Statements (1,089)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:theorem
|
| gptkbp:applies_to |
n=3
n=50 n=10 n=14 n=17 n=22 n=29 n=34 n=4 n=40 n=47 n=5 n=6 n=7 n=8 n=9 n=41 |
| gptkbp:associated_with |
gptkb:Elliptic_curves
gptkb:Modular_forms |
| gptkbp:awarded_for |
gptkb:Clay_Millennium_Prize
|
| gptkbp:challenges |
gptkb:Mathematician
Mathematicians Students. mathematicians. Researchers. Undergraduate students. High school students. Academics. students. to prove Amateur mathematicians Understand. undergraduate students. Students of mathematics. for non-mathematicians mathematical theorists. prove. theoretical physicists. For non-mathematicians. Prove for n > 2. Prove for all n Amateur Mathematicians. Analyze. Comprehend. For non-mathematicians Mathematical Students. Mathematical enthusiasts. Mathematical scholars. Professional Mathematicians. Prove for all n. Prove for larger n. Prove for specific values of n Prove. mathematical educators. Professional mathematicians. Research mathematicians. |
| gptkbp:completed |
gptkb:1994
|
| gptkbp:conjectured_in |
1637
|
| gptkbp:contributes_to |
The Langlands Program.
|
| gptkbp:cultural_impact |
Featured in popular science literature.
|
| gptkbp:documentary |
Fermat's Last Theorem (1996).
|
| gptkbp:duration_of_proof |
over 350 years
|
| gptkbp:example |
A theorem in number theory.
|
| gptkbp:field |
gptkb:Mathematics
Number theory Cryptography. Topology. Statistics. Algebra. Graph theory. Numerical analysis. Mathematical modeling. Mathematical physics. Mathematical logic. Game theory. Mathematical economics. Operations research. Analysis. Computer science. Combinatorics. Mathematical biology. Geometry. Mathematical aesthetics. Mathematical anthropology. Mathematical chemistry. Mathematical education. Mathematical ethics. Mathematical finance. Mathematical history. Mathematical linguistics. Mathematical philosophy. Mathematical psychology. Mathematical sociology. Set theory. |
| gptkbp:field_of_study |
gptkb:Mathematics
Number theory |
| gptkbp:first_published |
1637
Fermat's Enigma by Simon Singh. |
| gptkbp:has_applications_in |
gptkb:crypt
gptkb:Mathematics Computer Science Number Theory Mathematical Logic Cryptography. |
| gptkbp:has_been_verified_for |
Many values of n
|
| gptkbp:has_connection_to |
Algebraic geometry
Galois theory Galois Theory Galois theory. |
| gptkbp:has_historical_significance |
gptkb:Mathematics
gptkb:Yes It remained unproven for over 350 years. It remained unsolved for over 350 years. It was a long-standing problem in number theory. One of the most famous problems in mathematics over 350 years of attempts to prove it. |
| gptkbp:has_history |
17th century
17th Century 17th century mathematics the 17th century. related to the development of modern algebra. |
| gptkbp:has_implications_for |
gptkb:Mathematics
Algebraic geometry Number Theory number theory Number theory research mathematical logic. The field of algebra. |
| gptkbp:has_influence_on |
modern mathematics
Modern mathematics Modern Number Theory Mathematical research |
| gptkbp:has_influenced |
modern mathematics
Modern mathematics Mathematical research Computer Science. Mathematical Proof Techniques The development of modern algebraic geometry. |
| gptkbp:has_led_to |
Further mathematical discoveries.
