Science is the art of expressing the complex in simple words.
Mathematics studies the forms of reasoning,
quantitative as well as qualitative.
Mathematics consists in provable counting.
Mathematics is the science of the infinitude of abilities
of Homo finitus.
Mathematics is mostly a humanitarian science or, in other words, an
unnatural science. The definitive particularity of mathematics
is the desire of complete elimination of anything human.
Mathematics is not a divine gift. Mathematics is a human enterprise,
challenge, and endeavor.
Poincaré said that
mathematics is the art of giving the
same name to different things. It follows that
a few different names may be given to the same thing.
This is a trap for laymen: to invent new names for old things is
The mathematician seeks for common features of different things.
The grifter makes different things look alike.
Farfetched is any comparison between mathematics and physics or
Science is “supersensible,” implying that its
content cannot be wholly revealed without man.
Science is the soul of freedom and the harbor of free speech.
Nature will remain after the extinction of mankind. However,
gone for ever will be the “supersensible” human culture
that lies beyond material objects or is implanted in them
by man. This is how science will disappear, demonstrating its
Leadership and command have different
functions in science.
The leader paves ways, and the boss is needed for justice.
No leader must be just, and nobody needs an unjust boss.
Situation is much more intricate beyond science.
The boss must take final decisions, like
who endorsed the resolution:
“The Moon is firm.”
Science is not a trade but a service.
Science serves truth rather than justice.
Science is the logistics of knowledge and the art of decision making.
There is a chasm of estrangement between science and power.
Power confronts freedom which is the essence of mathematics and
The renegades of science lick the vertical of power.
Mediocrity hates talent deeply and passionately,
while lavishing all kinds of hindrance and obstacle to erect.
The academic community nurtures its own undertakers,
considering mediocrity harmless.
Shame goes to the academic community that
relinquishes the freedom of self-control.
Each scientist carries his own source of degradation of science.
Self-assurance, myopia, and senility are symptoms of academic provincialism.
The ideal academic community consists of the scientists by belief, i.e.,
the persons who consider the principles of science as imperatives.
Science enrolls common persons, each of which turns into a scientist by belief
from time to time.
These short epiphanies are the crux, essense, and value of life in science.
Schools and only schools make the people of science into scientists by belief.
The academic community is alive while there is a developing science.
Since quite a few can change science, the power of
the academic community is other than zero.
Great science tends to vanish and never resurrect in the history of particular
nations. Ancient Greece and Nazi Germany exhibited notorious examples.
If we fail to preserve science in Russia now, it
would possibly vanish for ever.
Science is propelled by inevitable theories and inevitable
problems. The great scientists propounded not only inevitable
theories and addressed not only inevitable problems.
However, only inevitable theories and inevitable problems
had made these scientists great.
What problems are more important—solved or unsolved? This is an example
of an ostensibly intelligent question that is incorrect to some extent.
Search of an answer seems to belong to philosophy.
However, we—the scientists of the chalk and
computer—are not adverse to the love of wisdom.
The above question might be a reason for
stopping and looking from aside at one's own life and work.
Reflection is a philosopher's bread which is edible
to us, the common persons of utilitarian specifics.
We know theorems of a genius whereas there are no evil theorems.
However, ingenious theories and experiments coexist in the
history of mankind with misanthropic theories and
vivisection. Science alienates villainy.
Evil is the stigma of pseudoscience.
Science serves. Pseudoscience dissolves.
Pseudoscience is more attractive than science.
Precaution must be exercised.
Science dislikes subjectivity and vanity from the times
Ecclesiastes. Far from haphazard is the idea of a scientist
living in an ebony or ivory tower.
Sexism pertains to personal inclinations. It is not a grammatical issue.
Service to science posed to man a highly intractable problem
of destroying his subjectivity. The subject destroying his
own subjectivity is the image that might inspire the
Rhodes sculptors of
Man is gifted and lazy to the utmost degree.
Talent lives in every body; genius, in a few.
Lenity is the mother of mediocrity.
Banality is the produce of mediocrity.
Every professor likes knowledge. The old professor prefers old knowledge;
and the young professor, new knowledge. This leads to
disharmony in education.
The researcher esteems novelty. The naturalist adores discoveries.
The employee of science respects publication, and the scientist
likes that which makes him wiser.
Homo vulgaris, a biological man, does not change in the sense that
he never transfers the acquired traits to his descendants.
Homo vulgaris is simple-minded and wily.
Homo socialis, a social man, transfers his skills and knowledge.
Homo socialis is selfless and optimistic.
