On the Infinite was Hilbert ’ s most important paper on the foundations of mathematics, serving as the heart of Hilbert's program to secure the foundation of transfinite numbers by basing them on finite methods.

This is philosophically unsatisfying to some and has motivated additional work in set theory and other methods of formalizing the foundations of mathematics such as New Foundations by Willard Van Orman Quine.

Naive set theory is one of several theories of sets used in the discussion of the foundations of mathematics.

After re-working the foundations of classical geometry, Hilbert could have extrapolated to the rest of mathematics.

Hilbert published his views on the foundations of mathematics in the 2-volume work Grundlagen der Mathematik.

" The logical foundations of mathematics ," 1134 – 47.

" The foundations of mathematics ," with comment by Weyl and Appendix by Bernays, 464 – 89.

After obtaining his PhD in mathematics, Husserl began analyzing the foundations of mathematics from a psychological point of view.

Combinatory logic and lambda calculus were both originally developed to achieve a clearer approach to the foundations of mathematics.

In logic and the foundations of mathematics, formal languages are used to represent the syntax of axiomatic systems, and mathematical formalism is the philosophy that all of mathematics can be reduced to the syntactic manipulation of formal languages in this way.

First-order logic is of great importance to the foundations of mathematics, because it is the standard formal logic for axiomatic systems.

Category: Theorems in the foundations of mathematics

Greek mathematician Archimedes, famous for his ideas regarding fluid mechanics and buoyancyIn the 3rd century BCE, the Greek mathematician Archimedes of Syracuse ( ( 287 BCE-212 BCE )-generally considered to be the greatest mathematician of antiquity and one of the greatest of all time-laid the foundations of hydrostatics, statics and calculated the underlying mathematics of the lever.

One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when many, such as Bertrand Russell, A. N. Whitehead and David Hilbert, were pioneering the use of logic and set theory to understand the foundations of mathematics.

The lambda calculus was introduced by mathematician Alonzo Church in the 1930s as part of an investigation into the foundations of mathematics.

Contemporary developments in logic and the foundations of mathematics, especially Bertrand Russell and Alfred North Whitehead's monumental Principia Mathematica, impressed the more mathematically minded logical positivists such as Hans Hahn and Rudolf Carnap.

A site and a language, that formalize mathematics from its foundations.

Mathematical logic ( also known as symbolic logic ) is a subfield of mathematics with close connections to the foundations of mathematics, theoretical computer science and philosophical logic.

Since its inception, mathematical logic has both contributed to, and has been motivated by, the study of foundations of mathematics.

Contemporary work in the foundations of mathematics often focuses on establishing which parts of mathematics can be formalized in particular formal systems ( as in reverse mathematics ) rather than trying to find theories in which all of mathematics can be developed.

Russell's fourth novel, Dreamers of the Day ( released in March 2008 ), revolves around the 1921 Cairo Peace Conference, which laid the foundations for the modern Middle East.

Russell's institutional clients include retirement plans, endowments, foundations and investment plans of all types.

One attempt after another to provide unassailable foundations for mathematics was found to suffer from various paradoxes ( such as Russell's paradox ) and to be inconsistent.

This may be contrasted with modern studies of self-referential paradoxes such as Russell's paradox, in which the problems are seen as fundamentally insoluble, and central to the foundations of logic.

In 1905, Couturat published a work on logic and the foundations of mathematics ( with an appendix on Kant's philosophy of mathematics ) which was originally conceived as a translation of Russell's Principles of Mathematics.

The consequence is a paradox that emerges repeatedly throughout Christian Scripture and the mysticism found in the early foundations of the Church.

Although Richard's solution to the paradox did not gain favor with mathematicians, predicativism is an important part of the study of the foundations of mathematics.

Carl Linnaeus ( Swedish original name Carl Nilsson Linnæus, 23 May 1707 – 10 January 1778 ), also known after his ennoblement as, was a Swedish botanist, physician, and zoologist, who laid the foundations for the modern scheme of binomial nomenclature.

The wall also has twelve foundations which are adorned with precious stones, and upon the foundations are written the names of the twelve apostles.

He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.

The 1907 Anglo-Russian Entente ( the Convention of St. Petersburg ) not only divided the region into separate areas of Russian and British influence but also established foundations for Afghan neutrality.

Martineau also wrote: “ Bopp's Sanskrit studies and Sanskrit publications are the solid foundations upon which his system of comparative grammar was erected, and without which that could not have been perfect.

Foundation donations are also rejected if the foundations attach unreasonable conditions, restrictions or constraints on Greenpeace activities or if the donation would compromise the independence and aims of Greenpeace.

Terzaghi also developed the framework for theories of bearing capacity of foundations, and the theory for prediction of the rate of settlement of clay layers due to consolidation.

He had made advances in the areas of analysis, foundations and logic, made many contributions to the teaching of calculus and also contributed to the fields of differential equations and vector analysis.

These works also influenced contemporary Italian scientist Galileo Galilei and provided one of the foundations for Englishman Isaac Newton's theory of universal gravitation.

These were partly caused by the explosion in population, but also to concentrate economic power at strategic locations, while formerly cities only existed in the shape of either old Roman foundations or older bishoprics.

The constitution's preamble also boasted that the foundations of religious belief in Albania had been abolished.

These works also provided one of the foundations for Isaac Newton's theory of universal gravitation.

What remains of the foundations of an early rectangular building near the southern part of the current cathedral might also be contemporary with Justus or may be part of a Roman building.

According to scholar James Butrica, lesbianism " challenged not only the Roman male's view of himself as the exclusive giver of sexual pleasure but also the most basic foundations of Rome's male-dominated culture ".

They also claim that much of the other low-level chemistry in Nanosystems requires extensive further work, and that Drexler's higher-level designs therefore rest on speculative foundations.

The Babylonian astrologers also laid the foundations of what would eventually become Western astrology.

Others have argued that the church is indeed built upon Jesus and faith, but also on the disciples as the roots and foundations of the church on the basis of Paul's teaching in Romans and Ephesians, though not primarily Peter.

Nevanlinna also published in Finnish a book on the foundations of geometry and a semipopular account of the Theory of Relativity.

It is also affiliated with 4 Gödel Prize winners, 4 Knuth Prize recipients, 10 IJCAI Computers and Thought Award winners, and about 15 Grace Murray Hopper Award winners for their work in the foundations of computer science.

They proposed a kind of Neuroanthropology which would lay the foundations for a more complete scientific account of cultural similarity and variation by requiring an integration of cultural anthropology and neuroscience — a program that theorists such as Victor Turner also embraced.

The battle also helped lay the foundations of the Carolingian Empire

He is also credited with predicting the rise of reality television and with establishing the conceptual foundations for the rapid growth of virtual environments such as video games and the World Wide Web.

1905 is also the annus mirabilis of Albert Einstein, publishing papers which lay the foundations of quantum physics, introduced the special theory of relativity, explained Brownian motion, and established mass-energy equivalence.