky's (1966-2017) intellectual and professional biography, which is partly based on the author's personal memories. Voevodsky's biologically-motivated mathematical works are considered in the context of his research in the Algebraic Geometry and in the Univalent Foundations of mathematics. Some biographical details, which are important for understanding Voevodsky's achievements and his personality, are provided.

A mathematician's view of the unreasonable ineffectiveness of mathematics in biology.

This paper discusses, from a mathematician's point of view, the thesis formulated by Israel Gelfand, one of the greatest mathematicians of the 20th century, and one of the pioneers of mathematical biology, about the unreasonable ineffectiveness of mathematics in biology as compared with the obvious success of mathematics in physics. The author discusses the limitations of the mainstream mathematics of today when it is used in biology. He suggests that some emerging directions in mathematics have potential to enhance the role of mathematics in biology.

Linear Programming from Fibonacci to Farkas.

At the beginning of the 13th century Fibonacci described the rules for making mixtures of all kinds, using the Hindu-Arabic system of arithmetic. His work was repeated in the early printed books of arithmetic, many of which contained chapters on 'alligation', as the subject became known. But the rules were expressed in words, so the subject often appeared difficult, and occasionally mysterious. Some clarity began to appear when Thomas Harriot introduced a modern form of algebraic notation around 1600, and he was almost certainly the first to express the basic rule of alligation in algebraic terms. Thus a link was forged with the work on Diophantine problems that occupied mathematicians like John Pell and John Kersey in the 17th century. Joseph Fourier's work on mechanics led him to suggest a procedure for handling linear inequalities based on a combination of logic and algebra; he also introduced the idea of describing the set of feasible solutions geometrically. In 1898, inspired by Fourier's work, Gyula Farkas proved a fundamental theorem about systems of linear inequalities. This topic eventually found many applications, and it became known as Linear Programming. The theorem of Farkas also plays a significant role in Game Theory.

New insight into the origins of the calculus war.

The consensus today is that both Newton and Leibniz created calculus independently. Yet, this was not so clear at the beginning of the eighteenth century. A bitter controversy took place at that time, which came to be known as the 'calculus war', probably the greatest clash in the history of science. While it is accepted that the debate started when Fatio de Duillier publicly accused Leibniz of plagiarism in 1699, earlier evidence of its origins can be found in an exchange of letters between Leibniz and Huygens.

A genealogical approach to academic success.

We analyse academic success using a genealogical approach to the careers of over 95,000 scientists in mathematics and associated fields in physics and chemistry. We look at the effect of Ph.D. supervisors (one's mentors) on the number of Ph.D. students that one supervises later on (one's mentees) as a measure of academic success. Supervisors generally provide important inputs in Ph.D. projects, which can have long-lasting effects on academic careers. Moreover, having multiple supervisors exposes one to a diversity of inputs. We show that Ph.D. students benefit from having multiple supervisors instead of a single one. The cognitive diversity of mentors has a subtler effect in that it increases both the likelihood of success (having many mentees later on) and failure (having no mentees at all later on). We understand the effect of diverse mentorship as a high-risk, high-gain strategy: the recombination of unrelated expertise often fails, but sometimes leads to true novelty.

Adolf Eugen Fick (1829-1901) - The Man Behind the Cardiac Output Equation.

Adolf Fick was a German physiologist, born in Kassel in 1829, who studied medicine at the University of Marburg and graduated in 1851. He worked first in Zurich and then in Wurzburg. Most of his studies were based on physics and mathematics, and deep analysis, and only later were proven by experiments. Fick's name in physics is associated to the laws of diffusion of solutions, and in medicine to the principle of cardiac output calculation. In 1855, he proposed Fick's laws on gas diffusion. In 1870, he devised Fick's principle, which allows the measurement of cardiac output and calculations of intracardiac shunts from the arteriovenous oxygen difference. The method was later generalized to the Fick principle, according to which the flow of an indicator taken up or released by an organ corresponds to the difference between the indicator flows in the inflow and outflow tracts. Fick invented several devices most of them aimed to improve precision in his physiologic experiments. In 1868, he invented the plethysmograph, for recording the speed of blood in the human artery. In 1888, the tonometer for measuring from outside the hydrostatic pressure inside the eyeball. After 3 decades as Professor in Wurzburg, he retired. Fick died at Blankenberge, Belgium in 1901 age 71 years old.