Homo vulgaris is mortal. Homo socialis is not eternal,
but capable of resurrection and immortality.
Homo vulgaris is the ideal of Nietzsche.
Homo socialis is the descendant of
Ego is the measure of Homo vulgaris.
The measure of Homo socialis is personality.
Superficiality and thoughtlessness are extenuating
circumstances for fools rather than geniuses.
Great men made quite a few mistakes, but it is indecent
to put buffoon's caps on them.
Religion, the ancient psychotherapy, is created by man for himself
and oriented to himself, alleviating him from the burdens
of the real world and promising regeneration or immortality
after death. It is the Lord or ancestors rather than man
who occupy the center of religion.
Science is created by man for future generations.
It enables man to overcome his biological
limits and to acquire immortality in descendants.
Man is the source and aim of science.
Religion is an idol of Homo vulgaris.
Science is a tool of Homo socialis.
Religion is confessed and professed.
Science is studied, developed, and improved.
Religion orders. Science teaches.
Religion serves to man; and
science, to mankind.
Religion separates. Knowledge unites.
Mankind is totally disconnected. Knowledge is not.
Religion bases on belief rather than facts and logic.
Science bases on facts and logic rather than belief.
It is not unusual that a man of science and a man of religion
agree with the first statement and quarrel about the second.
The believer says that the disbeliever does not understand
the impossibility of science without
belief and fails to discern the presence of belief as the ultimate
source of science. The disbeliever states a real fact
about religion, not offending his opponent.
The believer asserts that his opponent does believe but is unaware of that.
In other words, the disbeliever is a simpleton lost in his feelings.
Pseudoscience, in contrast to religion, is disguised in the
garments of science and passes its stupidities off as scientific achievements.
Pseudoscience exploits the authority of science, thus discrediting knowledge.
Pseudoscience hinders the intellectual liberation of humans,
destroying the scientific grounds of their outlook.
That is why pseudoscience is an enemy of freedom.
The proposition that touches and wakes up thought
was not pronounced in vain.
A universal proposition is vulgar.
Generalization makes a proposition commonplace.
The proposition that is pondered over liberates mind.
Beauty is a relation rather than property.
There is no beauty without man. Beauty is a harmony of the
properties of an object and the internal state of a subject.
Harmony can be traced objectively as consistency and falsifiability
of theories. There are subjective feelings of harmony,
evolving the endorphins of happiness.
Comprehension is the harmony of what is in reality and what
is perceived. That which is understood is beautiful.
The beauty of conceptions is in their inevitability.
The beauty of science is the comprehension of truth.
Common sense is a special gift of Homo sapiens. The senses of smell, touch, eyesight,
and hearing, as well as self-awareness to some extent and even the gift of speech,
are shared with animals who lack common sense. Common sense is the
comprehension that unites people. Common sense acts at the spur of the moment,
suggesting an immediate solution. Common sense is broader than science
as distinguishing good from evil. Science is deeper than common sense,
justifying solutions by comprehension.
Common sense is subjective and resembles the
spiritual elan of belief, that is the force superseding the capabilities of
facts and logic.
Common sense is a kind of the vestibular apparatus of reason.
The instantaneous, although not faultless, separation of right from wrong
is the principal disclosure of common sense.
Common sense is the moral law within.
Meaning is that which belongs to man. No man, no meaning.
Feelings separate humans, and reason unites.
Man produces circumstances and obeys them as time passes by.
The power of many stable institutions relies on
observation of written and unwritten protocols. Procedure and tradition
are not so bad tools of defence against the sins and weaknesses of man.
Everyone might compare themselves with
Gauss and try to equate themselves
to Gauss, but the averages and trends are treated in a different fashion.
By the way, this is done on using the tricks of Gauss whose gift was
far from the midpoint of the “Gaussian distribution”
of talent versus social environment.
It is hardly possible to discern no differences between national cultures.
For instance, the Russian words учёный, ученик, and
учитель have the same lexical base, whereas in English we encounter
scientist, pupil, and teacher. Student stems from study; and
professor, from profess.
The Russian words наука and совесть are not lexically dependent
in contrast to science and conscience.
Many mental distinctions between Russian and Western scientists become
clearer in this connection.
The teacher is responsible for the quality of
communication, despite his general neglect of the relevant duties.
It is an easy matter to avoid “bending over backward” and deliver lectures
from rotten sheets of paper, chanting that the grandparents
had learned that way and you all know how good this turned out.
The teacher must “do his utmost,” adapting his course
to the challenges of today.
