Theorem example sentences

"Theorem" Example Sentences

1. Pythagoras' theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
2. Conservation of energy is a fundamental theorem of physics.
3. According to Bayes' theorem, the conditional probability of A given B can be calculated from the probability of B given A.
4. Euclid wrote down the first theorems in geometry over two millennia ago.
5. The fundamental theorem of calculus relates differentiation and integration.
6. The Goldbach's conjecture, if proven, would become the Goldbach's theorem.
7. The mathematician spent years trying to prove his revolutionary new theorem.
8. Fermat's last theorem remained unsolved for over 350 years.
9. Complex analysis relies heavily on Cauchy's integral theorem.
10. Archimedes proved many geometric theorems during his lifetime.
11. The proof of the Riemann hypothesis would resolve many important number theoretic conjectures.
12. The four color theorem states that no more than four colors are needed to color any map.
13. Maxwell's equations form the foundation of electromagnetism and are truly remarkable theorems.
14. Newton's laws of motion are powerful yet simple theorems that describe the fundamentals of mechanics.
15. The Banach–Tarski paradox seems to disprove some of the intuitive notions in geometry.
16. Central limit theorem provides a framework for drawing statistical inferences.
17. The mathematician spent years developing a proof for her new graph theory theorem.
18. The law of detachment is a fundamental theorem of deductive logic.
19. The normal distribution arises from the De Moivre–Laplace theorem.
20. Liouville's theorem places restrictions on the existence of certain differential equations.
21. The Pythagorean theorem is one of the most well-known theorems in mathematics.
22. The Noether's theorem links symmetries to conservation laws in physics.
23. The weak law of large numbers was a precursor to the strong law of large numbers.
24. The fundamental theorem of arithmetic states that every integer has a unique prime factorization.
25. In projective geometry, Desargues' theorem reveals a deep relationship between conics.
26. The parallel postulate was an attempt to fill gaps in Euclid's other axioms and theorems.
27. The mathematician gave a compelling two hour lecture detailing his new mathematical theorem.
28. Stokes' theorem provides a generalization of several other theorems involving calculus.
29. Boolean algebra relies heavily on De Morgan's theorems.
30. Euler's formula is a mathematical theorem relating the trigonometric functions and the complex exponential function.
31. Modern algebra deals extensively with group theory and ring theory, two fundamental branches of abstract algebra.
32. The Pythagorean theorem enabled the ancient Greeks to tackled geometric problems involving right triangles.
33. The mathematician's conjecture turned into a widely accepted mathematical theorem after the breakthrough proof.
34. The fundamental theorems of calculus revolutionized mathematics and physics.
35. Bezout's theorem places an upper bound on the number of solutions to a system of polynomial equations.
36. The decidability theorem states that first-order logic is decidable.
37. Green's theorem and Stokes' theorem are closely related results in vector calculus.
38. The probability theorem provides a powerful mathematical tool for modeling random events.
39. The twin prime conjecture remains an unsolved mathematical problem despite many attempts to prove it as a theorem.
40. The pidgeonhole principle is an example of a combinatorial theorem.
41. The mathematician dedicated his life's work to proving one elusive mathematical theorem.
42. Gödel's incompleteness theorems shook the foundations of mathematical logic.
43. L'Hôpital's rule is a useful theorem in calculus for evaluating limits involving indeterminate forms.
44. Euler's theorem states that for any coefficient θ , there exists an integer n such that eiθ = cosθ + isinθ .
45. The binomial theorem provides an expansion of the power of a binomial.
46. The theorem had eluded mathematicians for decades before its groundbreaking proof was discovered.
47. The inclusion–exclusion principle is a useful counting theorem.
48. The mathematician's theorem will revolutionize the entire field of number theory if proven correct.
49. Descartes' theorem links the area of a polygon to its polar moment of inertia.
50. The axiom of choice is a rather counterintuitive theorem in set theory.
51. Cantor's theorem states that the set of all subsets of a set has higher cardinality than the original set.
52. The mathematician spent years developing an elegant proof for an important theoretical physics theorem.
53. The final value theorem relates the Laplace transform of a function to its limit as time approaches infinity.
54. Liouville's theorem states that bounded entire functions must be constants.
55. The extreme value theorem establishes the existence of minimum and maximum values for continuous functions.
56. Dirichlet's unity theorem deals with sums of unity roots.
57. Rochlin's theorem places constraints on embeddings in 3-manifolds.
58. The standard form of a quadratic equation arises from the proof of the quadratic formula.
59. Bézout's theorem establishes an upper bound on the number of solutions to systems of polynomial equations.
60. The Compactness theorem is a fundamental result in mathematical logic.