Early Emotion Knowledge and Later Academic Achievement Among Children of Color in Historically Disinvested Neighborhoods.

This study examined longitudinal relations between emotion knowledge (EK) in pre-kindergarten (pre-K; Mage  = 4.8 years) and math and reading achievement 1 and 3 years later in a sample of 1,050 primarily Black children (over half from immigrant families) living in historically disinvested neighborhoods. Participants were part of a follow-up study of a cluster randomized controlled trial. Controlling for pre-academic skills, other social-emotional skills, sociodemographic characteristics, and school intervention status, higher EK at the end of pre-K predicted higher math and reading achievement test scores in kindergarten and second grade. Moderation analyses suggest that relations were attenuated among children from immigrant families. Findings suggest the importance of enriching pre-K programs for children of color with EK-promotive interventions and strategies.

Stokes' mathematical education.

George Gabriel Stokes won the coveted title of Senior Wrangler in 1841, a year in which the examination papers for the Cambridge Mathematical Tripos were notoriously difficult. Coming top in the Mathematical Tripos was a notable achievement, but for Stokes it was a prize hard won after several years of preparation, and not only years spent at Cambridge. When Stokes arrived at Pembroke College, he had spent the previous two years at Bristol College, a school which prided itself on its success in preparing students for Oxford and Cambridge. This article follows Stokes' path to the senior wranglership, tracing his mathematical journey from his arrival in Bristol to the end of his final year of undergraduate study at Cambridge. This article is part of the theme issue 'Stokes at 200 (Part 1)'.

Sir George Gabriel Stokes in Skreen: how a childhood by the sea influenced a giant in fluid dynamics.

George Gabriel Stokes spent most of his life at the University of Cambridge, where he undertook his undergraduate degree and later became Lucasian Professor of Mathematics and Master of Pembroke College. However, he spent the first 13 years of his life in Skreen, County Sligo, Ireland, a rural area right by the coastline, overlooking the Atlantic Ocean. As this paper will discuss, the time he spent there was short but its influence on him and his research was long reaching, with his childhood activities of walking by and bathing in the sea being credited for first piquing Stokes' interest in ocean waves, which he would go on to write papers about. More generally, it marked the beginning of an interest in fluid dynamics and a curious nature regarding natural phenomena in his surroundings. Stokes held a special affinity for the ocean for the rest of his life, constantly drawing inspiration for it in his mathematical and physical studies and referencing it in his correspondences. This commentary was written to celebrate Stokes' 200th birthday as part of the theme issue of Philosophical Transactions A. This article is part of the theme issue 'Stokes at 200 (Part 1)'.

Playing mathematics.

We are used to thinking of mathematics as a symbolic activity. Here I argue that it may also be seen as a performative one. Making an analogy with music, I draw attention to the ways in which mathematics may not only be written down but also played out.

Visiting Newton's atelier before the Principia, 1679-1684.

The worksheets that presumably contained Newton's early development of the fundamental concepts in his Principia have been lost. A plausible reconstruction of this development is presented based on Newton's exchange of letters with Robert Hooke in 1679, with Edmund Halley in 1686, and on some clues in the diagram associated with Proposition 1 in Book 1 of the Principia that have been ignored in the past. A graphical construction associated with this proposition leads to a rapidly convergent method to obtain orbits for central forces, which elucidates how Newton may have have been led to formulate some of his most fundamental propositions in the Principia.