Learning and teaching is a duty and fun.
Dignity is the adequite positioning in life.
Happiness consists in keeping dignity.
In contrast to the general belief, happiness lies in harmony between dreams and wishes rather
than in harmony between wishes and possibilities. It is not by chance that
the Bible imposes restrictions on wishes rather than dreams. Had you wishes,
there would be possibilities. Rarely successful is the traversal
The employer always views the failure of performance or bad performance of a contract
as a fault of the contractor. In regard to the public contract,
people are the employer, and the contractor is power.
The principal mistake of power is the intention to benefit
people with what they did not ask. Power is convinced in the stupidity of
people who never know what they are truly in need of.
“They will be grateful to us later on”—this is the intrinsic motivation of power.
Absurdity remains absurdity, belief and eloquence notwithstanding.
The gift of mathematics goes from master to student.
The alternating chain of masters and students
is the true savior of mathematics.
Mental continuity is a precious gift allowing us
to preserve the experience of our ancestors.
The first transfinite act of mankind is the
invention of the idea of the total assembly of naturals.
From the writings by
Aristotle and the Psammites of
the idea of infinity is the focus of
intellectual search of all times and nations.
The definition of mathematics as the science of the infinite has religious roots.
The monads of
as well as the fluxions and fluents of
are products of the heroic epoch of the telescope and microscope.
universe of the mid-twentieth century
Pythagorean dictum—“All is number.”
Measuring infinity by number is the crux of the revealing research of
Geometry deals with the quantitative and qualitative
properties of spatial forms and relations.
The criteria for equality of triangles provide instances of
qualitative geometric knowledge. Finding lengths, areas, and volumes
exemplifies quantitative research. The incommensurability
of the side and diagonal of a square became an outstanding discovery
of Euclidean geometry.
Science has confronted the problem of counting the continuum
since remote ages.
When our ancestors had demonstrated the absence of any
common measure of the side and diagonal of a square, they understood that
rational numbers are scarce for practical purposes.
It is worth recalling that the set of rational numbers is equipollent with
the collection of natural numbers. This means that all rational numbers
comprise a countable set, thus serving as an instance
of the cardinal number that we use to express the size of the
imaginary collection of all entries of the natural series.
The most ancient idea of the potential infinity in the
form of consecutive counting turned out insufficient for
quantitative analysis in geometry.
The discovery that the side and diagonal of a square are incommensurable
is the height of mathematics as awesome and ethereal as
the independence of the fifth postulate,
the axiom of choice, and the continuum hypothesis.
Pythagorean triples. The result by
is of no interest to mankind,
although its existence feeds pride and curiosity.
The rise of the natural series is a transfinite act.
A straight line segment decomposes into points in the theory of convergence of
To measure parts of a segment with transfinite numbers
the problem of the continuum in the same sense in which
the ancient tried to commensurate the diagonal and side of a square.
A number is a measure of quantity. Calculus is reduction to numbers.
Truth is a state of reasoning. Proof is a way of reasoning.
Mathematics was and still is the craft of formulation, the art
of computation, and the science of calculus.
Analysis appeared as differential and integral calculus.
Differentiation discovers trends, and integration forecasts the future from
Geometry and topology are the calculus of spatial forms.
Algebra is the calculus of unknowns, and
logic is the calculus of truth and proof.
Probability is the calculus of chances, and statistics is
the calculus of data.
Arithmetic had been the prehistory of mathematics which was
born as the Hellenistic geometry, turned into the Oriental algebra, and became
the Occidental analysis.
The twentieth century demonstrated the benefits of reunion of the
hypostases of mathematics by way of set theory which inadvertently gave rise to
the utmost dogmatism.
Model theory evaluates and counts truth and proof.
Logic liberates mathematics by model theory.
Mathematics becomes logic.
We definitely feel truth, but we cannot define truth properly.
That is what Alfred Tarski explained to us in the 1930s.
We pursue truth by way of proof, as wittily phrased Saunders by Mac Lane.
Model theory evaluates and counts truth and proof.
The chase of truth not only leads us close to the truth we pursue but also enables
us to nearly catch up with many other
instances of truth which we were not aware nor even foresaw at the start
of the rally pursuit. That is what we have learned from
the Boolean models elaborated in the 1960s by Dana Scott,
Robert Solovay, and Petr Vop\v enka.
Logic organizes and orders our ways of thinking,
manumitting us from conservatism in choosing the objects and methods
of research. Logic of today is a fine instrument and
institution of mathematical freedom.