Common Phases

1. Pythagoras's theorem states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the two other sides.
2. The fundamental theorem of calculus links the concepts of differential calculus and integral calculus.
3. According to Newton's second law of motion, the rate of change of momentum is directly proportional to the applied force.
4. According to Pascal's principle, pressure exerted anywhere in a confined incompressible fluid is transmitted undiminished to all parts of the fluid.
5. Archimedes' principle states that the buoyant force on an object is equal to the weight of the fluid it displaces.
6. Fermat's last theorem was first conjectured in 1637 and finally proved in 1994 by Andrew Wiles.
7. Bernoulli's principle describes the motion of fluids based on the conservation of energy.
8. The Great Pyramid Theorem was a mathematical puzzle originally proposed by Andrew Gleason.
9. The Pythagorean theorem is used in various domains of mathematics, physics, and engineering.
10. The mathematicians set to work proving the newly proposed theorem.
11. The proposed conjecture remained unproven for centuries before it was finally established as a theorem.
12. The mathematician spent years attempting to prove the difficult theorem.
13. The student struggled to understand the complex theorem presented by the professor.
14. The theorist presented his latest theorem on particle physics at the conference.
15. Mathematicians heavily debated the conjecture before it became an accepted theorem.
16. She proved the theorem using novel algebraic techniques.
17. I learned several geometry theorems in my high school class.
18. They invoked Gödel's incompleteness theorem during the philosophical discussion.
19. The Goldbach conjecture remained unproven but is widely believed to be true despite lacking the status of a mathematical theorem.
20. The proof of the theorem relied on several previously established lemmas.
21. The problem was tackled using Brownian motion, an approach that finally led to a proof of the famous theorem.
22. The lecture focused on the history and applications of Pythagoras's famous triangle theorem.
23. The Little Theorem of Fermat states that if p is a prime number and a is an integer not divisible by p, then a^p - a is divisible by p.
24. She won the Fields Medal for her brilliant proof of the ABC conjecture, establishing it as a mathematical theorem.
25. He gave a rigorous proof of the demanding number theory theorem.
26. The celebrated axiom—theorem—proof pattern of mathematics fosters creativity and rigor.
27. Euler's theorem states that if n and φ(n) are relatively prime integers, then n^φ(n) − 1 is divisible by φ(n).
28. Complex analysis theorems allow us to compute integrals that are difficult to evaluate directly.
29. The Euclidean parallel postulate led to the development of non-Euclidean geometries after initial attempts to prove it as a theorem failed.
30. The fundamental theorem of arithmetic says that every integer greater than 1 is either a prime number itself or a product of prime numbers.
31. The probabilistic method has been used to prove many theorems in combinatorics and computer science.
32. The century-old theorem had provoked heated debates among leading mathematicians for decades.
33. A proof is the verification of a mathematical theorem.
34. The Hilbert–Waring theorem concerns representing integer numbers as the sum of powers.
35. He produced an elegant counterexample disproving the widely accepted conjecture, dashing the hopes of establishing it as a theorem.
36. One of the most famous problems in mathematics, Fermat's Last Theorem remained unproven for over 350 years.
37. Ramanujan's notebooks contain many unproven theorems and insights that have since been formally proved by mathematicians.
38. The Law of Large Numbers is a fundamental theorem in probability theory.
39. The four color theorem states that any map in a plane can be colored using no more than four colors in such a way that no two adjacent regions shares the same color.
40. The fundamental concept of understanding a theorem lies in being able to prove it.
41. The prime number theorem describes the asymptotic distribution of prime numbers among the integers.
42. She worked for years in an effort to prove the famous Goldbach conjecture and elevate it to the status of a mathematical theorem.
43. The probability of an event equals the limit of its relative frequency in a large number of trials, according to the law of large numbers theorem.
44. Bayes' theorem in statistics relies on conditional probability to calculate the probability of a hypothesis.
45. The number of proofs for a particular mathematical theorem is virtually infinite.
46. The proof by contradiction is a powerful technique used in proving mathematical theorems.
47. The century-old conjecture finally yielded to a brilliant proof by a young mathematician, establishing it as a celebrated theorem.
48. The proof of a theorem often relies on proving simpler lemmas first.
49. Attempts to prove Fermat's Last Theorem spanned over three centuries before a proof was finally found.
50. The Chinese Remainder Theorem allows solving a system of congruence equations.
51. The twin prime conjecture remains an unsolved problem but, if proven, would become a theorem.
52. The mathematician lectured on her pioneering proof of an important mathematical theorem.
53. The Poincaré conjecture took over 100 years to prove and transform into a mathematical theorem.
54. Witt's theorem was developed in the middle of the 20th century and has many applications in mathematics.
55. The Banach–Tarski paradox defies intuitions of congruence and measure but remains a mathematical theorem.
56. The mathematician brilliantly proved the mind-boggling Goldbach conjecture, transforming it into a well-established theorem.
57. Euler's work contains many important theorems, formulas, and mathematical insights.
58. The mathematician's proof of the famous theorem earned him widespread acclaim and made him famous overnight.
59. Her unorthodox approach led to a novel proof of the Pythagorean theorem and a related geometry insight.
60. The prime number theorem provides an important framework for understanding the distribution of prime numbers.