New mathematical discoveries. |
| gptkbp:has_produced |
Significant interest in number theory.
|
| gptkbp:has_proof |
gptkb:Yes
Wiles' proof uses sophisticated techniques. Based on the work of many mathematicians. Wiles' Proof by Wiles and Taylor. using the Taniyama-Shimura-Weil conjecture. |
| gptkbp:has_special_case |
n=3
n=4 n=48 n=5 n=6 |
| gptkbp:has_variants |
gptkb:Fermat's_Last_Theorem_for_n=9
gptkb:Fermat's_Last_Theorem_for_n=4 gptkb:Yes Generalizations Fermat's Last Theorem for n=5 Fermat's Last Theorem for n=10 Fermat's Last Theorem for n=11 Fermat's Last Theorem for n=12 Fermat's Last Theorem for n=13 Fermat's Last Theorem for n=14 Fermat's Last Theorem for n=15 Fermat's Last Theorem for n=16 Fermat's Last Theorem for n=17 Fermat's Last Theorem for n=18 Fermat's Last Theorem for n=19 Fermat's Last Theorem for n=20 Fermat's Last Theorem for n=21 Fermat's Last Theorem for n=22 Fermat's Last Theorem for n=23 Fermat's Last Theorem for n=24 Fermat's Last Theorem for n=25 Fermat's Last Theorem for n=26 Fermat's Last Theorem for n=27 Fermat's Last Theorem for n=28 Fermat's Last Theorem for n=29 Fermat's Last Theorem for n=3 Fermat's Last Theorem for n=30 Fermat's Last Theorem for n=31 Fermat's Last Theorem for n=32 Fermat's Last Theorem for n=33 Fermat's Last Theorem for n=34 Fermat's Last Theorem for n=35 Fermat's Last Theorem for n=36 Fermat's Last Theorem for n=37 Fermat's Last Theorem for n=38 Fermat's Last Theorem for n=39 Fermat's Last Theorem for n=40 Fermat's Last Theorem for n=41 Fermat's Last Theorem for n=42 Fermat's Last Theorem for n=43 Fermat's Last Theorem for n=44 Fermat's Last Theorem for n=45 Fermat's Last Theorem for n=46 Fermat's Last Theorem for n=48 Fermat's Last Theorem for n=49 Fermat's Last Theorem for n=50 Fermat's Last Theorem for n=6 Fermat's Last Theorem for n=7 Fermat's Last Theorem for n=8 Generalizations for n>2 Generalizations to higher dimensions. Generalizations to other forms. Generalizations to other number systems. generalizations to other forms. |
| gptkbp:historical_impact |
Influenced the development of modern mathematics.
|
| gptkbp:historical_significance |
It remained unproven for over 350 years.
over 350 years of attempts to prove it It remained unsolved for over 350 years. It was conjectured in 1637. It was famously noted in the margin of a book by Fermat. |
| https://www.w3.org/2000/01/rdf-schema#label |
Fermat's Last Theorem
|
| gptkbp:illustrated_by |
Counterexamples for n=2, n=3
Counterexamples for n=2. Examples for n=10. Examples for n=11. Examples for n=12. Examples for n=3. Examples for n=4. Examples for n=5. Examples for n=6. Examples for n=7. Examples for n=8. Examples for n=9. |
| gptkbp:impact |
in algebraic geometry
inspired further research in number theory. |
| gptkbp:influenced |
modern number theory
|
| gptkbp:influenced_by |
gptkb:Taniyama-Shimura-Weil_conjecture
Mathematical Community Taniyama-Shimura-Weil Conjecture |
| gptkbp:inspired |
gptkb:Fermat's_Last_Theorem_for_n=9
gptkb:Fermat's_Last_Theorem_for_n=4 Mathematical Research mathematical research further research in mathematics Further research in number theory. Fermat's Last Theorem for n=5 Fermat's Last Theorem for n=10 Fermat's Last Theorem for n=11 Fermat's Last Theorem for n=12 Fermat's Last Theorem for n=13 Fermat's Last Theorem for n=14 Fermat's Last Theorem for n=15 Fermat's Last Theorem for n=16 Fermat's Last Theorem for n=17 Fermat's Last Theorem for n=18 Fermat's Last Theorem for n=19 Fermat's Last Theorem for n=20 Fermat's Last Theorem for n=21 Fermat's Last Theorem for n=22 Fermat's Last Theorem for n=23 Fermat's Last Theorem for n=24 Fermat's Last Theorem for n=25 Fermat's Last Theorem for n=26 Fermat's Last Theorem for n=27 Fermat's Last Theorem for n=28 Fermat's Last Theorem for n=29 Fermat's Last Theorem for n=3 Fermat's Last Theorem for n=30 Fermat's Last Theorem for n=31 Fermat's Last Theorem for n=32 Fermat's Last Theorem for n=33 Fermat's Last Theorem for n=34 Fermat's Last Theorem for n=35 Fermat's Last Theorem for n=36 Fermat's Last Theorem for n=37 Fermat's Last Theorem for n=38 Fermat's Last Theorem for n=39 Fermat's Last Theorem for n=6 Fermat's Last Theorem for n=7 Fermat's Last Theorem for n=8 Many areas of number theory. many mathematical developments |