Abstraction is the freedom of generalization. Freedom is the loftiest ideal
and idea of man, but it is demanding, limited, and vexing.
So is abstraction.
Abstraction is the mother of reason and the gist of mathematics.
It enables us to collect the particular
instances of any many with some property we observe or study.
Abstraction entails generalization and proceeds by analogy.
Freedom is a many-place predicate.
No freedom is exercised in solitude.
To transform the noble desire for freedom into hatred and
cruelty is a popular fixation and hobby horse of humans through ages.
“Scholastic” differs from “scholar.”
Abstraction is limited
by taste, tradition, and common sense. The challenge of abstraction
is alike the call of freedom.
The loss of certainty is a colossal acquisition of mathematics
and liberation from the tethers of categoricity.
The refusal of unicity and the desire of unity are the bicolor
of mathematics in the twentieth century.
An expert in nonstandard analysis is
a nanoanalyst, nanalyst, or nonanalyst.
Isomorphism is in no way a ground for unification of names.
On the contrary, to speak of isomorphism we need two things
(and, hence, two names). It is not by chance that
mathematics is viewed as the art of saying the same in different words.
An algorithm is an artifact of a mathematical technology.
Any calculus is intentional.
Technology proceeds from problem to problem using theories as
signposts and tools. Theory proceeds from conception to
conception, using problems as tests.
Priority may be viewed as a binary relation.
Sometimes, priority means prevalence. For instance,
the interests of humans have priority over the interests of
animals. Speaking about priority, in most cases we simply imply
the first appearance at the time axis.
By default, the first in time has priority.
Independence of events is not directly tied with priority.
The phrase “independently and twenty years later”
is the testimony of the long-term ignorance and present-day stupidity
of its author.
Each great idea integrates a long prehistory, and so
the priority of its formulation is often a matter of convention.
Priority is useful, since its presence expunges accusations in plagiarism.
Priority exists between persons, never presenting a property of an object of science.
Of import to the scientist are the truth of his results and the public quest for them.
Priority and the place in the hierarchy of the academic community
are important things of shallow value to the scientist by belief.
Who created differential calculus? This is an example of an ill-posed problem.
Of use and relevance is to know how differential calculus had sprang to life.
The independence of the discoveries of
is obvious, since
their approaches, intellectual backgrounds, and intentions
were radically different. However, the groundless priority quarrel between
Leibniz and Newton has become the behavioral pattern
for many generations of scientists.
discovered the same formulas, part of which had already been known.
Leibniz, as well as Newton, had his own priority in the invention of
differential and integral calculus. Indeed, these scientists
suggested the versions of mathematical analysis which were based
on different grounds. Leibniz founded analysis on actual infinitesimals, resting on his
philosophical system known as monadology. The key of Newton was
his method of “prime and ultimate ratios” which is rightfully
associated with the modern limit theory.
The insane and sleazy attempts at preserving the memory of great scientists in the
names of the units of dimensional physical quantities brought to science the
esoteric features of obscurantism.
Differential calculus had appeared firstly as the technique of finite differences:
some continuous shape was spread over the discrete infinitesimal frame.
Fate puts everything in due order: the mechanistic ideas of
occupied an honorable place in the second row halls of the history of natural sciences,
leaving the central enfilade for the views of
The demand ever increases of the scientific optimism of
Leibniz—his dream of
Calculemus and belief in the best of the worlds.
Newton, who passed away as a top bureaucrat and pseudoscientist
honored by a flock of flatterers, steps aside in the human mind to
give room to the miserable and despised Leibniz whose funeral
was attended just by two persons.
There is no duality between algebra and geometry.
Algebra and geometry coexist in unity.
There are problems we fail to address: we do not know what an operator or space is
Definitions, axioms, and proofs were prior to Euclid.
The merit of
Euclid is that he had seen in these the universal
mechanism of defending knowledge from subjectivity.
Immortal is the exploit of
who made a universal
panorama of the antique mathematics. In the eighteenth century
the traditions of Euclid were sustained by
Euler whose textbooks are still alive.
The outstanding examples of universality belong to the twentieth century.
The collective project of
Bourbaki neighbors the unparallel generosity
of the mathematical encyclopedists
are giants of the world culture
who brought fame to their nations. The exploit of Smirnov who
continued the pedagogical tradition of Euler in Russia ranked him alongside
Luzin are equal in the universality
of creative contributions of their students.
The traditions of universality in Russia proliferate in
the best mathematical schools and, primarily, in Kolmogorov's school.
