Conjecture math questions. The Collatz Conjecture 8.
Conjecture math questions. If new, relevant conjectures are made, they may be added to this page. How to define inductive reasoning, how to find numbers in a sequence, Use inductive reasoning to identify patterns and make conjectures, How to define deductive reasoning and compare it to inductive reasoning, examples and step by step solutions, free video lessons suitable for High School Geometry - Inductive and Deductive Reasoning Challenging Questions Choose a number. Inductive Reasoning: characterized by drawing a general conclusion (make a conjecture) from repeated observations of specific examples. Conjectures are statements believed to be accurate but have yet to be proven. a) Make a conjecture about the relation between the number you picked and the final result. [13] However, a Mathematics has played a major role in so many life-altering inventions and theories. Hodge Conjecture 6. Or you make a kind of statement, but this is based only on your opinion, or again, guesswork - this is a conjecture once again. 2. The Collatz conjecture[a] is one of the most famous unsolved problems in mathematics. This question, the Poincaré conjecture, was a special case of Thurston’s geometrization conjecture. It is always possible that the next example would show that the conjecture is false. My word-choice is instead to emphasize the fact that the universe of math is so broad and intricate, that I imagine many people have stumbled upon miniature problems which Nov 29, 2022 · Has this weak version of Erdős Conjecture on arithmetic progressions been proven, or is it still an open problem? This question is motivated by Erdős conjecture on arithmetic progressions. Jul 23, 2025 · Collatz Conjecture or 3n + 1 Conjecture or Ulam Conjecture, is the problem in mathematics for almost a decade. There are many unsolved problems in mathematics. You will need to know topics like the definition of conjecture and identifying numbers in a given set. According to the function in which the Collatz Conjecture is defined, all even numbers must necessarily turn into an odd number. So for whatever reason, these puzzling problems have never been solved. How can you use reasoning to solve problems? Recall that conjecture is an unproven statement about a general mathematical concept that is based on observations. The Beal Conjecture 10. What "conjecture" am I supposed to be making? I assume I am trying to find a fact/pattern; something like " points can only be obtained in multiples of 6 ", but I am lost. Conjectures are often based on intuition, observation, or experience, and can provide insights into the nature of mathematical concepts and structures. CMI was founded in 1998 by American businessman Landon T. Then use your conjecture to in th 1 2 3 4 5 6 7 Oct 1, 2025 · From these examples, Arthur made this conjecture: If a convex polygon has n sides, then there are n 2 triangles formed when diagonals are drawn from any vertex of the polygon. What are Conjectures in Geometry Introduction When studying geometry, conjectures play a vital role in developing a deeper understanding of the subject. The Erdős Oct 22, 2023 · How to Master the World of Conjectures and Counterexamples In math, a conjecture is like a smart guess — something we think is true but haven't proven. Birch and Swinnerton-Dyer Conjecture Relates to elliptic curves in number theory May 24, 2000 · The answer to this conjecture determines how much of the topology of the solution set of a system of algebraic equations can be defined in terms of further algebraic equations. Jul 1, 2024 · The Riemann hypothesis is the most important open question in number theory—if not all of mathematics. It is a statement, grounded in observed patterns, numerical evidence, or theoretical insights, that is proposed as potentially true, but lacks definitive proof. Although extensively tested and always found true, this conjecture remains unproven, making it a persistent and enticing mystery in the world of mathematics. Divide by 4. Skewes number. Schinzel's Hypothesis H implies a great many conjectures in prime number theory. What are the possible characteristics of a conjecture and what makes one conjecture more interesting than others? Students should explicitly answer each of the following questions when they seek to evaluate a conjecture: Thus, we need to find a way to determine whether a conjecture is true for ALL possible cases. Definitions Conjecture: an educated guess based upon repeated observations of a particular process or pattern. For other problems, such as the 5th, experts have traditionally agreed on a single interpretation, and a The