| gptkbp:inspired_by |
gptkb:Fermat's_original_margin_note
gptkb:Fermat's_Last_Theorem_for_n=9 gptkb:Fermat's_Last_Theorem_for_n=4 gptkb:Fermat's_margin_note Fermat's Last Theorem for n=5 Fermat's Last Theorem for n=10 Fermat's Last Theorem for n=11 Fermat's Last Theorem for n=12 Fermat's Last Theorem for n=13 Fermat's Last Theorem for n=14 Fermat's Last Theorem for n=15 Fermat's Last Theorem for n=16 Fermat's Last Theorem for n=3 Fermat's Last Theorem for n=6 Fermat's Last Theorem for n=7 Fermat's Last Theorem for n=8 Fermat's Last Theorem for n=2 |
| gptkbp:inspired_research_in |
Number theory
|
| gptkbp:involves |
gptkb:Diophantine_equations
Number Theory Number theory exponentiation number theory Natural Numbers Diophantine Equations integer solutions exponential equations Mathematical proof techniques. |
| gptkbp:involves_concepts |
gptkb:crypt
modular forms Galois representations Diophantine Equations |
| gptkbp:is_a |
gptkb:Mathematics
Open Problem Diophantine equation Mathematical Conjecture Conjecture Diophantine Equation Fundamental concept in mathematics. Challenge for amateur mathematicians. Famous Conjecture Famous Theorem Historical Problem Landmark theorem in mathematics. Subject of popular science books. Theorem in Algebra Theorem in Diophantine Equations Theorem in Mathematical Analysis Theorem in Mathematical Foundations Theorem in Mathematical History Theorem in Mathematical Logic Theorem in Mathematical Philosophy Theorem in Modern Mathematics Theorem in Number Theory Theorem in Pure Mathematics Theorem in Theoretical Mathematics Theorem of Great Importance Theorem with Broad Implications Theorem with Cultural Significance Theorem with Historical Impact Topic of interest in mathematical circles. |
| gptkbp:is_a_solution_for |
gptkb:Cambridge_University
gptkb:1994 gptkb:Andrew_Wiles the 20th century Wiles and Richard Taylor |
| gptkbp:is_a_subject_of |
gptkb:Documentaries
Mathematical Interest |
| gptkbp:is_analyzed_in |
gptkb:students
Mathematicians mathematical journals Mathematical Journals Mathematical journals Research studies. academic research. theses. research papers. Mathematical conferences. academic journals. Mathematical research. Mathematical Analysis. mathematical reviews. mathematical studies. Mathematical Reviews. Mathematical Journals. Mathematical Research. Mathematical Studies. mathematical critiques. mathematical evaluations. |
| gptkbp:is_associated_with |
gptkb:Wiles's_proof
gptkb:Fermat's_Last_Theorem_for_n=9 gptkb:Fermat's_Last_Theorem_for_n=4 gptkb:Taniyama-Shimura-Weil_conjecture Mathematical proofs Fermat's Last Theorem proof Fermat's Last Theorem for n=5 Fermat's principle Fermat's Last Theorem for n=19 Fermat's Last Theorem for n=23 Fermat's Last Theorem for n=41 Fermat's Last Theorem: The Proof (book) Fermat's Last Theorem Conference. Fermat's Last Theorem conference Fermat's Last Theorem for n=10. Fermat's Last Theorem for n=11. Fermat's Last Theorem for n=12. Fermat's Last Theorem for n=13. Fermat's Last Theorem for n=14. Fermat's Last Theorem for n=15. Fermat's Last Theorem for n=16. Fermat's Last Theorem for n=17. Fermat's Last Theorem for n=18. Fermat's Last Theorem for n=19. Fermat's Last Theorem for n=20. Fermat's Last Theorem for n=21. Fermat's Last Theorem for n=22. Fermat's Last Theorem for n=23. Fermat's Last Theorem for n=24. Fermat's Last Theorem for n=25. Fermat's Last Theorem for n=26. Fermat's Last Theorem for n=27. Fermat's Last Theorem for n=28. Fermat's Last Theorem for n=3. Fermat's Last Theorem for n=30. Fermat's Last Theorem for n=31. Fermat's Last Theorem for n=32. Fermat's Last Theorem for