Summary of Ananyo Bhattacharya's The Man from the Future

Everest Media

Description

Please note: This is a companion version & not the original book.
Sample Book Insights:
#1 Johnny von Neumann was a brilliant mathematician and scientist who was born in Budapest in 1903. He was the first of three sons born to Miksa and Margit, educated, well-to-do parents who were plugged into the city’s dazzling intellectual and artistic life.
#2 The First World War would precipitate the downfall of the Austro-Hungarian Empire. The von Neumann brothers were held as enemy aliens in Vienna at the start of the war, but their father was able to have their place of internment officially moved to Budapest.
#3 The von Neumann brothers were intellectual prodigies. They both developed systems that they believed would inevitably lead to a win, but they lost consistently against their father even as teenagers.
#4 Max’s sons would participate in the business dinners that their father hosted. These guests would ask the boys questions about the companies in which their father was investing, and they would share their opinions.

Sujets

• Science and technology

Informations

• Publié par: Everest Media LLC
• Date de parution: 10 avril 2022
• Nombre de lectures: 0
• EAN13: 9781669382379
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

Insights on Ananyo Bhattacharya's The Man from the Future
Contents Insights from Chapter 1 Insights from Chapter 2 Insights from Chapter 3 Insights from Chapter 4 Insights from Chapter 5 Insights from Chapter 6 Insights from Chapter 7 Insights from Chapter 8
Insights from Chapter 1

#1

Johnny von Neumann was a brilliant mathematician and scientist who was born in Budapest in 1903. He was the first of three sons born to Miksa and Margit, educated, well-to-do parents who were plugged into the city’s dazzling intellectual and artistic life.

#2

The First World War would precipitate the downfall of the Austro-Hungarian Empire. The von Neumann brothers were held as enemy aliens in Vienna at the start of the war, but their father was able to have their place of internment officially moved to Budapest.

#3

The von Neumann brothers were intellectual prodigies. They both developed systems that they believed would inevitably lead to a win, but they lost consistently against their father even as teenagers.

#4

Max’s sons would participate in the business dinners that their father hosted. These guests would ask the boys questions about the companies in which their father was investing, and they would share their opinions.

#5

The Neumanns joined the European aristocracy in 1910, when Max was awarded a hereditary title by the Austrian emperor Franz Joseph I for meritorious services in the financial field. The younger von Kármán, who attended the Minta gimnázium, was to become the twentieth century’s leading expert on aerodynamics.

#6

The Hungarian school system was responsible for the great outpouring of Hungarian brilliance between 1880 and 1920. However, not all their ex-pupils agreed. Szilard, who attended the thoroughly modern and well-equipped Real school in District VI, found the maths classes intolerably boring.

#7

The foundations of mathematics were being shaken by the discovery of paradoxes that threatened to bring down the entire edifice. The seventeen-year-old von Neumann stepped in to put things right.
Insights from Chapter 2

#1

Von Neumann’s unique talents were noticed as soon as he started school. He attracted the attention of the Lutheran school’s legendary maths teacher, László Rátz, who arranged to teach him advanced mathematics.

#2

Hungary had fought in and lost a world war by the time Max von Neumann was born in 1883. But life for the wealthy denizens of Budapest continued largely as before. The Neumann family packed their bags and left for a vacation home on the Adriatic Sea in 1918, just after Hungary’s first communist government was established.

#3

The White Terror in Hungary in the 1920s was led by Admiral Miklós Horthy, who was a war hero. The von Neumann family was spared, and von Neumann’s schooling continued. Modernism was spreading through mathematics, and the assumptions of the past were being questioned.

#4

The roots of the foundational crisis lay in the discovery of flaws in Euclid’s Elements, the standard textbook in geometry for centuries. Bolyai and Lobachevsky, two Hungarian mathematical prodigies, developed geometries in which the last of Euclid’s five statements, the parallel postulate, was not true.

#5

The next step in geometry was taken by the German mathematician Bernhard Riemann in the 1850s. His mathematics could describe space with any number of dimensions, just as easily as the three familiar spatial ones.

#6

Hilbert’s book, Grundlagen der Geometrie, was published in 1899. It was the first book to be based on axioms rather than intuition, and it cemented Hilbert’s reputation as a great mathematician. But his project ran into the sand almost as soon as it was conceived.

#7

Russell’s paradox was a paradox found at the heart of set theory, a branch of mathematics pioneered by Georg Cantor. It showed that the set of all sets that are not members of themselves is not a member of itself, and should not be.

#8

The crisis that Russell’s paradox caused in mathematics threatened to kick away a cornerstone of mathematics, and with it Hilbert’s programme of re-establishing mathematics on more rigorous grounds.

#9

von Neumann’s paper exudes the confidence of an established master rather than a schoolboy. He begins by defining the ordinal 1st as the empty set. Then he defines a recursive relationship such that the next highest ordinal is the set of all smaller ordinals.

#10

The paradoxes were still present, however, and they continued to cast a shadow over the trustworthiness of set theory. Von Neumann was eager to help, but there was an obstacle in the shape of his father to overcome first.

#11

Von Neumann’s PhD thesis was on set theory, and he expanded the paper and published the longer version with the An changed back to a The in 1925. In it, he placed set theory on solid ground and provided a simple way out of Russell’s paradox.

#12

Hilbert’s paper proved that von Neumann was not a flash in the pan. It rigorously defined a class as a collection of sets that shared a property. In his theory, it is no longer possible to speak of a set of all sets or a class of all classes; only a class of all sets.

#13

Hilbert’s dream of a perfect mathematics was soon crushed. Within a decade, some of the brightest minds in mathematics answered his call. They would show that mathematics was neither complete nor consistent nor decidable.
Insights from Chapter 3

#1

In 1926, von Neumann arrived in Göttingen to study under Hilbert, the center of the mathematical world. He would eventually show that Heisenberg’s and Schrödinger’s theories were the same.

#2

The core ideas in Heisenberg’s revolutionary paper were assembled during a two-week stay in June 1925 at Heligoland, a sparsely populated rock shaped like a wizard’s hat that lies some 30 miles north of the German coast. He showed the frequencies of atomic emission lines could be represented conveniently in an array, with rows and columns representing the initial and final energy levels of electrons producing them.

#3

Heisenberg’s paper showed that the position and momentum of a particle could not be known at the same time.