Poincare conjecture was not deemed interesting because of practical questions -- it won't help you build a more efficient washing-machine, if that's what you're after. Yang-Mills Existence and Mass Gap 7. Sign up now to access Conjectures and Counterexamples in Mathematics materials and AI-powered study resources. Learn more… Top users Synonyms Newest Active Filter Mar 10, 2025 · The Kummer-Vandiver Conjecture One of the unsolved math problems that fascinates me is the Kummer-Vandiver conjecture in number theory. Navier-Stokes Existence and Smoothness 4. Therefore, it math-history collatz-conjecture open-problem user 117 asked Dec 13, 2024 at 16:10 10votes 3answers 2kviews Hilbert's problems ranged greatly in topic and precision. But a good conjecture will guide math forward, pointing the way into the mathematical unknown. If one of the problems is solved and accepted by the mathematics community, then they may be removed. Post comments on them. There are several famous unsolved math problems, including the "Millennium Prize Problems" or "The Seven Millennium Prize Problems" designated by the Clay Mathematics Institute. The Goldbach conjecture. 2 days ago · A conjecture is a mathematical statement that has not yet been rigorously proved. The Millennium Problems are a set of seven unsolved mathematical problems designated by the Clay Mathematics Institute in 2000. A conjecture can be thought of as the mathematicians way of saying “I believe that this is true, but I have no proof yet”. Nov 16, 2023 · In the realm of mathematics, conjectures play a pivotal role in guiding research and shaping our understanding of various mathematical structures and. Mar 25, 2020 · A modern day unsolved problem in mathematics involves a conjecture that has stumped mathematicians for over 80 years. Perelman’s proof tells us that every three manifold is built from a set of standard pieces, each with one of eight well Conjectures and Counter Examples Inductive Reasoning and Conjecture Inductive reasoning is the process of reaching a conclusion based on a pattern of examples. Conjectures arise when one notices a pattern that holds true for many cases. In order to celebrate mathematics in the new millennium, The Clay Mathematics Institute of Cambridge, Massachusetts (CMI) established seven Prize Problems. It looks like a simple, innocuous question, but Jul 23, 2013 · These formulas come with various numbers of free parameters and often have divisibility conditions/constraints associated with them that does not always guarantee correct solutions; especially in the case of the residue classes targeted by Mordell and of most interest in regard to the Erdős–Straus conjecture, that I have listed in the Jul 23, 2025 · Goldbach's Conjecture is one of the oldest unsolved problems in number theory. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1. Sometimes Jul 23, 2010 · 75 The wikipedia article on the Collatz conjecture gives these three examples of conjectures that were disproved with large numbers: Polya conjecture. It goes like this: is every even number greater than 2 the sum of two primes? It sounds obvious that the answer would be yes, after all, 3 + 1 = 4, 5 + 1 = 6 and so on. Should it accompany solid efforts at proof. A counterexample is an example that disproves a conjecture. artifactID: 7520 artifactRevisionID: 26571027 ShowHide Resources In mathematics, the Birch and Swinnerton-Dyer conjecture (often called the Birch–Swinnerton-Dyer conjecture) describes the set of rational solutions to equations defining an elliptic curve. Birch and Swinnerton-Dyer Conjecture The Birch and Swinnerton-Dyer Conjecture is an influential and complex problem in number theory that focuses on elliptic curves. 1. Suppose the statement is true. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include 1. Follow-up activities are provided to further demonstrate meanings and applications of concepts. Conjecture examples serve as the foundation for exploration, encouraging you to question, analyze, and discover new truths. Other equations, however, are simply too large to compute. Basic concepts, conjectures, and theorems found in typical geometry texts are introduced, explained, and investigated. Subtract 2. It would not be reasonable to examine all specific examples for a specific situation, so a more general method was developed to test conjectures. It is an open problem in the field of number theory and is widely recognized as one of the most challenging mathematical problems. b) Can you find a counterexample to your conjecture? What does this imply? Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. The Hodge conjecture is known in certain special cases, e. , when the solution set has dimension less than four. These are considered some of the most significant open questions in mathematics, with a $1 million prize for solving any one of them. [1] These challenges cover a wide range of mathematical disciplines, from number theory to Topology, and solving any one of them would earn the solver a $1 million prize. A conjecture is when a person makes a statement or proposition that seems likely to be true. Assuming students have been given the opportunity to explore a context, have noticed patterns and possible structures, and have worked systematically to generate more examples, they may then be in a position to conjecture, expressing ideas about what they think will happen Jul 5, 2023 · The Goldbach Conjecture The Goldbach Conjecture, formulated by Christian Goldbach in 1742, is a mathematical puzzle that revolves around expressing even numbers as the sum of two prime numbers. Jul 12, 2025 · In the realm of mathematical inquiry, a conjecture represents a pivotal stage bridging intuition and rigorous proof. Yang-Mills existence and mass gap: This problem concerns the existence of quantum Yang-Mills fields with a mass gap, which is essential for the consistent formulation of the quantum field theory. [1][2][3] Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to prove them. The Collatz conjecture is the simplest open problem in mathematics. 06 (Conjectures and Counterexamples - Geometry) . The Collatz Conjecture is the simplest math problem no one can solve — it is easy enough for almost anyone to understand but notoriously difficult to solve. The conjecture may or may not be true. , the conjecture that there are an infinite number of twin home | courses | topics | theorems | starters | worksheets | timeline | KS3 | KS4 | KS5 Conjecture is a kind of guesswork: you make a judgment based on some inconclusive or incomplete evidence and you call it a conjecture. Conjecture is an educated guess made using inductive reasoning. Learn about conjectures in math in 5 minutes! Explore their uses through real-life examples to deepen your understanding of mathematical reasoning, followed by a quiz. Famous mathematicians Paul Erdős said about the Collatz Conjecture, "Mathematics may This page was created to organize all the conjectures and unsolved problems involving prime numbers, listed from highest to least importance. The objective is to ensure that students develop Problems Birch and Swinnerton-Dyer Conjecture Main article: Birch and Swinnerton-Dyer Conjecture The Birch and Swinnerton-Dyer conjecture relates the rank of the abelian group of points over a number field of an elliptic curve to the order of the zero of the associated -function at . 1 EXPLORATION: Writi ite a conjecture about the pattern. And please don't use "we" when you refer only to yourself, for example, when you make a conjecture. An outrageous conjecture is qualified ONLY if: 1) It is most likely false (Being hopeless May 24, 2000 · Poincaré Conjecture In 1904 the French mathematician Henri Poincaré asked if the three dimensional sphere is characterized as the unique simply connected three manifold. A conjecture is a good guess or an idea about a pattern. But that’s useful feedback, because now you can adjust your conjecture and try again! The Universal Learning Structure When students learn to articulate conjectures and break them with counterexamples, they’ve learned a kind of habit that will help them learn math deeply. It says that there is a finite upper bound on the multiplicities of entries in Pascal's triangle (other than the number 1, which appears infinitely many times). GEO. Level up your studying with AI-generated flashcards, summaries, essay prompts, and practice tests from your own notes. Add 6. Let’s examine some of these. This conjecture is a fundamental question in number theory, a branch of mathematics devoted to the study of integers. And the problem appeared both in Nov 11, 2020 · Like most big list questions, please include one conjecture per answer. Whether you’re a student or just someone intrigued by mathematical concepts, understanding these conjectures can open doors to deeper insights. Sep 22, 2020 · Despite recent progress on the notorious Collatz conjecture, we still don’t know whether a number can escape its infinite loop. Illustrated definition of Conjecture: A statement that might be true (based on some research or reasoning) but is not proven. Mathematically it can be expressed as: For every even integer n≥4 there exist primes p and q such that: n = p + q Illustration of Golbach's Conjecture For Example: 4 = 2 + 2 6 = 3 + 3 8 = 3 + 5 10 = 5 + 5 or This concept sheet