n=33. Fermat's Last Theorem for n=34. Fermat's Last Theorem for n=35. Fermat's Last Theorem for n=36. Fermat's Last Theorem for n=37. Fermat's Last Theorem for n=38. Fermat's Last Theorem for n=39. Fermat's Last Theorem for n=4. Fermat's Last Theorem for n=40. Fermat's Last Theorem for n=41. Fermat's Last Theorem for n=42. Fermat's Last Theorem for n=43. Fermat's Last Theorem for n=44. Fermat's Last Theorem for n=45. Fermat's Last Theorem for n=46. Fermat's Last Theorem for n=47. Fermat's Last Theorem for n=48. Fermat's Last Theorem for n=49. Fermat's Last Theorem for n=5. Fermat's Last Theorem for n=50. Fermat's Last Theorem for n=6. Fermat's Last Theorem for n=7. Fermat's Last Theorem for n=8. Fermat's Last Theorem for n=9. The concept of mathematical rigor. the number 3. |
| gptkbp:is_based_on |
Fermat's principle of descent
|
| gptkbp:is_celebrated_in |
gptkb:Mathematician
Popular culture Mathematical Community mathematics community mathematical community Mathematics community Mathematicians worldwide Mathematical communities Mathematical conferences mathematical communities. mathematical history. Mathematical community. mathematical anniversaries Mathematical anniversaries. Mathematical Communities. Mathematics Community. Mathematics Competitions. mathematical achievements. |
| gptkbp:is_challenged_by |
Many mathematicians over the centuries.
|
| gptkbp:is_challenging_to_explain |
To laypersons
|
| gptkbp:is_challenging_to_prove |
for mathematicians
|
| gptkbp:is_challenging_to_teach |
In educational settings
|
| gptkbp:is_cited_in |
Books
Dissertations Research Papers Research papers Articles Theses Theses and Dissertations Academic Papers academic papers Encyclopedias Mathematical Journals Mathematical Reviews Educational materials. Mathematical papers mathematical journals. numerous mathematical papers. Academic journals. Research articles. Textbooks. Numerous academic papers. Theses. Research Articles. Scholarly Articles. Research Papers. academic theses. academic publications. Mathematical journals. Academic Journals. Academic Publications. Mathematical Citations. Mathematical archives. Mathematical references. Numerous Research Papers. Numerous mathematical journals Numerous mathematical papers. mathematical encyclopedias. Mathematical encyclopedias. Mathematical theses. |
| gptkbp:is_connected_to |
gptkb:Taniyama-Shimura-Weil_conjecture
Galois theory Galois Theory Mathematical conjectures Galois Theory. Mathematical Proof Techniques. Number Theory Problems Taniyama-Shimura-Weil Conjecture Taniyama-Shimura-Weil conjecture. |
| gptkbp:is_considered |
Advanced Mathematics Courses
Mathematical Competitions one of the most famous problems in mathematics. a milestone in mathematics a classic problem. a fundamental theorem. a milestone in mathematics. a significant theorem. One of the most famous problems in mathematics. a landmark theorem. A milestone in mathematics. a major theorem. a pivotal theorem. A milestone in mathematics A classic problem. a benchmark for mathematical proofs Ph D Research a significant achievement. A benchmark for mathematical proofs. A classic problem in mathematics. A fundamental theorem in mathematics. A fundamental theorem in number theory. A key result in the study of numbers. A landmark achievement in mathematics. A landmark theorem in mathematics. A milestone in the field of mathematics. A milestone in the history of mathematics. A pivotal moment in mathematical history. A pivotal moment in mathematics. A pivotal theorem in mathematics. A significant theorem in mathematics. A source of inspiration for mathematicians. A triumph of modern mathematics. One of the most famous problems in mathematics a foundational theorem. a milestone in the history of mathematics. a significant mathematical problem. A classic example of a problem that is easy to state but hard to prove. |
| gptkbp:is_considered_as |
One of the most famous problems in mathematics.
