Related Experiment Video
Updated: Jul 25, 2026
05:39
Generating Strictly Controlled Stimuli for Figure Recognition Experiments
Published on: March 18, 2019
Hilbert's sixth problem: the endless road to rigour
1Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK a.n.gorban@le.ac.uk.
Insights
This introduction discusses Hilbert's sixth problem, a foundational issue in mathematics and physics. It outlines the scope and content of this special journal issue dedicated to its exploration.
Area of Science:
- Mathematics
- Physics
- Foundational Science
Background:
- Hilbert's sixth problem addresses the axiomatization of physical theories.
- It seeks to rigorously define and unify concepts in geometry and analysis with physical laws.
Purpose of the Study:
- To introduce the theme issue on Hilbert's sixth problem.
- To provide an overview of the problem's significance and the scope of the included articles.
Main Methods:
- This section is an introduction and does not detail specific methods.
- It sets the stage for articles that will explore various mathematical and physical approaches.
Main Results:
- This section is an introduction and does not present specific results.
- It highlights the interdisciplinary nature and importance of Hilbert's sixth problem.
Conclusions:
- The introduction frames the subsequent articles within the context of Hilbert's sixth problem.
- It emphasizes the enduring relevance of this problem in modern science.
Abstract:
In this introduction, the essence of the sixth problem is discussed and the content of this issue is introduced.This article is part of the theme issue 'Hilbert's sixth problem'.
Related Concept Videos
01:12Theorems of Pappus and Guldinus: Problem Solving
Pappus and Guldinus's theorems are powerful mathematical principles that are used for finding the surface area and volume of composite shapes. For example, consider a cylindrical storage tank with a conical top. Finding the surface area or volume can be challenging for such complex shapes. These theorems are particularly useful in calculating the volume and surface area of such systems. Here, the cylindrical storage tank with a conical top can be broken down into two simple shapes: a cylinder...
01:14Castigliano's Theorem: Problem Solving
The deflection of a simply supported beam that carries a central point load can be analyzed using structural mechanics principles, particularly by applying Castigliano's theorem. This theorem relates the displacement at the load application point to the partial derivatives of the strain energy in the structure. The simply supported beam with a point load at its center has symmetric reaction forces at the supports, each bearing half of the load. The bending moment at any point along the beam is...
01:29Indeterminate Products
Indeterminate forms also arise in the evaluation of limits involving products, particularly when one factor approaches zero while the other tends to positive or negative infinity. This situation, commonly described as a zero-times-infinity form, does not have an immediately interpretable outcome. Depending on how the factors behave relative to one another, the limit of such a product may be zero, infinite, or a finite nonzero value.Product Limits and Algebraic RewritingTo analyze limits of this...
01:22Fundamental Theorem of Calculus I: Problem Solving
In many engineering and environmental applications, accumulated quantities are determined from rates that vary over time. A common example arises in water management, where a supply system pumps water into a storage tank at a rate that changes with time. Accurately determining how much water has entered the tank over a given period is essential for maintaining proper pressure, scheduling operations, and ensuring system safety.The flow rate of water into the tank is described by a time-dependent...
01:29Fundamental Theorem of Calculus II
In calculus, the computation of the area under a continuous curve has been fundamentally simplified by applying the Fundamental Theorem of Calculus, Part 2. Rather than relying on the limiting process of summing infinitely many infinitesimal rectangles, this theorem permits direct evaluation using antiderivatives, thereby streamlining the process of definite integration.The Fundamental Theorem of Calculus, Part 2, states that if a function f(x) is continuous on a closed interval [a, b], then...
01:26Introduction to Sequences
The ancient Greek philosopher Zeno of Elea proposed a series of paradoxes to challenge prevailing notions of motion and continuity. One such paradox imagines a man walking toward a door but only ever covering half the remaining distance with each step. This sequence of movements—first one-half, then one-quarter, then one-eighth of the total distance, and so on—forms a mathematical concept known as a geometric sequence. Each term is half of the previous one and can be written...