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Learn How to Solve Math Problems with Step-by-Step Videos

Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations. Some problems belong to more than one discipline and are studied using techniques from different areas. Prizes are often awarded for the solution to a long-standing problem, and some lists of unsolved problems, such as the Millennium Prize Problems, receive considerable attention.

This list is a composite of notable unsolved problems mentioned in previously published lists, including but not limited to lists considered authoritative. Although this list may never be comprehensive, the problems listed here vary widely in both difficulty and importance.

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Various mathematicians and organizations have published and promoted lists of unsolved mathematical problems. In some cases, the lists have been associated with prizes for the discoverers of solutions.

Our free math worksheets cover the full range of elementary school math skills from numbers and counting through fractions, decimals, word problems and more. All worksheets are printable files with answers on the 2nd page.

Dave Linkletter is a Ph.D. candidate in Pure Mathematics at the University of Nevada, Las Vegas. His research is in Large Cardinal Set Theory. He also teaches undergrad classes, and enjoys breaking down popular math topics for wide audiences.

In order to celebrate mathematics in the new millennium, The Clay Mathematics Institute of Cambridge, Massachusetts (CMI) established seven Prize Problems. 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 that in mathematics, the frontier is still open and abounds in important unsolved problems; to emphasize the importance of working towards a solution of the deepest, most difficult problems; and to recognize achievement in mathematics of historical magnitude.

The prizes were announced at a meeting in Paris, held on May 24, 2000 at the Collège de France. Three lectures were presented: Timothy Gowers spoke on The Importance of Mathematics; Michael Atiyah and John Tate spoke on the problems themselves.

Following the decision of the Scientific Advisory Board, the Board of Directors of CMI designated a $7 million prize fund for the solutions to these problems, with $1 million allocated to the solution of each problem.

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It is of note that one of the seven Millennium Prize Problems, the Riemann hypothesis, formulated in 1859, also appears in the list of twenty-three problems discussed in the address given in Paris by David Hilbert on August 9, 1900.

If it is easy to check that a solution to a problem is correct, is it also easy to solve the problem? This is the essence of the P vs NP question. Typical of the NP problems is that of the Hamiltonian Path Problem: given N cities to visit, how can one do this without visiting a city twice? If you give me a solution, I can easily check that it is correct. But I cannot so easily find a solution.

Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems.The motivation for starting Project Euler, and its continuation, is to provide a platform for the inquiring mind to delve into unfamiliar areas and learn new concepts in a fun and recreational context.

The intended audience include students for whom the basic curriculum is not feeding their hunger to learn, adults whose background was not primarily mathematics but had an interest in things mathematical, and professionals who want to keep their problem solving and mathematics on the cutting edge.

Currently we have1039318 registered members who have solved at least one problem, representing 220 locations throughout the world, and collectively using 111 different programming languages to solve the problems.

The problems range in difficulty and for many the experience is inductive chain learning. That is, by solving one problem it will expose you to a new concept that allows you to undertake a previously inaccessible problem. So the determined participant will slowly but surely work his/her way through every problem.

Have you ever wondered how math is used by scientists to make their discoveries?This resource offers over 1000 math problems that reveal the many waysmath and science work together to help us understand the universe. For more on this program, see the NASA press release at:[Press Release] Featured Books This book features innovative smart device-based experiments for elementary, middle and high school students along with relevant NGSS standards. Format: 151 pages, 25 experiments, 30 math problems, 85 illustrations, 3.1 Mby, PDF [Click here] This book supports the James Webb Space Telescope and is designed for high school students exploring infrared light and how astronomers use it to investigate a variety of objects. Format: 115 pages, 12 experiments, 29 math problems, 66 illustrations, 2.8 Mby, PDF [Click here] Search the entire 700-problem archive Follow this link to the page where you can perform a full keyword search on all 700 problems to find the one that exactly suits your needs for a specific science and math topic! SEARCH THE ARCHIVE Math problems sorted by space science topic Here you will find hundreds of math problems related to all of the major astronomical objects from asteroids and planets to galaxies and black holes! Click on the topic below to see which problems are available. Earth Moon Sun Planets Stars Universe Space Travel Astrobiology Black Holes Math problems sorted by grade level If you are a teacher or just someone who enjoys mathematics challenges, these problems cover space science topics but are sorted more-or-less by the kinds of mathematics you will encounter from simple counting and fractions problems through calculus. Click on the grade bands below to see the collections of problems.Grades 3-5 Grades 6-7 Algebra 1 Algebra 2 Geometry Calculus Math problems sorted by NASA Mission If you are looking for math problems specific to a particular mission's investigations, here you will find problems organized by NASA mission name. Click on the mission or program name in the grid below to go to the associated problem listing.

ACE Cassini Chandra Dawn Deep Impact Fermi GALEX Grail Hinode Gravity Probe-B Hubble IBEX IMAGE InSight Juno Kepler LADEE Landsat Lunar Orbiter LRO Manned Space Program MMS Curiosity Mars Rovers" MESSENGER NEAR New Horizons RHESSI SAGE-III SCOOL SOHO SDO Solar Probe Plus Spitzer STEREO Terra THEMIS TRACE Van Allen Belts Probe Webb Space Telescope WISE WMAP XMM Math problems sorted by Engineering Topics If you are looking for math problems related to engineering topics, here you will find problems organized by topic areas. Click on the topic in the grid below to go to the associated problem listing.

Design Issues Rocketry, Launches, and Launch Vehicles Telescopes and Remote Sensing Properties of Orbits Data and Telemetry Mission Planning Spacecraft Design Math problems related to NASA press releases If you enjoy hearing about the many space science discoveries made by NASA missions, here are problems derived from a variety of press releases covering most NASA missions. [Enter here]

Quantitative reasoning is one area in which language models still fall far short of human-level performance. Solving mathematical and scientific questions requires a combination of skills, including correctly parsing a question with natural language and mathematical notation, recalling relevant formulas and constants, and generating step-by-step solutions involving numerical calculations and symbolic manipulation. Due to these challenges, it is often believed that solving quantitative reasoning problems using machine learning will require significant advancements in model architecture and training techniques, granting models access to external tools such as Python interpreters, or possibly a more profound paradigm shift.

To promote quantitative reasoning, Minerva builds on the Pathways Language Model (PaLM), with further training on a 118GB dataset of scientific papers from the arXiv preprint server and web pages that contain mathematical expressions using LaTeX, MathJax, or other mathematical typesetting formats. Standard text cleaning procedures often remove symbols and formatting that are essential to the semantic meaning of mathematical expressions. By maintaining this information in the training data, the model learns to converse using standard mathematical notation.

We also evaluated Minerva on OCWCourses, a collection of college and graduate level problems covering a variety of STEM topics such as solid state chemistry, astronomy, differential equations, and special relativity that we collected from MIT OpenCourseWare.

While machine learning models have become impressive tools in many scientific disciplines, they are often narrowly scoped to solve specific tasks. We hope that general models capable of solving quantitative reasoning problems will help push the frontiers of science and education. Models capable of quantitative reasoning have many potential applications, including serving as useful aids for researchers, and enabling new learning opportunities for students. We present Minerva as a small step in this direction. To see more samples from Minerva, such as the one below, please visit the interactive sample explorer!

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