A milestone in mathematics A benchmark in mathematics Landmark in Mathematics One of the most famous problems in mathematics |
| gptkbp:is_considered_by |
gptkb:philosopher
Many as a milestone in mathematics. |
| gptkbp:is_debated_in |
gptkb:Andrew_Wiles
no three positive integers a, b, and c can satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2. |
| gptkbp:is_described_as |
gptkb:Workshops
gptkb:Seminars Books Community Events Exhibitions Lectures Online Courses Textbooks Educational Programs Interviews Blogs Forums Webinars Documentary Films Podcasts Television Shows Radio Shows Mathematical Textbooks News Articles Outreach Programs Math Competitions Public Lectures Science Fairs Social Media Posts Number theory textbooks Educational resources. Workshops for Teachers mathematical textbooks. Mathematical textbooks Number theory courses number theory concepts You Tube Videos Number Theory Textbooks Wiles' proof. |
| gptkbp:is_discussed_in |
gptkb:Documentaries
gptkb:Seminars Academic Journals Conferences Mathematicians Online Forums Webinars Podcasts Academic Papers Mathematical Textbooks mathematics courses mathematical literature Mathematical Literature Mathematical literature Mathematical Conferences Mathematical conferences academic forums. mathematical literature. mathematical forums mathematical communities. mathematical seminars. Mathematical literature. academic circles. Mathematical seminars Mathematical Seminars Mathematical forums Mathematical conferences. Mathematical seminars. Mathematical textbooks. mathematical forums. Online forums. Academic Seminars academic journals. mathematical blogs. lectures. Mathematical circles. Mathematical discussions. Mathematical forums. Online Courses. Popular Science Books mathematical conferences. mathematical societies. Mathematical Forums Mathematical Blogs Mathematical Conferences. Mathematical Discussions. Mathematical Forums. Mathematical Literature. Mathematical Research Groups Mathematical Seminars. Mathematical Symposia Mathematical Workshops Mathematical blogs. Mathematical communities. Mathematical debates. Mathematical societies. Mathematicians in seminars |
| gptkbp:is_documented_in |
Research papers
mathematical literature historical records. |
| gptkbp:is_explored_in |
gptkb:Documentaries
gptkb:Workshops gptkb:documentaries gptkb:Mathematics gptkb:educational_content Online Courses Research Collaborations Research Papers Research papers Online Articles Research Projects Computational methods mathematical conferences Mathematical Journals mathematical textbooks Advanced Mathematics Courses Online courses. Mathematical journals Mathematical Conferences mathematical discussions Mathematical research papers Mathematical communities popular science literature Mathematical competitions Mathematical conferences mathematical literature. mathematical research. mathematical theory. documentaries. mathematical discussions. mathematical seminars. Mathematical literature. Mathematical textbooks Documentaries. Number theory courses Mathematical conferences. Mathematical seminars. Mathematical textbooks. computational methods. online courses. mathematical workshops. Mathematical research. Mathematical theories. graduate studies. textbooks. number theory courses. mathematical research papers. Documentaries and books. Computational methods. Mathematical competitions. Mathematical discussions. Mathematical studies. Mathematicians worldwide. mathematical explorations. research mathematicians. Mathematical analysis. Number Theory Research Computational Methods. Mathematical research papers. mathematical conferences. Mathematical Research Papers Books on mathematics. Mathematical documentaries. Historical Analysis. Historical Context. Mathematical Experts. Mathematical Research Communities Mathematical Research Discussions Mathematical Research Initiatives Mathematical Research Papers. Mathematical Research. Mathematical Researchers. Mathematical Scholars. Mathematical Studies. Mathematical Textbooks. Mathematical Workshops Mathematical blogs. Mathematical concepts. Mathematical frameworks. Mathematical lectures. Mathematical podcasts. Mathematical workshops. mathematical theories. |
| gptkbp:is_famous_for |
Its historical context.
