Related Experiment Video
Updated: Jul 12, 2026
04:45
Morris Water Maze Experiment
Published on: September 24, 2008
On a question of Mordell
Andrew R Booker1, Andrew V Sutherland2
1School of Mathematics, University of Bristol, Bristol BS8 1UG, United Kingdom; Andrew.Booker@bristol.ac.uk drew@math.mit.edu.
Summary
Researchers improved methods for finding integer solutions to sums of three cubes. Using a global compute grid, they discovered new representations for k=3 and k=42, completing a decades-long mathematical challenge.
Area of Science:
- Number Theory
- Computational Mathematics
Background:
- The problem of finding integer solutions for sums of three cubes (x³ + y³ + z³ = k) is a long-standing challenge in number theory.
- Previous searches for solutions were limited by computational power.
Purpose of the Study:
- To develop and implement improved methods for finding integer solutions to the sums of three cubes problem.
- To resolve a challenge posed by Mordell in 1953 and complete a search initiated by Miller and Woollett in 1954.
Main Methods:
- Enhancements to algorithms for identifying integer solutions.
- Large-scale distributed computing utilizing Charity Engine's grid of 500,000 volunteer PCs.
Main Results:
- Discovery of new integer solutions for specific values of k.
- Found new representations for k=3 and k=42.
- Successfully completed the computational search for these values.
Conclusions:
- The improved methods and computational power have successfully resolved the challenge.
- This work provides a significant advancement in the computational exploration of Diophantine equations.
Related Concept Videos
02:20Milgram's Obedience to Authority
Obedience to authority is classically demonstrated in a more famous series of social psychology experiments performed by Stanley Milgram. He was a social psychology professor at Yale who was influenced by the trial of Adolf Eichmann, a Nazi war criminal. Eichmann’s defense for the atrocities he committed was that he was “just following orders.”
01:30Ethical Dilemmas II
Resolving an ethical dilemma in healthcare involves a systematic approach that considers every aspect of the issue, respecting both the patient's needs and values and the healthcare professional's ethical obligations. Here are potential steps to resolve an ethical dilemma:
01:14Torts I
Torts in nursing are wrongful acts that can harm patients and potentially lead to civil liability for the involved nurse. These wrongful acts range from unintentional errors to deliberate actions. Depending on the nature and severity of the tort, a nurse found liable may face financial penalties or disciplinary actions. Understanding the distinctions between intentional, quasi-intentional, and unintentional torts is crucial for nurses to mitigate risks and provide safe patient care.
Intentional...
Intentional...
01:13Torts II
Intentional torts in healthcare refer to deliberate actions that cause harm or infringe on the rights of others. Understanding these torts is crucial for healthcare professionals to avoid legal liabilities and maintain ethical standards in patient care.
01:26Torts III
Types of Quasi-intentional Torts in Healthcare
Quasi-intentional torts in healthcare involve acts where intent is not directed to harm an individual but results in harm due to careless or reckless speech.
Quasi-intentional torts in healthcare involve acts where intent is not directed to harm an individual but results in harm due to careless or reckless speech.
01:20Mason's Rule
Mason's rule is a powerful tool in control systems and signal processing. It simplifies the calculation of transfer functions from signal-flow graphs. This method leverages various elements, including loop gains, forward-path gains, and non-touching loops, to determine the transfer function efficiently.
Loop gain is determined by identifying and tracing a path from a node back to itself. This involves computing the product of branch gains along the loop. Each loop's gain is crucial for further...
Loop gain is determined by identifying and tracing a path from a node back to itself. This involves computing the product of branch gains along the loop. Each loop's gain is crucial for further...