offers tips for solving a conjecture problem. Mar 7, 2024 · The Collatz conjecture can be worked on by 9-year-old math whizzes, but it's flummoxed some of the greatest minds of the past century. The Riemann Hypothesis The Riemann Hypothesis, proposed by German mathematician Bernhard Riemann in 1859, deals with the Riemann zeta function. Students should re-write their conjectures if their mathematical language is unnecessarily confusing. Nov 12, 2020 · Will 1/21 and 1/28 have the same digits too? Conjecture: 1/ (7n) will always have the same 6 digits repeating in some order. Which conjecture, - Studocu Information AI Chat May 24, 2000 · Birch and Swinnerton-Dyer Conjecture Supported by much experimental evidence, this conjecture relates the number of points on an elliptic curve mod p to the rank of the group of rational points. Atiyah conjecture (not a conjecture to start with) Borsuk's conjecture Chinese hypothesis (not a conjecture to start with) Doomsday conjecture Euler's sum of powers conjecture Ganea conjecture Generalized Smith conjecture Hauptvermutung Hedetniemi's conjecture, counterexample announced The classification of closed surfaces gives an affirmative answer to the analogous question in two dimensions. The conjecture has been shown to hold for all even integers less than 4 × 1018, but remains unproven despite considerable effort. The conjecture connects the Math Questions Inductive and Deductive - Inductive and Deductive Reasoning ____ 1. The twin prime conjecture (i. They represent some of the most profound and perplexing questions in mathematics, captivating This page has been designed to provide an interactive technological resource for students studying elementary high school geometry. For questions about Goldbach's conjecture: every even integer greater than two is the sum of two primes. The Riemann hypothesis. A . However, just because a pattern holds true for many cases does not mean that the pattern will hold true for all cases. P vs NP Problem 3. If you want to understand why people care about the Poincare conjecture you should start with a more elementary question "why do people care about manifolds?" Dec 28, 2023 · These ten brutally difficult math problems once seemed impossible until mathematicians eventually solved them—even if it took them years, decades, or centuries. It is like a hypothesis, Q&A for professional mathematiciansThe Collatz Conjecture, also known as the 3n+1 conjecture, is a famous open problem named after Lothar Collatz. Clay “to increase and disseminate mathematical knowledge. g. The abc-conjecture tag has no summary. Create and edit open problems pages (please contact us and we will set you up an account. My questions is - Why is Kurepa's conjecture, also known as the Left Factorial Hypothesis, so less commonly known and relatively less studied in the field of Number Theory and mathematics as a whole? Conjecture plays an important role in mathematics, as it often serves as a starting point for further investigation and discovery. The Twin Prime Conjecture 9. This video is sponsored by Brilliant. The Goldbach Conjecture is considered to be one of the hardest math problems. ) Help us Grow! We are eager to expand, so we are inviting Jun 7, 2023 · Edit: After discussing the reasons for past-closure on meta here, it's come to my attention that some have interpreted this question to put emphasis on the fact that these conjectures are yours, which is not the point. It is called deductive reasoning. Feb 19, 2023 · Schanuel's Conjecture implies a great many known theorems and open conjectures in transcendence theory. It states that every even natural number greater than 2 is the sum of two prime numbers. Numerous examples may make you believe a conjecture. So what is the Collatz Conjecture and what makes it so difficult? Veritasium investigates. The only even prime is 2, so Q&A for professional mathematiciansfor question related to conjectures. In this guide, we'll look at these two ideas, breaking them down in easy-to-understand terms. The Riemann Hypothesis 2. There are many unanswered questions in Number Theory. Erdős conjecture on arithmetic progressions Aug 21, 2024 · There were several announcements about the final solution of Kurepa’s conjecture, even papers with incorrect proof were proposed. ” The conjecture describes Feb 11, 2021 · If you can’t, then something’s probably off with your conjecture. ” The seven problems, which were announced in 2000, are the Riemann hypothesis, P versus NP problem, Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier-Stokes equation, Yang-Mills theory, and Poincaré conjecture. I had a quick question about the Collatz Conjecture. In