its simplicity and difficulty. Its long history of attempts to prove it. Its simplicity in statement but complexity in proof. Its proof requiring advanced mathematics. Its simplicity and difficulty Its simplicity and difficulty. Its long-standing unsolved status. |
| gptkbp:is_influential_in |
Mathematical Education
Modern mathematics Mathematical research. Mathematical education. Mathematical philosophy. Mathematical culture. Mathematical thought. Modern Mathematics. Modern Number Theory. |
| gptkbp:is_linked_to |
gptkb:Fermat's_little_theorem
gptkb:Fermat's_Last_Theorem_for_n=9 Diophantine Equations Fermat's Little Theorem the study of algebraic structures. the concept of proof. the study of mathematical logic. the study of prime numbers. The exploration of mathematical conjectures. the concept of infinity. the study of algebra. the study of integers. Fermat's Last Theorem for n=5 Fermat's Last Theorem: A Genetic Introduction Fermat's Last Theorem: The Proof Fermat's principle Fermat's Last Theorem for n=14 Fermat's Last Theorem for n=6 Fermat's Last Theorem for n=7 Fermat's Last Theorem for n=8 Fermat's principle. the study of equations. Fermat's Last Theorem: The Proof (documentary). Fermat's conjecture. Fermat's Last Theorem conjecture Fermat's Last Theorem Proof. Fermat's Last Theorem Solutions. Fermat's Last Theorem conjectures. Fermat's Last Theorem for n=23. Fermat's Last Theorem proof. Fermat's Last Theorem proofs. Fermat's Last Theorem solutions. Fermat's Little Theorem. Number Theory. The concept of mathematical proof. The development of proof techniques. The history of Fermat's work. |
| gptkbp:is_mentioned_in |
popular culture.
|
| gptkbp:is_notable_for |
Its simplicity in statement but complexity in proof.
Its proof using modern techniques Its simplicity and difficulty. its long history. |
| gptkbp:is_often_discussed_in |
Mathematical Literature
|
| gptkbp:is_part_of |
gptkb:Mathematics
Number Theory Number theory Mathematical Education Mathematical Research number theory Mathematical Literature history of mathematics mathematical folklore theoretical mathematics. mathematical folklore. mathematical history. the study of Diophantine equations. mathematical history Mathematical Challenges Mathematical History Mathematical history Mathematical Culture mathematical challenges the history of number theory. the study of prime numbers. Mathematical competitions. The history of mathematics. the study of algebra. Mathematical inquiry. Mathematical education. Mathematical history. the legacy of Fermat. the mathematical canon. Mathematical folklore. Mathematical folklore Fermat's work. Mathematical Challenges. Mathematical Concepts. Mathematical Education. Mathematical Heritage. Mathematical History. Mathematical Knowledge. Mathematical Theorems. Mathematical Theories. Mathematical Theory. Mathematical challenges. Mathematical discourse. Mathematical exploration. Mathematical heritage. Mathematical theory. The curriculum in advanced mathematics. The history of number theory. The legacy of Andrew Wiles. The legacy of Pierre de Fermat. the legacy of mathematics. |
| gptkbp:is_recognized_as |
a major achievement in mathematics
A milestone in mathematics. A significant theorem. |
| gptkbp:is_recognized_by |
Mathematical community
Mathematicians worldwide Mathematical historians. Mathematical educators. Mathematical institutions. Mathematical practitioners. Mathematical scholars. Mathematical societies. Mathematical theorists. Nobel laureates. |
| gptkbp:is_referenced_in |
gptkb:literature
Popular culture Popular science literature documentaries. Popular Science Books Mathematical Blogs. Mathematical Discussions. Popular Culture. |
| gptkbp:is_reflected_in |
mathematical competitions.