The mathematician is not a know-it-all nor a trickster.
The mathematician is the one who distinguishes between what is proved
and what is unproved. Mathematics requires proofs, thus setting
mind in order.
It is not shameful to be a mathematician.
It is shameful to be only a mathematician.
a co-founder of
category theory, coined the term
“working mathematician” and confronted the work in
mathematics with excellent mathematics that must be inevitable, illuminating,
deep, relevant, responsive, and timely.
Excellent mathematics belongs to excellent mathematicians,
mathematicians par excellence.
The slovenly style is not the only danger for the authоr.
Any well-written but ill-positioned article distracts the reader
from whatever seminal and practicable ideas. The deceptive title and
improper perspectives confuse the reader not less than the
meticulous details of relevance to the author and immaterial to the reader.
The clever author presumes the wit of the reader.
Do not disappoint the clever author by neglecting the essence of his writings.
Breakthroughs happen at the boundary with the unbeknown, i.e.,
at the frontiers of science.
The boundary of knowledge is fractal and there are no reasons to assume it
rectifiable or measurable.
The proofs of the fractality of the boundary of knowledge are galore.
Among them we list the ceaseless growth of pseudoscience and other
instances of obscurantism.
Any thesis is an instance of saying.
Any saying is an instance of common sense.
Sayings are in common parlance but it is
de mauvais ton to proclaim that which
defies the stock of adages, saws, and proverbs.
Mathematics belongs to man, whereas formalization is
the primogenitor of the computer. The computer rules over
the realms of formalization. Therefore, any claim of universal
formalization contradicts the most ancient and noble saying
of mathematics, the
Euclid Thesis which reads:
“There are no king's ways to mathematics.”
The quality of translation
depends on many factors. In particular, it is directly proportional to
the translator's knowledge of the subject of the article under translation
as well as to his mastery over the language of translation.
At the same time it is inversely proportional to
the translator's confidence in his familiarity with the subject and
to the self-conceit of his skills.
Professionalism implies wit and, consequently, profound criticism
which manifests itself primarily in self-control.
Self-esteem by clear communication—is one of the most
important mottoes of a perfect translator. In particular,
there is no need in preserving the flaws you meet.
Eliminate all misprints and obvious shortcomings.
Battle inaccuracies and senseless expressions,
but introduce any changes with utmost care, correcting only those
stylistic, grammatical, terminological, and similar defects
that are utterly conspicuous.
Mathematics and economics have antipodal standards of scientific thought.
Despite antediluvian opinions,
mathematics will come in handy for the working economist.
Calculation will supersede prophecy.
Economics as a boon companion of mathematics will avoid merging
into any esoteric part of the humanities, or politics, or belles-lettres.
The new generations of mathematicians will treat the puzzling problems
of economics as an inexhaustible source of inspiration and
an attractive arena for applying and refining their formal methods.
Ignorance is not an argument but the state
revealing indolence in the past, immaturity at present, and
degradation in the future. It is impossible to know everything.
Therefore, ignorance is an improper positioning of oneself
with respect to the boundary between the known and the unknown
rather than some gaps in education.
Ignorance is oppressive, but leaves room for perfection.
What is watery sinks lower.
The theory of a “mathematical superman” is the
standpoint that the stronger mathematician has more rights than
the weaker colleague, implying that humans are not equal
in facing the longstanding laws of morality and ethics.
It is this ideology that
and hates with a vengeance.
Sycophancy of the present day, pompous moralizing, and offense
to the past and ancestors are the evil deeds of a lout.
Rudeness on bones is vile.
It is instructive to see the absence of fastidiousness
and conscience in those who consider the public rostrum for apologizing murder
an indispensable call of freedom.
The nasty things of the past are the support of the scoundrels of today and
the hope of the scoundrels of the future.
Self-conceit and boasting disparage oneself.
Any good piece of research will be noticed and understood when possible.
Criticism is a necessary trait of wit, implying self-criticism.
Self-critisism is a cricial test for intelligence.
The task of a scientist is to preserve and enhance knowledge.
To evaluate the contribution of a scientist is a secondary matter
of concern to the environment and descendants.
A jubilee is not a rehearsal of a funeral service, but a feast of acquaintance.
The life of a person is a unique experiment, the sequence of events
governed by some hidden rules of control.
There are appropriated technologies of pattern recognition,
for instance, in cryptology. To see what is deciphered is sometimes possible
by splitting the sequence under study and comparing the remnants in pairs.
A jubilee is a day of the cameral treatment of life's data and the search for
the hidden laws of the itinerary of the person whose anniversary we celebrate.
