>Mathematicians can be subdivided into two types: problem solvers and theorizers. Most mathematicians are a mixture of the two although it is easy to find extreme examples of both types.
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>To the problem solver, the supreme achievement in mathematics is the solution to a problem that had been given up as hopeless. It matters little that the solution may be clumsy; all that counts is that it should be the first and that the proof be correct. Once the problem solver finds the solution, he will permanently lose interest in it, and will listen to new and simplified proofs with an air of condescension suffused with boredom.
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>The problem solver is a conservative at heart. For him, mathematics consists of a sequence of chellenges to be met, an obstacle course of problems. The mathematical concepts required to state mathematical problems are tacitly assumed to be eternal and immutable.
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>Mathematical exposition is regarded as an inferior undertaking. New theories are viewed with deep suspicion, as intruders who must prove their worth by posing challenging problems before they can gain attention. The problem solver resents generalizations, especially those that may succeed in trivializing the solution to one of his problems.
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>The problem solver is the role model for budding young mathematicians. When we describe to the public the conquests of mathematics, our shining heroes are the problem solvers.
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>To the theorizer, the supreme achievement of mathematics is a theory that sheds sudden light on some incomprehensible phenomenon. Success in mathematics does not lie in solving problems but in their trivialization. The moment of glory comes with the discovery of a new theory that does not solve any of the old problems but renders them irrelevant.
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>The theorizer is a revolutionary at heart. Mathematical concepts received from the past are regarded as imperfect instances of more general ones yet to be discovered. Mathematical exposition is considered a more difficult undertaking than mathematical research.
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>Theorizers often have difficulty being recognized by the community of mathematicians. Their consolation is the certainty, which may or may not be borne out by history, that their theories will survive long after the problems of the day have been forgotten.
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>If I were a space engineer looking for a mathematician to help me send a rocket into space, I would choose a problem s
In The Pernicious Influence of Mathematics upon Philosophy, philosopher and mathematician Gian-Carlo Rota argues "that the attempt carried out by certain philosophers in this century to parrot the language, the method, and the results of mathematics has harmed philosophy. Such an attempt results from a misunderstanding of both mathematics and philosophy, and has harmed both subjects."
Given that Rota is reasonably well-known and his criticism is harsh and "very important if accurate", I wonder if there have been any reactions or counter-arguments that are somewhat well-known?
> 'What can you prove with exterior algebra that you cannot prove without it?' Whenever you hear this question raised about some new piece of mathematics, be assured that you are likely to be in the presence of something important. In my time, I have heard it repeated for random variables, Laurent Schwartz’ theory of distributions, ideles and Grothendieck’s schemes, to mention only a few. A proper retort might be: 'You are right. There is nothing in yesterday’s mathematics that could not also be proved without it. Exterior algebra is not meant to prove old facts, it is meant to disclose a new world. Disclosing new worlds is as worthwhile a mathematical enterprise as proving old conjectures.'
-- "Indiscrete Thoughts"
> It takes an effort that is likely to go unrewarded and unappreciated to write an interesting exposition for the lay public at the cutting edge of mathematics. Most mathematicians (self-destructive and ungrateful wretches that they are, always ready to bite the hand that feeds them) turn their noses at the very thought. Little do they realize that in our science-eat-science world such expositions are the lifeline of mathematics.
-- "Indiscrete thoughts"
From Indiscrete Thoughts: "Group theory, like lattice theory, is the whipping boy of mathematicians in need of concealing their feelings of insecurity"
Gian-Carlo Rota, in his book "Indiscrete Thoughts", wrote the following:
"Some subjects can be roughly associated with geographic locations: graph theory is a Canadian subject, singular integrals is an Argentine subject, class field theory an Austrian subject, algebraic topology an American subject, algebraic geometry an Italian subject, special functions a Wisconsin subject, point-set topology a Southern subject, probability a Russian subject."
Two questions: 1) What is he basing this on? Some make sense (Russia:Probability:Kolgomorov) but others I don't understand (Wisconsin:Special Functions:??)
- How does this hold present day? Are there countries/nationalities that have a certain mathematical flavor?
Ward 9 desperately needs better representation moving forward!! I know there is a lot of distain for this guy.
Ward 9 includes the following communities: Albert Park/Radisson Heights, Applewood Park, Belvedere, Bridgeland/Riverside, Dover, Erin Woods, Fairview, Forest Heights, Forest Lawn, Inglewood, Manchester, Ogden, Penbrooke Meadows, Ramsay, Red Carpet, Renfrew, and Southview.
This year the administration of Formula Imola SpA completes its term, therefore on December 21st the company that manages the circuit and its activities has elected its new board which will be in charge from January 1st to December 31st 2023. The president of the board will be Gian Carlo Minardi, the founder of the Scuderia Minardi that competed in F1 from 1985 to 2005; one of the board members will be Aldo Costa, who was a prominent engineer for Ferrari between 1998 and 2011, then for Mercedes between 2012 and 2018, from 2020 he is the chief technical officer of Dallara.
It is believed that this new administration will be closer to ACI, the Italian Automobile Club and national member of the FIA, as Minardi has been the President of Circuit Racing for ACI Sport and also Supervisor of their Racing School; ACI has mostly supported Monza and Monza only for holding F1 Italian Grand Prixs but this might change with this new board.
During the long period in which the previous board was in charge Imola hosted various national and international races and championships of cars and motorbikes; a number of investments were also made including the new permanent medical centre that was completed right before this year's F1 Gran Prix.