mathematical discussions. mathematical explorations. mathematical advancements. mathematical culture. mathematical theories. |
| gptkbp:is_related_to |
gptkb:Fermat's_little_theorem
gptkb:Mathematics gptkb:Diophantine_equations gptkb:Modular_forms Number theory Mathematical Logic Mathematical Concepts Mathematical Proofs Diophantine Equations Galois Theory Langlands Program Mathematical Theories Algebraic Number Theory Galois Representations Pythagorean triples Fermat's Little Theorem Pythagorean Triples Pythagorean triples. Diophantine equations. Galois theory. Mathematical Frameworks The concept of infinity. The study of algebraic structures. The study of prime numbers. Fermat's principle Fermat's Last Theorem for n=48 Fermat's principle. Fermat's conjecture. Fermat's Last Theorem generalizations Fermat's Last Theorem for n=23. Fermat's theorem. Mathematical Proof Strategies Number Theory Problems Ribet's Theorem Taniyama-Shimura-Weil Conjecture Taniyama-Shimura-Weil conjecture. |
| gptkbp:is_standardized_by |
gptkb:Fermat's_Last_Theorem_for_n=9
gptkb:Fermat's_Last_Theorem_for_n=4 Fermat's Last Theorem for n=5 Fermat's Last Theorem for n=10 Fermat's Last Theorem for n=11 Fermat's Last Theorem for n=12 Fermat's Last Theorem for n=13 Fermat's Last Theorem for n=14 Fermat's Last Theorem for n=15 Fermat's Last Theorem for n=16 Fermat's Last Theorem for n=17 Fermat's Last Theorem for n=18 Fermat's Last Theorem for n=3 Fermat's Last Theorem for n=6 Fermat's Last Theorem for n=7 Fermat's Last Theorem for n=8 |
| gptkbp:is_studied_for |
Its implications in mathematics
|
| gptkbp:is_studied_in |
gptkb:Mathematics
Algebraic geometry Mathematicians algebraic geometry Graduate Programs Mathematical Research Undergraduate Courses Mathematical research Mathematics Departments Mathematics courses Graduate mathematics courses advanced mathematics courses. algebraic geometry. graduate mathematics programs number theory research. mathematical analysis. mathematical courses. Advanced Mathematics Courses. Graduate Programs. Many mathematicians over centuries. Mathematical Research Institutions Mathematicians Worldwide. Number Theory. Students of Mathematics. Graduate mathematics. |
| gptkbp:is_taught_in |
Mathematics Courses
Mathematics courses Advanced mathematics courses Advanced Mathematics Courses. |
| gptkbp:is_tested_for |
mathematical competitions.
Numerous mathematical proofs. |
| gptkbp:issues |
n=3
positive integers equations of the form x^n + y^n = z^n n greater than 2 n=19 n=4 n=43 n=5 |
| gptkbp:led_to |
new mathematical techniques
|
| gptkbp:mathematical_significance |
Led to advancements in modern mathematics.
