What are the latest discoveries in mathematics
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Answer:
10. Mochizuki’s claimed proof of the abc conjecture. The countdown kicks off on an awkward note. If Shinichi Mochizuki’s 2012 claimed proof of the abc conjecture had gained widespread acceptance, it would definitely top this list. As it is, it remains in limbo, to the enormous frustration of everyone involved.
9. The weak Goldbach conjecture. “From 7 onwards, every odd number is the sum of three primes.” We have known since 1937 that this holds for all large enough odd numbers, but in 2013 Harald Helfgott brought the threshold down to 1030, and separately with David Platt checked odd numbers up to that limit by computer.
8. Ngô Bảo Châu’s proof of the Fundamental Lemma. Bending the rules to scrape in (time-wise) is this 2009 proof of a terrifyingly technical but highly important plank of the Langlands Program.
7. Seventeen Sudoku Clues. In 2012, McGuire, Tugemann, and Civario proved that the smallest number of clues which uniquely determine a Sudoku puzzle is 17. (Although not every collection of 17 clues yields a unique solution, their theorem establishes that there can never be a valid Sudoku puzzle with only 16 clues.)
6. The Growth of Univalent Foundations/ Homotopy Type Theory. This new approach to the foundations of mathematics, led by Vladimir Voevodsky, is attracting huge attention. Apart from its inherent mathematical appeal, it promises to recast swathes of higher mathematics in a language more accessible to computerised proof-assistants.
5. Untriangulatable spaces. In sixth position is the stunning discovery, by Ciprian Manolescu, of untriangilatable manifolds in all dimensions from 5 upwards.
4. The Socolar–Taylor tile. Penrose tiles, famously, are sets of tiles which can tile the plane, but only aperiodically. It was an open question, for many years, whether it is possible to achieve the same effect with just one tile. Then Joan Taylor and Joshua Socolar found one (pictured above).
3. Completion of the Flyspeck project. In 1998, Thomas Hales announced a proof of the classic Kepler conjecture on the most efficient way to stack cannon-balls. Unfortunately, his proof was so long and computationally involved that the referees assigned to verify it couldn’t complete the task. So Hales and his team set about it themselves, using the Isabelle and HOL Light computational proof assistants. The result is not only a milestone in discrete geometry, but also in automated reasoning.
2. Partition numbers. In how many ways can a positive integer be written as a sum of smaller integers? In 2011, Ken Ono and Jan Bruinier provided the long-sought answer.
1. Bounded gaps between primes. It’s no real surprise to find that the top spot is taken by Yitang Zhang’s wonderful 2013 result that there is some number n, below 70 million, such that there are infinitely many pairs of consecutive primes exactly n apart. The subsequent flurry of activity saw James Maynard, and a Polymath Project organised by Terence Tao, bring the bound down to 246.
Step-by-step explanation:
The 10 Biggest Math Breakthroughs of 2019
Progress on the Riemann Hypothesis. Creative Commons. ...
The Sum of Three Cubes. Andrew Daniels. ...
The Collatz Conjecture. ...
The Sensitivity Conjecture. ...
A Great Year for Cancer Research. ...
Kirigami Gets Mathematized. ...
The Sunflower Conjecture. ...
A Breakthrough in Ramsey Theory.