mathematics, a conjecture is a proposition that is proffered on a tentative basis without proof. It is a weaker version of Erdős Conjecture, but I do not know how to prove it. May 7, 2019 · Prove that your conjecture is true. This worksheet and quiz will test what you know about conjectures in math. Double it. For dimensions greater than three, one can pose the Generalized Poincaré conjecture: is a homotopy n -sphere homeomorphic to the n -sphere? A stronger assumption than simply-connectedness is necessary; in dimensions four and higher there are simply-connected, closed manifolds which Lori Jordan Andrew Gloag Victor Cifarelli Jim Sconyers Bill Zahner Difficulty Level Basic 10 , 8 , 9 Date Created: Last Modified: Subjects: mathematics Geometry Tags: conjecture counterexample English Concept Nodes: MAT. It states the following Every even integer greater than 2 can be expressed as the sum of two prime numbers. Conjectures and Counterexamples A conjecture is an “educated guess” that is based on examples in a pattern. Birch and Swinnerton-Dyer Conjecture 5. The Collatz conjecture states that all paths eventually lead to 1. It states that every even integer greater than 2 can be expressed as a sum of two primes. If someone finds an example that shows the guess is wrong, that's a counterexample. From these examples, Arthur made this conjecture: If a convex polygon has n sides, then there are n 2 triangles formed when diagonals are drawn from any vertex of the polygon. It has occupied experts for more than 160 years. Double again. Oct 17, 2023 · The Twin Prime Conjecture posits that there are infinitely many such pairs. 6 days ago · Q&A for people studying math at any level and professionals in related fields Aug 4, 2011 · What are the basic things (about when and how) to be kept in mind while proposing a conjecture in Mathematics. Subtract 4. The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture at the The Collatz Conjecture is the simplest math problem no one can solve — it is easy enough for almost anyone to understand but notoriously difficult to solve. Here you may: Read descriptions of open problems. You may be proved right or wrong. Welcome to the Open Problem Garden, a collection of unsolved problems in mathematics. The Prizes were conceived to record some of the most difficult problems with which mathematicians were grappling at the turn of the second millennium; to elevate in the consciousness of the general public the fact […] Oct 9, 2024 · After German mathematician Gerd Faltings proved the Mordell conjecture in 1983, he was awarded the Fields Medal, often described as the “Nobel Prize of Mathematics. It's a bit like playing a detective game in mathematics. In this blog, we will explore what conjectures are in geometry Singmaster's conjecture is a conjecture in combinatorial number theory in mathematics, named after the British mathematician David Singmaster who proposed it in 1971. Will it ever be solved? Jan 29, 2025 · Riemann hypothesis: This is a conjecture about the distribution of prime numbers and is one of the most famous open problems in mathematics. If p and q have an odd di erence, then they have di erent parity, so one of them is even. The conjecture that there exists a Hadamard matrix for every positive multiple of 4. Think of it as a hypothesis in the scientific method, but operating within the abstract, […] Jan 18, 2017 · The purpose of this question is to collect the most outrageous (or ridiculous) conjectures in mathematics. 201. But what A conjecture may be difficult to understand because of the way it is written or because the mathematics involved is inherently complicated. Some of them, like the 3rd problem, which was the first to be solved, or the 8th problem (the Riemann hypothesis), which still remains unresolved, were presented precisely enough to enable a clear affirmative or negative answer. Elliptic curves, defined by cubic equations in two variables, are fundamental mathematical objects that arise in many areas: Wiles’ proof of the Fermat Conjecture, factorization of numbers into Jan 26, 2018 · Goldbach's conjecture Similar to the Twin Prime conjecture, Goldbach's conjecture is another famous and seemingly simple question about primes. 