|
| gptkbp:named_after |
gptkb:Pierre_de_Fermat
gptkb:Fermat |
| gptkbp:originally_conjectured_by |
gptkb:Pierre_de_Fermat
|
| gptkbp:proposed_by |
gptkb:Pierre_de_Fermat
|
| gptkbp:proved_in |
gptkb:1994
|
| gptkbp:proved_in_year |
gptkb:1994
|
| gptkbp:proven_by |
gptkb:Andrew_Wiles
|
| gptkbp:published_in |
gptkb:Annals_of_Mathematics
gptkb:1995 gptkb:The_Annals_of_Mathematics |
| gptkbp:recognized_by |
gptkb:Royal_Society
|
| gptkbp:related_concept |
gptkb:Diophantine_equations
Pythagorean triples |
| gptkbp:related_to |
gptkb:crypt
gptkb:Fermat's_Last_Theorem_for_n=9 gptkb:Fermat's_Last_Theorem_for_n=4 gptkb:Diophantine_equations gptkb:Elliptic_curves gptkb:Modular_forms gptkb:Taniyama-Shimura-Weil_conjecture Number theory Galois theory number theory modular forms Elliptic Curves Modular Forms Fermat's Last Theorem for n=5 Fermat's Last Theorem for n=10 Fermat's Last Theorem for n=11 Fermat's Last Theorem for n=12 Fermat's Last Theorem for n=13 Fermat's Last Theorem for n=14 Fermat's Last Theorem for n=15 Fermat's Last Theorem for n=16 Fermat's Last Theorem for n=17 Fermat's Last Theorem for n=18 Fermat's Last Theorem for n=19 Fermat's Last Theorem for n=20 Fermat's Last Theorem for n=21 Fermat's Last Theorem for n=22 Fermat's Last Theorem for n=23 Fermat's Last Theorem for n=24 Fermat's Last Theorem for n=25 Fermat's Last Theorem for n=26 Fermat's Last Theorem for n=27 Fermat's Last Theorem for n=28 Fermat's Last Theorem for n=29 Fermat's Last Theorem for n=3 Fermat's Last Theorem for n=30 Fermat's Last Theorem for n=31 Fermat's Last Theorem for n=32 Fermat's Last Theorem for n=33 Fermat's Last Theorem for n=34 Fermat's Last Theorem for n=35 Fermat's Last Theorem for n=36 Fermat's Last Theorem for n=37 Fermat's Last Theorem for n=38 Fermat's Last Theorem for n=39 Fermat's Last Theorem for n=40 Fermat's Last Theorem for n=41 Fermat's Last Theorem for n=42 Fermat's Last Theorem for n=43 Fermat's Last Theorem for n=44 Fermat's Last Theorem for n=45 Fermat's Last Theorem for n=46 Fermat's Last Theorem for n=47 Fermat's Last Theorem for n=48 Fermat's Last Theorem for n=49 Fermat's Last Theorem for n=50 Fermat's Last Theorem for n=6 Fermat's Last Theorem for n=7 Fermat's Last Theorem for n=8 Fermat's principle. |
| gptkbp:resulted_in |
Wiles' proof
|
| gptkbp:significance |
one of the most famous problems in mathematics
It is one of the most famous problems in mathematics. solved a problem that remained unsolved for over 350 years. It was a long-standing problem in mathematics. It was a long-standing problem in number theory. |
| gptkbp:special_case |
n=11
n=16 |
| gptkbp:specific_case |
n=3
n=13 n=23 n=7 |
| gptkbp:specifically_for |
n=33
|
| gptkbp:state |
There are no three positive integers a, b, and c that satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2.
no three positive integers a, b, and c can satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2. no three positive integers x, y, and z can satisfy the equation for any integer value of n greater than 2. No three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than 2. There are no three positive integers a, b, and c such that a^n + b^n = c^n for any integer value of n greater than 2. x^n + y^n = z^n has no solutions for n > 2 No three positive integers a, b, and c can satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2. There are no three positive integers a, b, and c that satisfy the equation a^n + b^n = c^n for n greater than 2. |
| gptkbp:was_conjectured_in |
1637
|
| gptkbp:was_involved_in |
Modularity Theorem
n=3 n=10 n=11 n=12 n=13 n=14 n=15 n=16 n=17 n=18 n=19 n=20 n=21 n=22 n=23 n=24 n=25 n=26 n=27 n=28 n=29 n=30 n=31 n=32 n=4 n=5 n=6 n=7 n=8 n=9 |
| gptkbp:was_proven_in |
gptkb:1994
|
| gptkbp:was_proven_using |
Advanced Mathematical Techniques
|
| gptkbp:wiles'_proof |
Collaborated with Richard Taylor.
Involved the use of Galois representations. Published in a series of papers. Used techniques from algebraic geometry. |
| gptkbp:year_proved |
gptkb:1994
|
| gptkbp:year_proven |
gptkb:1994
|
| gptkbp:bfsParent |
gptkb:Andrew_Wiles
|
| gptkbp:bfsLayer |
3
|