Man is responsible to himself and the others.
Responsibility is an ingredient of the person's outlook:
“This world is the world of mine, and I am responsible
for my world.”
Self-responsibility is conscience,
that is shame and blame directed to
The presence or absence of conscience has nothing in common
with responsibility to the others.
Quite a few persons who served their jail terms remain absolutely
irresponsible. History collects heaps of data about
the pharaohs, basileis, secretary generals, and presidents that
were completely devoid of conscience.
Conscience is superior to necessity.
To obey conscience is a chance.
Sour is the taste of order.
Power yields the force of order; and conscience, moral authority.
Stupidity is inborn, but wisdom is acquired.
Respect is higher than love and hatred. Sympathy is impossible
without respect; and compassion, without sympathy.
The highest gift is comprehension without which there is
no compassion. Comprehension leads to truth and good,
to refusal of hatred in favor of love.
Do not that which is usual, but do that which must be done.
Behave yourself not as usual but as noblesse oblige.
The past is that which was. The present is that which is.
The future is that which will be. This clear-cut statement
is irrefutable but prefatory. The past is the zone of responsibility.
The present is the arena of action. The future is the field of possibility.
Moral nihilism consists in oblivion of the past.
“The past crimes are buried in the past. The past is absent at
present. Therefore, the past crimes are absent now. So,
let bygones be bygones.” This sophism brings about the wrong opinion that
nobody could recall and take into account the crimes of the past
in view of the period of limitations.
We are responsible for the past and choose the version of the future today.
Relationships between us are exactly the instances of our attitude to one another.
Our means effect our aims and can lead to the latter or somewhere aside.
No fact is ever destroyed by any repeals.
No error disappears unless it had been repaired.
Always evil is to forget the past and its lessons.
No one can change the past. Any one can repair some mistakes.
Any one can expiate part of one's guilt.
Dominance in population is the wild-beast instinct behind most of
the ugly human passions and sins.
Neither anti-Semite nor racist is the obligatory epithet of a rapscallion.
It is not true that each of the distinguished persons branded as anti-Semite
or racist was such indeed. However all of them deserve this notoriety since they
never disdain antisemitism nor racism, making filth into means for achieving
There are plenteous choices between good and evil,
and all of them are nobody's else but yours.
The scientist and the columnist are of the same blood, belonging
to the people of free speech.
Blood has limitations.
To err is human, which is revealed in the
presumption that everyone differs their defeats from
victories. However this is groundless. We should not distinguish
between defeats and victories since these are inseparable.
There is neither victory free of defeat nor defeat free of victory.
However, success and failure are definitely different.
Defeat is connected with mistakes. The defeated learn from their mistakes
and have a chance to become wiser. The victors
are in a worse position: the victims surrender to the victors, pleading mercy
rather than appealing to wisdom.
Entropy grows and good turns into evil with
the necessity of the second law of thermodynamics.
Adaptability, adequacy, and openness transform into
self-conceit, incompetence, and
Machiavellianism in the conditions of uncontrollable and
Science is not an exception. History exhibits plenty of examples,
demonstrating that no branch of science inoculates its servants with morality,
and any power carries the dominant gene of tyranny.
Gerontological demarcation is useful.
The enthusiasm and enterprise of the young must be commended
alongside the potential of innovation and the experience of leadership
of the senior generations of scientists.
Man must know, understand, and be capable of something rather than
participate in, preside over, and be a member of anything.
Life rushes to its twilight, and so always reasonable is
to do something important rather than
wasting time on trifles. Pay debts to the elders, exhibit examples
to the youngsters, and finish that which is still undone.
Science has never betrayed and will never compromise its principles.
Ostensibly bigoted and prone to indolence every now and then,
mankind is pragmatic and even greedy but cares for its hard-earned
treasures. Anyone likes commanding, but everyone
displays vigilance and distrust of any power and any
attempt of any person or crew to manipulate others and enforce
on the others whatever personal or corporate volitions and views.
Humans are not impeccable but far from hopeless.
Their scepticism, curiosity , and free mind are the never-ending sources
of the inexorable powers and astounding miracles of science.
Sowing truth as a tool of good is a tradition of the Russian mathematical school.
Egocentrism, jealousy, hatred, and idiocy in the form of
patriotic xenophobia are the pernicious weeds of science in Russia.
Neither these nor other kinds of human passions
can ever exterminate the shoots of truth and good as demonstrated
by the tragic history of the Russian science.
This leaves us hope.