4. We would like to show you a description here but the site won’t allow us. Sep 23, 2021 · Prime numbers are one of the most basic topics of study in the branch of mathematics called number theory. Unfortunately, the automatic process is too prone to spammers at this moment. Oct 14, 2024 · A new proof about prime numbers illuminates the subtle relationship between addition and multiplication — and raises hopes for progress on the famous abc conjecture. In mathematics, a conjecture is a mathematical statement which appears to be true, but has not been formally proven. You may have heard of Collatz Conjecture, as it recently has gotten some press due to Terence Tao working on the problem, and surprisingly making some progress! Yet, it’s simple enough to explore with a 2nd grader or maybe Q&A for professional mathematiciansThe Collatz Conjecture, also known as the 3n+1 conjecture, is a famous open problem named after Lothar Collatz. But there are still some math equations that have managed to elude even the greatest minds, like Einstein and Hawkins. There exist prime numbers p and q such that p q = 513: False. Oct 31, 2020 · Sometimes one needs to mention questions in an article, which are also answered in the article, and mentioning a question as an open question is a good way to contrast this kind of question from the former. Not only is the focus on questions and conjecture much more alive than math, students who have this kind of experience will retain a much deeper and robust understanding of what’s actually true. They are as follows: Goldbach's conjecture: Can every even integer greater than 2 be written as the The conjectures in following list were not necessarily generally accepted as true before being disproved. Dec 8, 2023 · The Conjecture lives in the math discipline known as Dynamical Systems, or the study of situations that change over time in semi-predictable ways. Most of the big list questions have many answers, so, for the sake of convenience of the reader who wants to read all the answers, I am including the answers: Goldbach's conjecture. These problems were characterised in his speech as "unattackable at the present state of mathematics" and are now known as Landau's problems. Counterexample is an example that shows a conjecture is incorrect. Edmund Landau, German mathematician At the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime numbers. But in dimension four it is unknown. I only managed to find that the two provided numbers, 6 and 13, are relatively prime. 3. However, no number of examples can actually prove a conjecture. Mertens conjecture. It explains how to prove, complete and formulate a conjecture. Inductive reasoning is a logical process in which multiple premises, all believed true or found true most of the time, are combined to obtain a specific conclusion. The Collatz Conjecture 8. Nov 17, 2016 · The definition of conjecture on google says that: A conjecture is an opinion or conclusion formed on the basis of incomplete information. May 7, 2019 · It’s an educated guess, not a proof. They serve as starting points for further investigation and the formulation of mathematical theorems. e. Jul 23, 2025 · Table of Content Introduction Why It's Important to Solve These Problems The Top 10 Unsolved Mathematical Problems 1. Algebraic Conjectures Make a conjecture about the sum of the squares of two consecutive natural numbers For questions related to conjectures which are suspected to be true due to preliminary supporting evidence, but for which no proof or disproof has yet been found Oct 1, 2025 · Conjectures and Counterexamples A conjecture is an “educated guess” that is based on examples in a pattern. You can explain it to all your non-mathematical friends, and even to small children who have just learned to divide by 2. 23 The conjecture in question can also be thought of as the $4$ -dimensional PL Poincare conjecture (because low-dimensional PL manifolds, including those of dimension $4$, carry a unique smooth structure) and this is how it is understood in most references mentioned below. When should any one think of proposing a Of the original seven Millennium Prize Problems listed by the Clay Mathematics Institute in 2000, six remain unsolved to date: [6] Birch and Swinnerton-Dyer conjecture Hodge conjecture Navier–Stokes existence and smoothness P versus NP Riemann hypothesis Yang–Mills existence and mass gap The seventh problem, the Poincaré conjecture, was solved by Grigori Perelman in 2003. Now the question which is stuck in my mind is: What is the use of conjectures in modern mathematics?" Are they used in problem solving as we use theorems/lemma? The generalized Riemann hypothesis can be used to prove many open questions in number theory, including Artin's conjecture on primitive roots and the so-called weak Goldbach conjecture that every odd prime greater than 5 is the sum of three odd primes. It is proposed in 1937 by Lothar Collatz. Mathematicians are not only interested in answering questions, they also pose questions, make conjectures and test ideas. npi5lw 5ga5 gfd xoh lvr 2piomr 0mda2 ohth 6hl vieh